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we 've already seen scenarios where we start with a differential equation and then we generate a slope field that describes the solutions to the differential equation and then we use that to visualize those solutions . what i want to do in this video is do an exercise that takes us the other way , start with a slope field and figure out which differential equation is the slope field describing the solutions for . and so i encourage you to look at each of these options and think about which of these differential equations is being described by this slope field . i encourage you to pause the video right now and try it on your own . so i 'm assuming you have had a go at it . so let 's work through each of them . and the way i 'm going to do it is i 'm just going to find some points that seem to be easy to do arithmetic with , and we 'll see if the slope described by the differential equation at that point is consistent with the slope depicted in the slope field . and , i do n't know , just for simplicity , maybe i 'll do x equals one and y equals one for all of these . so , when x equals one and y is equal to one . so , this first differential equation right over here , if x is one and y is one , then dy/dx would be negative one over one or negative one . dy/dx would be negative one . now , is that depicted here ? when x is equal to one and y is equal to one , our slope is n't negative one . our slope here looks positive . so we can rule this one out . now , let 's try the next one . so , if x is equal to one and y is equal to one , well then dy/dx would be equal to one minus one or zero . and , once again , i just picked x equals one and y equals one for convenience . i could have picked any other . i could have picked negative five and negative seven . this just makes the arithmetic a little easier . once again , when you look at that point that we 've already looked at , our slope is clearly not zero . we have a positive slope here , so we can rule that out . once again , for this magenta differential equation , if x and y are both equal to one , then one minus one is once again going to be equal to zero . and we 've already seen this slope is not zero here , so rule that one out . and now here we have x plus y , so when x is one and y is one , our derivate of y with respect to x is going to be one plus one , which is equal to two . now , this looks interesting . it looks like this slope right over here could be two . this looks like one . this looks like two . i would want to validate some other points , but this looks like a really , really good candidate . and you can also see what is happening here . when dy/dx is equal to x plus y , you would expect that as x increases for a given y your slope would increase and as y increases for a given x your slope increases . and we see that . if we were to just hold y constant at one but increase x along this line , we see that the slope is increasing . it is getting steeper . and if we were to keep x constant and increase y across this line , we see that the slope increases . and , in general , we see that the slope increases as we go to the top right . and we see that it decreases as we go to the bottom left and both x and y become much , much more negative . so , i 'm feeling pretty good about this , especially if we can knock this one out here , if we can knock that one out . so , dy/dx is equal to x over y . well , then when x equals one and y equals one , dy/dx would be equal to one , and this slope looks larger than one . it looks like two , but since we are really just eyeballing it , let 's see if we can find something where this more clearly falls apart . so , let 's look at the situation when they both equal negative one . so , x equals negative one and y is equal to negative one . well , in that case , dy/dx should still be equal to one because you have negative one over one . do we see that over here ? so , when x is equal to negative one , y is equal to negative one . our derivative here looks negative . it looks like negative two , which is consistent with this yellow differential equation . the slope here is definitely not a positive one , so we could rule this one out as well . and so we should feel pretty confident that this is the differential equation being described . and now that we 've done it , we can actually think about well , okay , what are the solutions for this differential equation going to look like . well , it depends where they start or what points they contain . if you have a solution that contains that point , it looks like it might do something like this . if you had a solution that contained this point , it might do something like that . and , of course , it keeps going . it looks like it would asymptote towards y is equal to negative x , this downward sloping . this essentially is the line y is equal to negative x . actually , no that is not the line y equals negative x . this is the line y is equal to negative x minus one , so that 's this line right over here . and it looks like if the solution contained , say , this point right over here , that would actually be a solution to the differential equation y is equal to negative x minus one and you can verify that . if y is equal to negative x minus one , then the x and negative x cancel out and you are just left with dy/dx is equal to negative one , which is exactly what is being described by this slope field . anyway , hopefully you found that interesting .
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when x is equal to one and y is equal to one , our slope is n't negative one . our slope here looks positive . so we can rule this one out .
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can the slope of a function be defined where the function does not exist ?
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we 've already seen scenarios where we start with a differential equation and then we generate a slope field that describes the solutions to the differential equation and then we use that to visualize those solutions . what i want to do in this video is do an exercise that takes us the other way , start with a slope field and figure out which differential equation is the slope field describing the solutions for . and so i encourage you to look at each of these options and think about which of these differential equations is being described by this slope field . i encourage you to pause the video right now and try it on your own . so i 'm assuming you have had a go at it . so let 's work through each of them . and the way i 'm going to do it is i 'm just going to find some points that seem to be easy to do arithmetic with , and we 'll see if the slope described by the differential equation at that point is consistent with the slope depicted in the slope field . and , i do n't know , just for simplicity , maybe i 'll do x equals one and y equals one for all of these . so , when x equals one and y is equal to one . so , this first differential equation right over here , if x is one and y is one , then dy/dx would be negative one over one or negative one . dy/dx would be negative one . now , is that depicted here ? when x is equal to one and y is equal to one , our slope is n't negative one . our slope here looks positive . so we can rule this one out . now , let 's try the next one . so , if x is equal to one and y is equal to one , well then dy/dx would be equal to one minus one or zero . and , once again , i just picked x equals one and y equals one for convenience . i could have picked any other . i could have picked negative five and negative seven . this just makes the arithmetic a little easier . once again , when you look at that point that we 've already looked at , our slope is clearly not zero . we have a positive slope here , so we can rule that out . once again , for this magenta differential equation , if x and y are both equal to one , then one minus one is once again going to be equal to zero . and we 've already seen this slope is not zero here , so rule that one out . and now here we have x plus y , so when x is one and y is one , our derivate of y with respect to x is going to be one plus one , which is equal to two . now , this looks interesting . it looks like this slope right over here could be two . this looks like one . this looks like two . i would want to validate some other points , but this looks like a really , really good candidate . and you can also see what is happening here . when dy/dx is equal to x plus y , you would expect that as x increases for a given y your slope would increase and as y increases for a given x your slope increases . and we see that . if we were to just hold y constant at one but increase x along this line , we see that the slope is increasing . it is getting steeper . and if we were to keep x constant and increase y across this line , we see that the slope increases . and , in general , we see that the slope increases as we go to the top right . and we see that it decreases as we go to the bottom left and both x and y become much , much more negative . so , i 'm feeling pretty good about this , especially if we can knock this one out here , if we can knock that one out . so , dy/dx is equal to x over y . well , then when x equals one and y equals one , dy/dx would be equal to one , and this slope looks larger than one . it looks like two , but since we are really just eyeballing it , let 's see if we can find something where this more clearly falls apart . so , let 's look at the situation when they both equal negative one . so , x equals negative one and y is equal to negative one . well , in that case , dy/dx should still be equal to one because you have negative one over one . do we see that over here ? so , when x is equal to negative one , y is equal to negative one . our derivative here looks negative . it looks like negative two , which is consistent with this yellow differential equation . the slope here is definitely not a positive one , so we could rule this one out as well . and so we should feel pretty confident that this is the differential equation being described . and now that we 've done it , we can actually think about well , okay , what are the solutions for this differential equation going to look like . well , it depends where they start or what points they contain . if you have a solution that contains that point , it looks like it might do something like this . if you had a solution that contained this point , it might do something like that . and , of course , it keeps going . it looks like it would asymptote towards y is equal to negative x , this downward sloping . this essentially is the line y is equal to negative x . actually , no that is not the line y equals negative x . this is the line y is equal to negative x minus one , so that 's this line right over here . and it looks like if the solution contained , say , this point right over here , that would actually be a solution to the differential equation y is equal to negative x minus one and you can verify that . if y is equal to negative x minus one , then the x and negative x cancel out and you are just left with dy/dx is equal to negative one , which is exactly what is being described by this slope field . anyway , hopefully you found that interesting .
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and you can also see what is happening here . when dy/dx is equal to x plus y , you would expect that as x increases for a given y your slope would increase and as y increases for a given x your slope increases . and we see that .
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for example the slope of f ( x ) = x^2 at x = 1 and y = 5 and what does this value mean in relation to the function ?
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( bouncy piano music ) > > a few hundred yards after sant'andrea al quirinale , we 've come to another busy intersection in rome , and this is the church of san carlo , st. charles . known as san carlino , little st. charles because it 's a small church . alle quattro san fontane the church of st. charles of the four fountains because we have at this intersection four fountains . like bernini 's st. andrews church , sant'andrea al quirinale , this has a very limited space and the great architect , borromini , francesco borromini , who was the exact contemporary of bernini . a great friend , colleague and then rival built this basically for free . he was so grateful to this order of religion , the trinitarians who were his first clients in rome that he said i will waive my fee . of course , he allowed himself full creative freedom as well . > > ( laughs ) well , that 's what you get when you work for free . > > when you work for free . michaelangelo also worked for free when he was consulted architect of st. peters , so he could n't get sued either . the exterior , what strikes me first is it 's a wave . it 's this undulating surface . > > yes , i think that 's the key word for one of them anyway , for borromini . mathematics perhaps before everything , the pure science of mathematics , but then undulation , curving and in particular , a balance between convex and concave and this is a well-known feature of his architecture . this is a very pure example of his work . > > let 's go inside . for borromini , more than bernini , the science of mathematics . you have to read what galileo wrote about this too . the idea of nature and geometry being inseparably connected and just pure light and shapes comes to the fore . what we have here is an oval shape , but it 's an undulating oval . > > the basic concept does n't really come from an oval , but from the main theme of the order of religion , that this church was owned by at this time and it still owns it , the trinitarians , that is the followers of the holy trinity . now the trinity is a triad , god the father , the son and the holy spirit . if you think of it as a triangle and make two triangles , draw them on a piece of paper , put them side by side , that is one of the flat sides against one of the other flat sides and you have a diamond shape or a lozenge shape . if you then inscribe around that , it becomes an oval . if you inscribe within each triangle a circle and then start to draw lines from one point to another , those are the lines of the architecture of this church . from the minute we walk in , we see one series of circles intersected by the beginning of a line at what appears to be a right angle . then we realize that this is not a right angle because it 's a curve , we have a very sophiticated inter-connection of geometrical shapes . > > but there 's a unity here . > > of course all of this geometrical complexity resolves and this is also very musical and mathematical . that is a complicated equation that ends up resolving itself in a perfect number . when the eye is drawn up by these great , white columns and again a series of undulating lines that divided the lower part of the church from the upper part , we go into a purer oval and then above that , the pure white light of the real sunlight coming in through the latern and the ceiling is made of inter-connected square shapes , crosses , hexagons and octagons . these are derived by borromini from the early christian church of santa costanza outside the walls of rome which was built in the 4th century and has exactly this series of inter-connected geometrical shapes . this is the early christian fascination , we could say even the byzantine one at that point , with inter-connecting shapes that then resolve because they all fit together . > > this reminds me of renaissance architecture in its appeal to the intellect . you have to sit and think and pay attention visually . > > yes . i think that apparent paradox of on the one hand imagination and fantasy and emotion , on the other intelluct actually do resolve here because in the end it 's this question of numbers that is so mysterious and yet it resolves in the end . returning to music , we have to think of a great piece of music by bach , let 's say . now the counterpart , you do not have to be an expert in counterpoint to appreciate the music of bach , to appreciate the extraordinary melodies and harmonies and yet of course if you deconstruct , if you analyze it , we have something highly intellectual and mathematical , but we do n't feel that we have to be at that level because the impact of that music is emotional . this is where we get the crossing of those two worlds . just as when we entered this church , we feel the impact of it immediately visually without having , again as i say , to involve ourselves too intellectually . > > yes . > > i love the decorative elements here above the entrance , foliage . > > his decorations is again symmetrical , but they all look different to begin with but actually it 's one rosette . that is a rose or flower shaped piece of architectural decoration flanked by two others that are different , but they are symmetrical to each other and two more . the other thing that borromini was very fond of and we find it throughout his architecure is , well first of all carving . i should say that he 's a stone cutter by trade and his passion for detailed painstaking stone cutting is visible in every single detail of these capitols and flowers and in particular , the cherubs . now if we look at any of his churches , we see very ornate cherubs . these are from the words in judaism , cherubim and seraphim , those are the plural words , bodiless creatures who are closest to god . we might just call them angels , but they 're something slightly different . they have a head and wings , but really no body . he makes an endless variation on that theme with very broad wings spreading out and the wings become like curly brackets that enclose another piece of architecture and sculpture . > > fill those spaces , those complex spaces , beautifully . > > yes . > > when you were saying that carving is critical , it actually made me think of some of the ornate rosary beads that come out of the medieval period . the entire interior space almost feels as if it was carved out . light unifies this entire space beautifully . as you were speaking of light , a shaft of sunlight came right down through the latern . > > it 's brilliant and this is the advantage , of course , having white architecture as we see it now . ( bouncy piano music )
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this is the early christian fascination , we could say even the byzantine one at that point , with inter-connecting shapes that then resolve because they all fit together . > > this reminds me of renaissance architecture in its appeal to the intellect . you have to sit and think and pay attention visually .
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how did baroque architecture emerge ?
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( bouncy piano music ) > > a few hundred yards after sant'andrea al quirinale , we 've come to another busy intersection in rome , and this is the church of san carlo , st. charles . known as san carlino , little st. charles because it 's a small church . alle quattro san fontane the church of st. charles of the four fountains because we have at this intersection four fountains . like bernini 's st. andrews church , sant'andrea al quirinale , this has a very limited space and the great architect , borromini , francesco borromini , who was the exact contemporary of bernini . a great friend , colleague and then rival built this basically for free . he was so grateful to this order of religion , the trinitarians who were his first clients in rome that he said i will waive my fee . of course , he allowed himself full creative freedom as well . > > ( laughs ) well , that 's what you get when you work for free . > > when you work for free . michaelangelo also worked for free when he was consulted architect of st. peters , so he could n't get sued either . the exterior , what strikes me first is it 's a wave . it 's this undulating surface . > > yes , i think that 's the key word for one of them anyway , for borromini . mathematics perhaps before everything , the pure science of mathematics , but then undulation , curving and in particular , a balance between convex and concave and this is a well-known feature of his architecture . this is a very pure example of his work . > > let 's go inside . for borromini , more than bernini , the science of mathematics . you have to read what galileo wrote about this too . the idea of nature and geometry being inseparably connected and just pure light and shapes comes to the fore . what we have here is an oval shape , but it 's an undulating oval . > > the basic concept does n't really come from an oval , but from the main theme of the order of religion , that this church was owned by at this time and it still owns it , the trinitarians , that is the followers of the holy trinity . now the trinity is a triad , god the father , the son and the holy spirit . if you think of it as a triangle and make two triangles , draw them on a piece of paper , put them side by side , that is one of the flat sides against one of the other flat sides and you have a diamond shape or a lozenge shape . if you then inscribe around that , it becomes an oval . if you inscribe within each triangle a circle and then start to draw lines from one point to another , those are the lines of the architecture of this church . from the minute we walk in , we see one series of circles intersected by the beginning of a line at what appears to be a right angle . then we realize that this is not a right angle because it 's a curve , we have a very sophiticated inter-connection of geometrical shapes . > > but there 's a unity here . > > of course all of this geometrical complexity resolves and this is also very musical and mathematical . that is a complicated equation that ends up resolving itself in a perfect number . when the eye is drawn up by these great , white columns and again a series of undulating lines that divided the lower part of the church from the upper part , we go into a purer oval and then above that , the pure white light of the real sunlight coming in through the latern and the ceiling is made of inter-connected square shapes , crosses , hexagons and octagons . these are derived by borromini from the early christian church of santa costanza outside the walls of rome which was built in the 4th century and has exactly this series of inter-connected geometrical shapes . this is the early christian fascination , we could say even the byzantine one at that point , with inter-connecting shapes that then resolve because they all fit together . > > this reminds me of renaissance architecture in its appeal to the intellect . you have to sit and think and pay attention visually . > > yes . i think that apparent paradox of on the one hand imagination and fantasy and emotion , on the other intelluct actually do resolve here because in the end it 's this question of numbers that is so mysterious and yet it resolves in the end . returning to music , we have to think of a great piece of music by bach , let 's say . now the counterpart , you do not have to be an expert in counterpoint to appreciate the music of bach , to appreciate the extraordinary melodies and harmonies and yet of course if you deconstruct , if you analyze it , we have something highly intellectual and mathematical , but we do n't feel that we have to be at that level because the impact of that music is emotional . this is where we get the crossing of those two worlds . just as when we entered this church , we feel the impact of it immediately visually without having , again as i say , to involve ourselves too intellectually . > > yes . > > i love the decorative elements here above the entrance , foliage . > > his decorations is again symmetrical , but they all look different to begin with but actually it 's one rosette . that is a rose or flower shaped piece of architectural decoration flanked by two others that are different , but they are symmetrical to each other and two more . the other thing that borromini was very fond of and we find it throughout his architecure is , well first of all carving . i should say that he 's a stone cutter by trade and his passion for detailed painstaking stone cutting is visible in every single detail of these capitols and flowers and in particular , the cherubs . now if we look at any of his churches , we see very ornate cherubs . these are from the words in judaism , cherubim and seraphim , those are the plural words , bodiless creatures who are closest to god . we might just call them angels , but they 're something slightly different . they have a head and wings , but really no body . he makes an endless variation on that theme with very broad wings spreading out and the wings become like curly brackets that enclose another piece of architecture and sculpture . > > fill those spaces , those complex spaces , beautifully . > > yes . > > when you were saying that carving is critical , it actually made me think of some of the ornate rosary beads that come out of the medieval period . the entire interior space almost feels as if it was carved out . light unifies this entire space beautifully . as you were speaking of light , a shaft of sunlight came right down through the latern . > > it 's brilliant and this is the advantage , of course , having white architecture as we see it now . ( bouncy piano music )
|
this is the early christian fascination , we could say even the byzantine one at that point , with inter-connecting shapes that then resolve because they all fit together . > > this reminds me of renaissance architecture in its appeal to the intellect . you have to sit and think and pay attention visually .
|
is it possible that the extensive use of the curve in baroque architecture is related to the discovery of calculus ?
|
( bouncy piano music ) > > a few hundred yards after sant'andrea al quirinale , we 've come to another busy intersection in rome , and this is the church of san carlo , st. charles . known as san carlino , little st. charles because it 's a small church . alle quattro san fontane the church of st. charles of the four fountains because we have at this intersection four fountains . like bernini 's st. andrews church , sant'andrea al quirinale , this has a very limited space and the great architect , borromini , francesco borromini , who was the exact contemporary of bernini . a great friend , colleague and then rival built this basically for free . he was so grateful to this order of religion , the trinitarians who were his first clients in rome that he said i will waive my fee . of course , he allowed himself full creative freedom as well . > > ( laughs ) well , that 's what you get when you work for free . > > when you work for free . michaelangelo also worked for free when he was consulted architect of st. peters , so he could n't get sued either . the exterior , what strikes me first is it 's a wave . it 's this undulating surface . > > yes , i think that 's the key word for one of them anyway , for borromini . mathematics perhaps before everything , the pure science of mathematics , but then undulation , curving and in particular , a balance between convex and concave and this is a well-known feature of his architecture . this is a very pure example of his work . > > let 's go inside . for borromini , more than bernini , the science of mathematics . you have to read what galileo wrote about this too . the idea of nature and geometry being inseparably connected and just pure light and shapes comes to the fore . what we have here is an oval shape , but it 's an undulating oval . > > the basic concept does n't really come from an oval , but from the main theme of the order of religion , that this church was owned by at this time and it still owns it , the trinitarians , that is the followers of the holy trinity . now the trinity is a triad , god the father , the son and the holy spirit . if you think of it as a triangle and make two triangles , draw them on a piece of paper , put them side by side , that is one of the flat sides against one of the other flat sides and you have a diamond shape or a lozenge shape . if you then inscribe around that , it becomes an oval . if you inscribe within each triangle a circle and then start to draw lines from one point to another , those are the lines of the architecture of this church . from the minute we walk in , we see one series of circles intersected by the beginning of a line at what appears to be a right angle . then we realize that this is not a right angle because it 's a curve , we have a very sophiticated inter-connection of geometrical shapes . > > but there 's a unity here . > > of course all of this geometrical complexity resolves and this is also very musical and mathematical . that is a complicated equation that ends up resolving itself in a perfect number . when the eye is drawn up by these great , white columns and again a series of undulating lines that divided the lower part of the church from the upper part , we go into a purer oval and then above that , the pure white light of the real sunlight coming in through the latern and the ceiling is made of inter-connected square shapes , crosses , hexagons and octagons . these are derived by borromini from the early christian church of santa costanza outside the walls of rome which was built in the 4th century and has exactly this series of inter-connected geometrical shapes . this is the early christian fascination , we could say even the byzantine one at that point , with inter-connecting shapes that then resolve because they all fit together . > > this reminds me of renaissance architecture in its appeal to the intellect . you have to sit and think and pay attention visually . > > yes . i think that apparent paradox of on the one hand imagination and fantasy and emotion , on the other intelluct actually do resolve here because in the end it 's this question of numbers that is so mysterious and yet it resolves in the end . returning to music , we have to think of a great piece of music by bach , let 's say . now the counterpart , you do not have to be an expert in counterpoint to appreciate the music of bach , to appreciate the extraordinary melodies and harmonies and yet of course if you deconstruct , if you analyze it , we have something highly intellectual and mathematical , but we do n't feel that we have to be at that level because the impact of that music is emotional . this is where we get the crossing of those two worlds . just as when we entered this church , we feel the impact of it immediately visually without having , again as i say , to involve ourselves too intellectually . > > yes . > > i love the decorative elements here above the entrance , foliage . > > his decorations is again symmetrical , but they all look different to begin with but actually it 's one rosette . that is a rose or flower shaped piece of architectural decoration flanked by two others that are different , but they are symmetrical to each other and two more . the other thing that borromini was very fond of and we find it throughout his architecure is , well first of all carving . i should say that he 's a stone cutter by trade and his passion for detailed painstaking stone cutting is visible in every single detail of these capitols and flowers and in particular , the cherubs . now if we look at any of his churches , we see very ornate cherubs . these are from the words in judaism , cherubim and seraphim , those are the plural words , bodiless creatures who are closest to god . we might just call them angels , but they 're something slightly different . they have a head and wings , but really no body . he makes an endless variation on that theme with very broad wings spreading out and the wings become like curly brackets that enclose another piece of architecture and sculpture . > > fill those spaces , those complex spaces , beautifully . > > yes . > > when you were saying that carving is critical , it actually made me think of some of the ornate rosary beads that come out of the medieval period . the entire interior space almost feels as if it was carved out . light unifies this entire space beautifully . as you were speaking of light , a shaft of sunlight came right down through the latern . > > it 's brilliant and this is the advantage , of course , having white architecture as we see it now . ( bouncy piano music )
|
known as san carlino , little st. charles because it 's a small church . alle quattro san fontane the church of st. charles of the four fountains because we have at this intersection four fountains . like bernini 's st. andrews church , sant'andrea al quirinale , this has a very limited space and the great architect , borromini , francesco borromini , who was the exact contemporary of bernini .
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what materials were used to build san carlo alle quattro fontane ?
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( bouncy piano music ) > > a few hundred yards after sant'andrea al quirinale , we 've come to another busy intersection in rome , and this is the church of san carlo , st. charles . known as san carlino , little st. charles because it 's a small church . alle quattro san fontane the church of st. charles of the four fountains because we have at this intersection four fountains . like bernini 's st. andrews church , sant'andrea al quirinale , this has a very limited space and the great architect , borromini , francesco borromini , who was the exact contemporary of bernini . a great friend , colleague and then rival built this basically for free . he was so grateful to this order of religion , the trinitarians who were his first clients in rome that he said i will waive my fee . of course , he allowed himself full creative freedom as well . > > ( laughs ) well , that 's what you get when you work for free . > > when you work for free . michaelangelo also worked for free when he was consulted architect of st. peters , so he could n't get sued either . the exterior , what strikes me first is it 's a wave . it 's this undulating surface . > > yes , i think that 's the key word for one of them anyway , for borromini . mathematics perhaps before everything , the pure science of mathematics , but then undulation , curving and in particular , a balance between convex and concave and this is a well-known feature of his architecture . this is a very pure example of his work . > > let 's go inside . for borromini , more than bernini , the science of mathematics . you have to read what galileo wrote about this too . the idea of nature and geometry being inseparably connected and just pure light and shapes comes to the fore . what we have here is an oval shape , but it 's an undulating oval . > > the basic concept does n't really come from an oval , but from the main theme of the order of religion , that this church was owned by at this time and it still owns it , the trinitarians , that is the followers of the holy trinity . now the trinity is a triad , god the father , the son and the holy spirit . if you think of it as a triangle and make two triangles , draw them on a piece of paper , put them side by side , that is one of the flat sides against one of the other flat sides and you have a diamond shape or a lozenge shape . if you then inscribe around that , it becomes an oval . if you inscribe within each triangle a circle and then start to draw lines from one point to another , those are the lines of the architecture of this church . from the minute we walk in , we see one series of circles intersected by the beginning of a line at what appears to be a right angle . then we realize that this is not a right angle because it 's a curve , we have a very sophiticated inter-connection of geometrical shapes . > > but there 's a unity here . > > of course all of this geometrical complexity resolves and this is also very musical and mathematical . that is a complicated equation that ends up resolving itself in a perfect number . when the eye is drawn up by these great , white columns and again a series of undulating lines that divided the lower part of the church from the upper part , we go into a purer oval and then above that , the pure white light of the real sunlight coming in through the latern and the ceiling is made of inter-connected square shapes , crosses , hexagons and octagons . these are derived by borromini from the early christian church of santa costanza outside the walls of rome which was built in the 4th century and has exactly this series of inter-connected geometrical shapes . this is the early christian fascination , we could say even the byzantine one at that point , with inter-connecting shapes that then resolve because they all fit together . > > this reminds me of renaissance architecture in its appeal to the intellect . you have to sit and think and pay attention visually . > > yes . i think that apparent paradox of on the one hand imagination and fantasy and emotion , on the other intelluct actually do resolve here because in the end it 's this question of numbers that is so mysterious and yet it resolves in the end . returning to music , we have to think of a great piece of music by bach , let 's say . now the counterpart , you do not have to be an expert in counterpoint to appreciate the music of bach , to appreciate the extraordinary melodies and harmonies and yet of course if you deconstruct , if you analyze it , we have something highly intellectual and mathematical , but we do n't feel that we have to be at that level because the impact of that music is emotional . this is where we get the crossing of those two worlds . just as when we entered this church , we feel the impact of it immediately visually without having , again as i say , to involve ourselves too intellectually . > > yes . > > i love the decorative elements here above the entrance , foliage . > > his decorations is again symmetrical , but they all look different to begin with but actually it 's one rosette . that is a rose or flower shaped piece of architectural decoration flanked by two others that are different , but they are symmetrical to each other and two more . the other thing that borromini was very fond of and we find it throughout his architecure is , well first of all carving . i should say that he 's a stone cutter by trade and his passion for detailed painstaking stone cutting is visible in every single detail of these capitols and flowers and in particular , the cherubs . now if we look at any of his churches , we see very ornate cherubs . these are from the words in judaism , cherubim and seraphim , those are the plural words , bodiless creatures who are closest to god . we might just call them angels , but they 're something slightly different . they have a head and wings , but really no body . he makes an endless variation on that theme with very broad wings spreading out and the wings become like curly brackets that enclose another piece of architecture and sculpture . > > fill those spaces , those complex spaces , beautifully . > > yes . > > when you were saying that carving is critical , it actually made me think of some of the ornate rosary beads that come out of the medieval period . the entire interior space almost feels as if it was carved out . light unifies this entire space beautifully . as you were speaking of light , a shaft of sunlight came right down through the latern . > > it 's brilliant and this is the advantage , of course , having white architecture as we see it now . ( bouncy piano music )
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> > yes , i think that 's the key word for one of them anyway , for borromini . mathematics perhaps before everything , the pure science of mathematics , but then undulation , curving and in particular , a balance between convex and concave and this is a well-known feature of his architecture . this is a very pure example of his work .
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is n't concave and convex for reflections ?
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triangle abc undergoes a translation , and we 're using the notation capital t for it , and then we see what the translation has to be . we 're gon na move , it 's kind of small , i hope you can see it on your video screen . we 're gon na move positive eight . every point here is gon na move positive eight in the x direction . its x coordinate is going to increase by eight , or the corresponding point in the image , its x coordinate , is going to increase by eight , and the corresponding point in the image 's y coordinate is going to decrease by one , so let 's do that . and i 'll focus on the vertices , whoops , let me drag that to the trash , i did n't mean to do that . i 'm going to focus on the vertices well , that 's just the easiest thing for my brain to worth with . and actually , this is what the tool expects as well . so the point b , is going to move eight to the right , or its corresponding point in the image is going to have an x coordinate eight larger . so right now , the x coordinate is negative four , if you added eight to that , it would be positive four , and its y coordinate is going to be one lower . right now , point b 's y coordinate is eight , one lower than that is seven . so , in the image , the corresponding point of the image would going to be right over there . and you see we moved eight to the right , and one down . let 's do that with point c. it 's at x equals negative seven , if you move eight to the right , if you increase your x coordinate by eight , you 're gon na move to x equals one , and then if you change your y coordinate by negative one , you 're gon na move down one , then you 're gon na get to that point right over there . now , let 's do it with point a . so point a 's x coordinate is negative one . if you add eight to it , it 's going to be positive seven , and its current y coordinate is two . if you take one away from it , you 're gon na get to a y coordinate of one . and so there you have it . let 's see , how do i connect these two ? oh , there you go , and we can check our answer . and we got it right . we have performed the translation .
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its x coordinate is going to increase by eight , or the corresponding point in the image , its x coordinate , is going to increase by eight , and the corresponding point in the image 's y coordinate is going to decrease by one , so let 's do that . and i 'll focus on the vertices , whoops , let me drag that to the trash , i did n't mean to do that . i 'm going to focus on the vertices well , that 's just the easiest thing for my brain to worth with .
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why ca n't i put than a fourth dot on the pratice ?
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triangle abc undergoes a translation , and we 're using the notation capital t for it , and then we see what the translation has to be . we 're gon na move , it 's kind of small , i hope you can see it on your video screen . we 're gon na move positive eight . every point here is gon na move positive eight in the x direction . its x coordinate is going to increase by eight , or the corresponding point in the image , its x coordinate , is going to increase by eight , and the corresponding point in the image 's y coordinate is going to decrease by one , so let 's do that . and i 'll focus on the vertices , whoops , let me drag that to the trash , i did n't mean to do that . i 'm going to focus on the vertices well , that 's just the easiest thing for my brain to worth with . and actually , this is what the tool expects as well . so the point b , is going to move eight to the right , or its corresponding point in the image is going to have an x coordinate eight larger . so right now , the x coordinate is negative four , if you added eight to that , it would be positive four , and its y coordinate is going to be one lower . right now , point b 's y coordinate is eight , one lower than that is seven . so , in the image , the corresponding point of the image would going to be right over there . and you see we moved eight to the right , and one down . let 's do that with point c. it 's at x equals negative seven , if you move eight to the right , if you increase your x coordinate by eight , you 're gon na move to x equals one , and then if you change your y coordinate by negative one , you 're gon na move down one , then you 're gon na get to that point right over there . now , let 's do it with point a . so point a 's x coordinate is negative one . if you add eight to it , it 's going to be positive seven , and its current y coordinate is two . if you take one away from it , you 're gon na get to a y coordinate of one . and so there you have it . let 's see , how do i connect these two ? oh , there you go , and we can check our answer . and we got it right . we have performed the translation .
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triangle abc undergoes a translation , and we 're using the notation capital t for it , and then we see what the translation has to be . we 're gon na move , it 's kind of small , i hope you can see it on your video screen .
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how do you rotate around a center of origin if there is no center of rotation ?
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triangle abc undergoes a translation , and we 're using the notation capital t for it , and then we see what the translation has to be . we 're gon na move , it 's kind of small , i hope you can see it on your video screen . we 're gon na move positive eight . every point here is gon na move positive eight in the x direction . its x coordinate is going to increase by eight , or the corresponding point in the image , its x coordinate , is going to increase by eight , and the corresponding point in the image 's y coordinate is going to decrease by one , so let 's do that . and i 'll focus on the vertices , whoops , let me drag that to the trash , i did n't mean to do that . i 'm going to focus on the vertices well , that 's just the easiest thing for my brain to worth with . and actually , this is what the tool expects as well . so the point b , is going to move eight to the right , or its corresponding point in the image is going to have an x coordinate eight larger . so right now , the x coordinate is negative four , if you added eight to that , it would be positive four , and its y coordinate is going to be one lower . right now , point b 's y coordinate is eight , one lower than that is seven . so , in the image , the corresponding point of the image would going to be right over there . and you see we moved eight to the right , and one down . let 's do that with point c. it 's at x equals negative seven , if you move eight to the right , if you increase your x coordinate by eight , you 're gon na move to x equals one , and then if you change your y coordinate by negative one , you 're gon na move down one , then you 're gon na get to that point right over there . now , let 's do it with point a . so point a 's x coordinate is negative one . if you add eight to it , it 's going to be positive seven , and its current y coordinate is two . if you take one away from it , you 're gon na get to a y coordinate of one . and so there you have it . let 's see , how do i connect these two ? oh , there you go , and we can check our answer . and we got it right . we have performed the translation .
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now , let 's do it with point a . so point a 's x coordinate is negative one . if you add eight to it , it 's going to be positive seven , and its current y coordinate is two .
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what happens when the x axis is 0 ?
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so here we have our vascular man and he 's got blood vessels that supply every part of the body . he 's got blood vessels supplying the heart , blood vessels supplying the lungs , some supplying the kidney , the liver , the intestines , the skin , the nerves , really all over the place . so here 's a blood vessel i 'm drawing , of course your blood vessels will be carrying blood , but they also carry nutrients and oxygen and all sorts of proteins . now what happens if these blood vessels get damaged , or inflamed ? what if the inside of the wall of the blood vessel gets very inflamed ? well intuitively it makes sense , blood will not be able to pass as well through here and be delivered to the different organs . you know the intestines , the livers , the lung . all of the organs of the body need blood and need nutrients . this damage is precisely what happens in the disease known as vasculitis . vasculitis is damage of blood vessels and inflammation of blood vessels . itis means inflammation and vascul means vasculature or blood vessels . essentially this damage is caused by the immune system . white blood cells mistakenly release small molecules that can damage the blood vessels . essentially the immune system makes a mistake and thinks that blood vessels are foreign . so vasculitis is an autoimmune disease . now i know what you 're probably thinking , you might be thinking if i destroy all my blood vessels , how is that compatible with life ? well there are different types of vasculitides , the plural for vasculitis and these different types might affect different parts of the body . for example one type of vasculitis might affect the lungs and the kidneys only . another type might affect the intestines , the kidney , the heart and the lungs and still another type might only affect the big blood vessels that come out of the heart . the different organs affected in patients lead to the different symptoms that you might see . for example loss of blood flow and nutrients to the heart tissue means heart cell death , this is known as a heart attack and this might cause symptoms such as chest pain . the severity of symptoms might also be different , so for example with abdominal pain a patient might have a range from a small amount of blood in their stool to full on bowel perforation . this all depends on how severely the blood vessels are damaged . now along with these local symptoms patients might also experience general symptoms such as night sweats or fever , so there 's a little thermometer right here , as the patient might have a fever or the patient might have chills or generalized muscle aches , or they may also experience lethargy or a feeling of being very tired . this all comes from what 's causing this problem , remember white blood cells are releasing little immune molecules , these immune molecules can travel down to the rest of the body . these immune molecules are normally used to fight off pathogens and so a patient might feel like they have a general illness or a virus . now let 's take a step back . why are only certain types of vessels affected in vasculitis ? the different types of vessels that are affected usually depends on the size of those blood vessels and so vasculitis has been classified into three different categories . large vessel vasculitis , medium vessel vasculitis and small vessel vasculitis . here i 'll draw a blood vessel to show a little bit about what 's going on . here let me draw this large blood vessel and i 've got the blood vessel wall and the outside and the inside of the blood vessel , out and in , and of course on the inside you have the things i have mentioned before . blood , oxygen , nutrients , that all travel through your blood vessels like water through pipes . now the purpose of large blood vessels is to get blood distributed quickly through the body to where it needs to go . so if we have inflammation and damage of the blood vessel wall so it 's bulging out from inflammation , swelling , scaring and then repeating that process , the blood trying to pass through ca n't do so effectively and so there 's decreased blood flow and also after this constriction you 'll see decreased blood pressure as well . and now a physician listening over the skin using a stethoscope may actually hear this blockage , it 's the same thing that happens when you put pressure on a hose . if you put a kink in the hose , not only will water stop flowing through as quickly but also if you listen at the kink you can hear that blood trying to rush through and that 's the same thing the physician hears . this is known as a bruit and if the physician feels the area they may also feel what 's called thrill , this feeling of blood rushing through . now for medium sized blood vessels . when scaring occurs for these vessels it can potentially block flow all together . this leads to blood cells kind of getting stuck behind the blockage and little proteins in the blood known as clotting proteins can form a clot and completely stop blood flow . along with clot formation , you can also see the blood vessel wall bulge out . this is due to increased pressure , the blood has nowhere to go so it pushes up against the walls . and since medium sized blood vessel walls are thinner they are prone to this bulging . it 's kind of like when you take a water balloon and squeeze it on one area , all the water bulges to one side of the wall . the bulging and weakening of the blood vessel walls are known as aneurysms . the most fear complication from aneurysms is rupture , leading to blood spilling out of the blood vessels . last of all the final classification of blood vessels are small blood vessels . and by small i mean microscopic so we 've got blood cells marching through nearly single file and a very thin blood vessel wall . you can imagine that damage to this wall can lead to breakage of the blood vessel really easily and depending on where the blood vessel is that 's where you might see symptoms . for example if the small blood vessels are in the intestines you might see bloody stool . if the blood vessels are in the kidneys you might see bloody urine . if the blood vessels are just under the skin you might actually see a rash that kind of gives a dotted pattern where all these different small little blood vessels have ruptured . so in general the symptoms you see in vaculitis depends on where the blood vessels are that are affected , what size they are and how sever the damage is .
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it 's kind of like when you take a water balloon and squeeze it on one area , all the water bulges to one side of the wall . the bulging and weakening of the blood vessel walls are known as aneurysms . the most fear complication from aneurysms is rupture , leading to blood spilling out of the blood vessels . last of all the final classification of blood vessels are small blood vessels . and by small i mean microscopic so we 've got blood cells marching through nearly single file and a very thin blood vessel wall . you can imagine that damage to this wall can lead to breakage of the blood vessel really easily and depending on where the blood vessel is that 's where you might see symptoms . for example if the small blood vessels are in the intestines you might see bloody stool . if the blood vessels are in the kidneys you might see bloody urine . if the blood vessels are just under the skin you might actually see a rash that kind of gives a dotted pattern where all these different small little blood vessels have ruptured . so in general the symptoms you see in vaculitis depends on where the blood vessels are that are affected , what size they are and how sever the damage is .
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should n't the blood pressure increase , due to the increase of resistance , caused by the the decraese of blood vessel diameter ?
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so here we have our vascular man and he 's got blood vessels that supply every part of the body . he 's got blood vessels supplying the heart , blood vessels supplying the lungs , some supplying the kidney , the liver , the intestines , the skin , the nerves , really all over the place . so here 's a blood vessel i 'm drawing , of course your blood vessels will be carrying blood , but they also carry nutrients and oxygen and all sorts of proteins . now what happens if these blood vessels get damaged , or inflamed ? what if the inside of the wall of the blood vessel gets very inflamed ? well intuitively it makes sense , blood will not be able to pass as well through here and be delivered to the different organs . you know the intestines , the livers , the lung . all of the organs of the body need blood and need nutrients . this damage is precisely what happens in the disease known as vasculitis . vasculitis is damage of blood vessels and inflammation of blood vessels . itis means inflammation and vascul means vasculature or blood vessels . essentially this damage is caused by the immune system . white blood cells mistakenly release small molecules that can damage the blood vessels . essentially the immune system makes a mistake and thinks that blood vessels are foreign . so vasculitis is an autoimmune disease . now i know what you 're probably thinking , you might be thinking if i destroy all my blood vessels , how is that compatible with life ? well there are different types of vasculitides , the plural for vasculitis and these different types might affect different parts of the body . for example one type of vasculitis might affect the lungs and the kidneys only . another type might affect the intestines , the kidney , the heart and the lungs and still another type might only affect the big blood vessels that come out of the heart . the different organs affected in patients lead to the different symptoms that you might see . for example loss of blood flow and nutrients to the heart tissue means heart cell death , this is known as a heart attack and this might cause symptoms such as chest pain . the severity of symptoms might also be different , so for example with abdominal pain a patient might have a range from a small amount of blood in their stool to full on bowel perforation . this all depends on how severely the blood vessels are damaged . now along with these local symptoms patients might also experience general symptoms such as night sweats or fever , so there 's a little thermometer right here , as the patient might have a fever or the patient might have chills or generalized muscle aches , or they may also experience lethargy or a feeling of being very tired . this all comes from what 's causing this problem , remember white blood cells are releasing little immune molecules , these immune molecules can travel down to the rest of the body . these immune molecules are normally used to fight off pathogens and so a patient might feel like they have a general illness or a virus . now let 's take a step back . why are only certain types of vessels affected in vasculitis ? the different types of vessels that are affected usually depends on the size of those blood vessels and so vasculitis has been classified into three different categories . large vessel vasculitis , medium vessel vasculitis and small vessel vasculitis . here i 'll draw a blood vessel to show a little bit about what 's going on . here let me draw this large blood vessel and i 've got the blood vessel wall and the outside and the inside of the blood vessel , out and in , and of course on the inside you have the things i have mentioned before . blood , oxygen , nutrients , that all travel through your blood vessels like water through pipes . now the purpose of large blood vessels is to get blood distributed quickly through the body to where it needs to go . so if we have inflammation and damage of the blood vessel wall so it 's bulging out from inflammation , swelling , scaring and then repeating that process , the blood trying to pass through ca n't do so effectively and so there 's decreased blood flow and also after this constriction you 'll see decreased blood pressure as well . and now a physician listening over the skin using a stethoscope may actually hear this blockage , it 's the same thing that happens when you put pressure on a hose . if you put a kink in the hose , not only will water stop flowing through as quickly but also if you listen at the kink you can hear that blood trying to rush through and that 's the same thing the physician hears . this is known as a bruit and if the physician feels the area they may also feel what 's called thrill , this feeling of blood rushing through . now for medium sized blood vessels . when scaring occurs for these vessels it can potentially block flow all together . this leads to blood cells kind of getting stuck behind the blockage and little proteins in the blood known as clotting proteins can form a clot and completely stop blood flow . along with clot formation , you can also see the blood vessel wall bulge out . this is due to increased pressure , the blood has nowhere to go so it pushes up against the walls . and since medium sized blood vessel walls are thinner they are prone to this bulging . it 's kind of like when you take a water balloon and squeeze it on one area , all the water bulges to one side of the wall . the bulging and weakening of the blood vessel walls are known as aneurysms . the most fear complication from aneurysms is rupture , leading to blood spilling out of the blood vessels . last of all the final classification of blood vessels are small blood vessels . and by small i mean microscopic so we 've got blood cells marching through nearly single file and a very thin blood vessel wall . you can imagine that damage to this wall can lead to breakage of the blood vessel really easily and depending on where the blood vessel is that 's where you might see symptoms . for example if the small blood vessels are in the intestines you might see bloody stool . if the blood vessels are in the kidneys you might see bloody urine . if the blood vessels are just under the skin you might actually see a rash that kind of gives a dotted pattern where all these different small little blood vessels have ruptured . so in general the symptoms you see in vaculitis depends on where the blood vessels are that are affected , what size they are and how sever the damage is .
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this damage is precisely what happens in the disease known as vasculitis . vasculitis is damage of blood vessels and inflammation of blood vessels . itis means inflammation and vascul means vasculature or blood vessels .
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does inflamation of the blood vessels also include atherosclerosis ?
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so here we have our vascular man and he 's got blood vessels that supply every part of the body . he 's got blood vessels supplying the heart , blood vessels supplying the lungs , some supplying the kidney , the liver , the intestines , the skin , the nerves , really all over the place . so here 's a blood vessel i 'm drawing , of course your blood vessels will be carrying blood , but they also carry nutrients and oxygen and all sorts of proteins . now what happens if these blood vessels get damaged , or inflamed ? what if the inside of the wall of the blood vessel gets very inflamed ? well intuitively it makes sense , blood will not be able to pass as well through here and be delivered to the different organs . you know the intestines , the livers , the lung . all of the organs of the body need blood and need nutrients . this damage is precisely what happens in the disease known as vasculitis . vasculitis is damage of blood vessels and inflammation of blood vessels . itis means inflammation and vascul means vasculature or blood vessels . essentially this damage is caused by the immune system . white blood cells mistakenly release small molecules that can damage the blood vessels . essentially the immune system makes a mistake and thinks that blood vessels are foreign . so vasculitis is an autoimmune disease . now i know what you 're probably thinking , you might be thinking if i destroy all my blood vessels , how is that compatible with life ? well there are different types of vasculitides , the plural for vasculitis and these different types might affect different parts of the body . for example one type of vasculitis might affect the lungs and the kidneys only . another type might affect the intestines , the kidney , the heart and the lungs and still another type might only affect the big blood vessels that come out of the heart . the different organs affected in patients lead to the different symptoms that you might see . for example loss of blood flow and nutrients to the heart tissue means heart cell death , this is known as a heart attack and this might cause symptoms such as chest pain . the severity of symptoms might also be different , so for example with abdominal pain a patient might have a range from a small amount of blood in their stool to full on bowel perforation . this all depends on how severely the blood vessels are damaged . now along with these local symptoms patients might also experience general symptoms such as night sweats or fever , so there 's a little thermometer right here , as the patient might have a fever or the patient might have chills or generalized muscle aches , or they may also experience lethargy or a feeling of being very tired . this all comes from what 's causing this problem , remember white blood cells are releasing little immune molecules , these immune molecules can travel down to the rest of the body . these immune molecules are normally used to fight off pathogens and so a patient might feel like they have a general illness or a virus . now let 's take a step back . why are only certain types of vessels affected in vasculitis ? the different types of vessels that are affected usually depends on the size of those blood vessels and so vasculitis has been classified into three different categories . large vessel vasculitis , medium vessel vasculitis and small vessel vasculitis . here i 'll draw a blood vessel to show a little bit about what 's going on . here let me draw this large blood vessel and i 've got the blood vessel wall and the outside and the inside of the blood vessel , out and in , and of course on the inside you have the things i have mentioned before . blood , oxygen , nutrients , that all travel through your blood vessels like water through pipes . now the purpose of large blood vessels is to get blood distributed quickly through the body to where it needs to go . so if we have inflammation and damage of the blood vessel wall so it 's bulging out from inflammation , swelling , scaring and then repeating that process , the blood trying to pass through ca n't do so effectively and so there 's decreased blood flow and also after this constriction you 'll see decreased blood pressure as well . and now a physician listening over the skin using a stethoscope may actually hear this blockage , it 's the same thing that happens when you put pressure on a hose . if you put a kink in the hose , not only will water stop flowing through as quickly but also if you listen at the kink you can hear that blood trying to rush through and that 's the same thing the physician hears . this is known as a bruit and if the physician feels the area they may also feel what 's called thrill , this feeling of blood rushing through . now for medium sized blood vessels . when scaring occurs for these vessels it can potentially block flow all together . this leads to blood cells kind of getting stuck behind the blockage and little proteins in the blood known as clotting proteins can form a clot and completely stop blood flow . along with clot formation , you can also see the blood vessel wall bulge out . this is due to increased pressure , the blood has nowhere to go so it pushes up against the walls . and since medium sized blood vessel walls are thinner they are prone to this bulging . it 's kind of like when you take a water balloon and squeeze it on one area , all the water bulges to one side of the wall . the bulging and weakening of the blood vessel walls are known as aneurysms . the most fear complication from aneurysms is rupture , leading to blood spilling out of the blood vessels . last of all the final classification of blood vessels are small blood vessels . and by small i mean microscopic so we 've got blood cells marching through nearly single file and a very thin blood vessel wall . you can imagine that damage to this wall can lead to breakage of the blood vessel really easily and depending on where the blood vessel is that 's where you might see symptoms . for example if the small blood vessels are in the intestines you might see bloody stool . if the blood vessels are in the kidneys you might see bloody urine . if the blood vessels are just under the skin you might actually see a rash that kind of gives a dotted pattern where all these different small little blood vessels have ruptured . so in general the symptoms you see in vaculitis depends on where the blood vessels are that are affected , what size they are and how sever the damage is .
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the different types of vessels that are affected usually depends on the size of those blood vessels and so vasculitis has been classified into three different categories . large vessel vasculitis , medium vessel vasculitis and small vessel vasculitis . here i 'll draw a blood vessel to show a little bit about what 's going on .
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would you see symptoms of hypovolemic shock with venous vasculitis ( in other words , inflammation of the veins ) ?
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so here we have our vascular man and he 's got blood vessels that supply every part of the body . he 's got blood vessels supplying the heart , blood vessels supplying the lungs , some supplying the kidney , the liver , the intestines , the skin , the nerves , really all over the place . so here 's a blood vessel i 'm drawing , of course your blood vessels will be carrying blood , but they also carry nutrients and oxygen and all sorts of proteins . now what happens if these blood vessels get damaged , or inflamed ? what if the inside of the wall of the blood vessel gets very inflamed ? well intuitively it makes sense , blood will not be able to pass as well through here and be delivered to the different organs . you know the intestines , the livers , the lung . all of the organs of the body need blood and need nutrients . this damage is precisely what happens in the disease known as vasculitis . vasculitis is damage of blood vessels and inflammation of blood vessels . itis means inflammation and vascul means vasculature or blood vessels . essentially this damage is caused by the immune system . white blood cells mistakenly release small molecules that can damage the blood vessels . essentially the immune system makes a mistake and thinks that blood vessels are foreign . so vasculitis is an autoimmune disease . now i know what you 're probably thinking , you might be thinking if i destroy all my blood vessels , how is that compatible with life ? well there are different types of vasculitides , the plural for vasculitis and these different types might affect different parts of the body . for example one type of vasculitis might affect the lungs and the kidneys only . another type might affect the intestines , the kidney , the heart and the lungs and still another type might only affect the big blood vessels that come out of the heart . the different organs affected in patients lead to the different symptoms that you might see . for example loss of blood flow and nutrients to the heart tissue means heart cell death , this is known as a heart attack and this might cause symptoms such as chest pain . the severity of symptoms might also be different , so for example with abdominal pain a patient might have a range from a small amount of blood in their stool to full on bowel perforation . this all depends on how severely the blood vessels are damaged . now along with these local symptoms patients might also experience general symptoms such as night sweats or fever , so there 's a little thermometer right here , as the patient might have a fever or the patient might have chills or generalized muscle aches , or they may also experience lethargy or a feeling of being very tired . this all comes from what 's causing this problem , remember white blood cells are releasing little immune molecules , these immune molecules can travel down to the rest of the body . these immune molecules are normally used to fight off pathogens and so a patient might feel like they have a general illness or a virus . now let 's take a step back . why are only certain types of vessels affected in vasculitis ? the different types of vessels that are affected usually depends on the size of those blood vessels and so vasculitis has been classified into three different categories . large vessel vasculitis , medium vessel vasculitis and small vessel vasculitis . here i 'll draw a blood vessel to show a little bit about what 's going on . here let me draw this large blood vessel and i 've got the blood vessel wall and the outside and the inside of the blood vessel , out and in , and of course on the inside you have the things i have mentioned before . blood , oxygen , nutrients , that all travel through your blood vessels like water through pipes . now the purpose of large blood vessels is to get blood distributed quickly through the body to where it needs to go . so if we have inflammation and damage of the blood vessel wall so it 's bulging out from inflammation , swelling , scaring and then repeating that process , the blood trying to pass through ca n't do so effectively and so there 's decreased blood flow and also after this constriction you 'll see decreased blood pressure as well . and now a physician listening over the skin using a stethoscope may actually hear this blockage , it 's the same thing that happens when you put pressure on a hose . if you put a kink in the hose , not only will water stop flowing through as quickly but also if you listen at the kink you can hear that blood trying to rush through and that 's the same thing the physician hears . this is known as a bruit and if the physician feels the area they may also feel what 's called thrill , this feeling of blood rushing through . now for medium sized blood vessels . when scaring occurs for these vessels it can potentially block flow all together . this leads to blood cells kind of getting stuck behind the blockage and little proteins in the blood known as clotting proteins can form a clot and completely stop blood flow . along with clot formation , you can also see the blood vessel wall bulge out . this is due to increased pressure , the blood has nowhere to go so it pushes up against the walls . and since medium sized blood vessel walls are thinner they are prone to this bulging . it 's kind of like when you take a water balloon and squeeze it on one area , all the water bulges to one side of the wall . the bulging and weakening of the blood vessel walls are known as aneurysms . the most fear complication from aneurysms is rupture , leading to blood spilling out of the blood vessels . last of all the final classification of blood vessels are small blood vessels . and by small i mean microscopic so we 've got blood cells marching through nearly single file and a very thin blood vessel wall . you can imagine that damage to this wall can lead to breakage of the blood vessel really easily and depending on where the blood vessel is that 's where you might see symptoms . for example if the small blood vessels are in the intestines you might see bloody stool . if the blood vessels are in the kidneys you might see bloody urine . if the blood vessels are just under the skin you might actually see a rash that kind of gives a dotted pattern where all these different small little blood vessels have ruptured . so in general the symptoms you see in vaculitis depends on where the blood vessels are that are affected , what size they are and how sever the damage is .
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essentially this damage is caused by the immune system . white blood cells mistakenly release small molecules that can damage the blood vessels . essentially the immune system makes a mistake and thinks that blood vessels are foreign .
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why would the blood pressure reduce when the resistance increases ?
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i 've been wanting to make a video on a couple of terms that people have really thrown around for a while now . and i think it really hits the core of some of the issues we 're dealing with now with the credit debacle but it 's kind of at a deeper level . so the things i want to go over are the ideas of savings , consumption , and investment . and you hear these a lot . everyone obviously says , i 've invested in the stock market or i 've invested in a house and i really want to give you a framework for how i think about these ideas . and frankly , i have n't seen them depicted this way in any economics book , although they 've kind of touched on this , but i think this is really how you should think about these things . so if you save money , and i think we all know what that means , that 's money that you did n't spend , there 's a couple of things that you can do with it . you can either consume your money or you could invest your money . so , let 's just think about a bunch of different situations and think about whether those things are consumption or investment . so let 's say , i have $ 100,000 that i 'm dealing with . so let 's say , i take that $ 100,000 and i build a factory . and i think that that factory is going to be able to produce -- i 'll make up some product -- it 'll be able to produce cars more efficiently and cheaper than any other car factory out there . well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 . in fact , i 'm expecting some type of a return on this investment . and i 've made a bunch of videos on what a return on investment is , and you can usually quantify it . if i take a $ 100,000 and i build this factory and this factory spits out $ 50,000 a year , it 's probably creating at least $ 50,000 a year value , assuming that nothing corrupt is happening in our system . in fact , it 's normally creating more than $ 50,000 a year of value . it may be creating a $ 100,000 a year of value and $ 50,000 of that may be going to the person who 's doing the production and then the other half of the value is actually going to the consumer of whatever this factory is making . and you have to think about it , because if all of the value went to the person who produced the factory then there 's not a huge incentive for someone to use his products anymore . but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment . so building a factory is an investment . now let 's say that i 'm homeless and i have this $ 100,000 . and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs . let 's say build a simple house , and i 'll do that in a neutral color . this is my other use of this $ 100,000 , instead of building a factory , i 'm going to build a simple house . and this house , it provides shelter for me and my family , it allows us that security that now my kids can go to school and they can themselves become more productive citizens . i now have an address . i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ? because i 'm taking this $ 100,000 , that maybe i had or someone gave to me , and it 's generating a return . and what is that return ? well , with a factory , it 's maybe a little easier to quantify . but at minimum , it 's this work that i 'm able to do because i now have a house . because i have the security , i have the address . i have the shelter . i 'm able to relax . it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society . it 's hard to value , maybe i did n't have any job before and now i have a job and i can contribute $ 30,000 a year to society . maybe i 'm working at someone 's factory . maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment . so i also consider this to be an investment . now , my question to you is , let 's say that i already had a house -- so this is an investment . let 's say i already had a house and my family is happy and we have everything we need . we have food on the table and my kids go to school and i 'm able to get a job and all of that exists . but let 's say , i still have a $ 100,000 and i use that $ 100,000 -- i 'll do it in yellow -- to put in some granite counter tops . i have some money left over , let 's say , i 'm going to add a bathroom to my house and i will put the latest hardwood floors , so that my family will be impressed . you can imagine . and maybe i add 2,000 square feet . you normally ca n't get all that for a $ 100,000 but i think you 'll bear with me . so i 'm essentially doing some major home improvements . so my question to you is -- is this an investment or is this consumption ? now , in our everyday world , with most people we deal with , they will call this investment in my house . and why are they saying that ? because they say , by spending a $ 100,000 in the house in this way , that maybe -- if you watch the home and garden channel , they 're doing this all the time -- that if you pour this a $ 100,000 into your house , that maybe the value of your house is going to increase by $ 150,000 . or someone else , all of a sudden , is going to perceive the value of your house as being $ 150,000 . they 'll say , well , you got a $ 50,000 return on investment . i 'd argue that that is not investment . that it 's speculation . you are , essentially , piling money into this stuff -- and i 'll do this in red , consumption is red . what 's happening here truly economically ? when you add granite , or you add an extra bathroom or hardwood floors or this extra 2,000 square feet , is it making anyone who 's living in that house more productive ? is it making you harder working ; is it making you more likely to invent the cure for cancer , or more likely to invent a way of getting cheap energy , or produce more widgets ? no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society . in fact , in no way is this going to contribute to the collective wealth of society . the last two examples i gave contribute to the collective wealth society , some of which you share , and that is your return on the investment . but as a whole , this is an investment into society . and it 's going to make the pie bigger . this right here , does not make the pie bigger . it might make you a little bit happier , make your ego feel a little bit better , let your pride grow , and your self righteousness grow , and show other people that you 've arrived , but it 's not going to increase the wealth of society . and when you say that you 've invested , you are really just saying i 've speculated . what you 're saying is -- by paying this $ 100,000 , you 're going to find , essentially , a greater fool out there . they could have done the same thing , they could have bought your house , spent $ 100,000 and done this , if this is what would have made them happy . but what you 're saying is , essentially , that you 're going to find somebody out there who 's willing to pay $ 150,000 extra for something that should have only cost $ 100,000 . and in fact , if anything , if you use this at all , the value of this is going to go down . so you 're just somehow assuming that the granite counter tops that you choose are going to be the taste that someone else would like or that the hardwood floors are going to be the taste someone else would like . i would actually argue that when you customize your house in this way , you are creating $ 100,000 of consumption to your taste . and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation . one might find some other guy willing to emotionally pay more for something . but it 's money that 's burned ; it 's not creating more value for society . i continue this in the next video .
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i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ?
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so would renting then be considered an investment ?
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i 've been wanting to make a video on a couple of terms that people have really thrown around for a while now . and i think it really hits the core of some of the issues we 're dealing with now with the credit debacle but it 's kind of at a deeper level . so the things i want to go over are the ideas of savings , consumption , and investment . and you hear these a lot . everyone obviously says , i 've invested in the stock market or i 've invested in a house and i really want to give you a framework for how i think about these ideas . and frankly , i have n't seen them depicted this way in any economics book , although they 've kind of touched on this , but i think this is really how you should think about these things . so if you save money , and i think we all know what that means , that 's money that you did n't spend , there 's a couple of things that you can do with it . you can either consume your money or you could invest your money . so , let 's just think about a bunch of different situations and think about whether those things are consumption or investment . so let 's say , i have $ 100,000 that i 'm dealing with . so let 's say , i take that $ 100,000 and i build a factory . and i think that that factory is going to be able to produce -- i 'll make up some product -- it 'll be able to produce cars more efficiently and cheaper than any other car factory out there . well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 . in fact , i 'm expecting some type of a return on this investment . and i 've made a bunch of videos on what a return on investment is , and you can usually quantify it . if i take a $ 100,000 and i build this factory and this factory spits out $ 50,000 a year , it 's probably creating at least $ 50,000 a year value , assuming that nothing corrupt is happening in our system . in fact , it 's normally creating more than $ 50,000 a year of value . it may be creating a $ 100,000 a year of value and $ 50,000 of that may be going to the person who 's doing the production and then the other half of the value is actually going to the consumer of whatever this factory is making . and you have to think about it , because if all of the value went to the person who produced the factory then there 's not a huge incentive for someone to use his products anymore . but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment . so building a factory is an investment . now let 's say that i 'm homeless and i have this $ 100,000 . and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs . let 's say build a simple house , and i 'll do that in a neutral color . this is my other use of this $ 100,000 , instead of building a factory , i 'm going to build a simple house . and this house , it provides shelter for me and my family , it allows us that security that now my kids can go to school and they can themselves become more productive citizens . i now have an address . i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ? because i 'm taking this $ 100,000 , that maybe i had or someone gave to me , and it 's generating a return . and what is that return ? well , with a factory , it 's maybe a little easier to quantify . but at minimum , it 's this work that i 'm able to do because i now have a house . because i have the security , i have the address . i have the shelter . i 'm able to relax . it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society . it 's hard to value , maybe i did n't have any job before and now i have a job and i can contribute $ 30,000 a year to society . maybe i 'm working at someone 's factory . maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment . so i also consider this to be an investment . now , my question to you is , let 's say that i already had a house -- so this is an investment . let 's say i already had a house and my family is happy and we have everything we need . we have food on the table and my kids go to school and i 'm able to get a job and all of that exists . but let 's say , i still have a $ 100,000 and i use that $ 100,000 -- i 'll do it in yellow -- to put in some granite counter tops . i have some money left over , let 's say , i 'm going to add a bathroom to my house and i will put the latest hardwood floors , so that my family will be impressed . you can imagine . and maybe i add 2,000 square feet . you normally ca n't get all that for a $ 100,000 but i think you 'll bear with me . so i 'm essentially doing some major home improvements . so my question to you is -- is this an investment or is this consumption ? now , in our everyday world , with most people we deal with , they will call this investment in my house . and why are they saying that ? because they say , by spending a $ 100,000 in the house in this way , that maybe -- if you watch the home and garden channel , they 're doing this all the time -- that if you pour this a $ 100,000 into your house , that maybe the value of your house is going to increase by $ 150,000 . or someone else , all of a sudden , is going to perceive the value of your house as being $ 150,000 . they 'll say , well , you got a $ 50,000 return on investment . i 'd argue that that is not investment . that it 's speculation . you are , essentially , piling money into this stuff -- and i 'll do this in red , consumption is red . what 's happening here truly economically ? when you add granite , or you add an extra bathroom or hardwood floors or this extra 2,000 square feet , is it making anyone who 's living in that house more productive ? is it making you harder working ; is it making you more likely to invent the cure for cancer , or more likely to invent a way of getting cheap energy , or produce more widgets ? no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society . in fact , in no way is this going to contribute to the collective wealth of society . the last two examples i gave contribute to the collective wealth society , some of which you share , and that is your return on the investment . but as a whole , this is an investment into society . and it 's going to make the pie bigger . this right here , does not make the pie bigger . it might make you a little bit happier , make your ego feel a little bit better , let your pride grow , and your self righteousness grow , and show other people that you 've arrived , but it 's not going to increase the wealth of society . and when you say that you 've invested , you are really just saying i 've speculated . what you 're saying is -- by paying this $ 100,000 , you 're going to find , essentially , a greater fool out there . they could have done the same thing , they could have bought your house , spent $ 100,000 and done this , if this is what would have made them happy . but what you 're saying is , essentially , that you 're going to find somebody out there who 's willing to pay $ 150,000 extra for something that should have only cost $ 100,000 . and in fact , if anything , if you use this at all , the value of this is going to go down . so you 're just somehow assuming that the granite counter tops that you choose are going to be the taste that someone else would like or that the hardwood floors are going to be the taste someone else would like . i would actually argue that when you customize your house in this way , you are creating $ 100,000 of consumption to your taste . and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation . one might find some other guy willing to emotionally pay more for something . but it 's money that 's burned ; it 's not creating more value for society . i continue this in the next video .
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and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society .
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think about it : when you buy a stock from another person , are you generating wealth for society ?
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i 've been wanting to make a video on a couple of terms that people have really thrown around for a while now . and i think it really hits the core of some of the issues we 're dealing with now with the credit debacle but it 's kind of at a deeper level . so the things i want to go over are the ideas of savings , consumption , and investment . and you hear these a lot . everyone obviously says , i 've invested in the stock market or i 've invested in a house and i really want to give you a framework for how i think about these ideas . and frankly , i have n't seen them depicted this way in any economics book , although they 've kind of touched on this , but i think this is really how you should think about these things . so if you save money , and i think we all know what that means , that 's money that you did n't spend , there 's a couple of things that you can do with it . you can either consume your money or you could invest your money . so , let 's just think about a bunch of different situations and think about whether those things are consumption or investment . so let 's say , i have $ 100,000 that i 'm dealing with . so let 's say , i take that $ 100,000 and i build a factory . and i think that that factory is going to be able to produce -- i 'll make up some product -- it 'll be able to produce cars more efficiently and cheaper than any other car factory out there . well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 . in fact , i 'm expecting some type of a return on this investment . and i 've made a bunch of videos on what a return on investment is , and you can usually quantify it . if i take a $ 100,000 and i build this factory and this factory spits out $ 50,000 a year , it 's probably creating at least $ 50,000 a year value , assuming that nothing corrupt is happening in our system . in fact , it 's normally creating more than $ 50,000 a year of value . it may be creating a $ 100,000 a year of value and $ 50,000 of that may be going to the person who 's doing the production and then the other half of the value is actually going to the consumer of whatever this factory is making . and you have to think about it , because if all of the value went to the person who produced the factory then there 's not a huge incentive for someone to use his products anymore . but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment . so building a factory is an investment . now let 's say that i 'm homeless and i have this $ 100,000 . and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs . let 's say build a simple house , and i 'll do that in a neutral color . this is my other use of this $ 100,000 , instead of building a factory , i 'm going to build a simple house . and this house , it provides shelter for me and my family , it allows us that security that now my kids can go to school and they can themselves become more productive citizens . i now have an address . i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ? because i 'm taking this $ 100,000 , that maybe i had or someone gave to me , and it 's generating a return . and what is that return ? well , with a factory , it 's maybe a little easier to quantify . but at minimum , it 's this work that i 'm able to do because i now have a house . because i have the security , i have the address . i have the shelter . i 'm able to relax . it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society . it 's hard to value , maybe i did n't have any job before and now i have a job and i can contribute $ 30,000 a year to society . maybe i 'm working at someone 's factory . maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment . so i also consider this to be an investment . now , my question to you is , let 's say that i already had a house -- so this is an investment . let 's say i already had a house and my family is happy and we have everything we need . we have food on the table and my kids go to school and i 'm able to get a job and all of that exists . but let 's say , i still have a $ 100,000 and i use that $ 100,000 -- i 'll do it in yellow -- to put in some granite counter tops . i have some money left over , let 's say , i 'm going to add a bathroom to my house and i will put the latest hardwood floors , so that my family will be impressed . you can imagine . and maybe i add 2,000 square feet . you normally ca n't get all that for a $ 100,000 but i think you 'll bear with me . so i 'm essentially doing some major home improvements . so my question to you is -- is this an investment or is this consumption ? now , in our everyday world , with most people we deal with , they will call this investment in my house . and why are they saying that ? because they say , by spending a $ 100,000 in the house in this way , that maybe -- if you watch the home and garden channel , they 're doing this all the time -- that if you pour this a $ 100,000 into your house , that maybe the value of your house is going to increase by $ 150,000 . or someone else , all of a sudden , is going to perceive the value of your house as being $ 150,000 . they 'll say , well , you got a $ 50,000 return on investment . i 'd argue that that is not investment . that it 's speculation . you are , essentially , piling money into this stuff -- and i 'll do this in red , consumption is red . what 's happening here truly economically ? when you add granite , or you add an extra bathroom or hardwood floors or this extra 2,000 square feet , is it making anyone who 's living in that house more productive ? is it making you harder working ; is it making you more likely to invent the cure for cancer , or more likely to invent a way of getting cheap energy , or produce more widgets ? no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society . in fact , in no way is this going to contribute to the collective wealth of society . the last two examples i gave contribute to the collective wealth society , some of which you share , and that is your return on the investment . but as a whole , this is an investment into society . and it 's going to make the pie bigger . this right here , does not make the pie bigger . it might make you a little bit happier , make your ego feel a little bit better , let your pride grow , and your self righteousness grow , and show other people that you 've arrived , but it 's not going to increase the wealth of society . and when you say that you 've invested , you are really just saying i 've speculated . what you 're saying is -- by paying this $ 100,000 , you 're going to find , essentially , a greater fool out there . they could have done the same thing , they could have bought your house , spent $ 100,000 and done this , if this is what would have made them happy . but what you 're saying is , essentially , that you 're going to find somebody out there who 's willing to pay $ 150,000 extra for something that should have only cost $ 100,000 . and in fact , if anything , if you use this at all , the value of this is going to go down . so you 're just somehow assuming that the granite counter tops that you choose are going to be the taste that someone else would like or that the hardwood floors are going to be the taste someone else would like . i would actually argue that when you customize your house in this way , you are creating $ 100,000 of consumption to your taste . and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation . one might find some other guy willing to emotionally pay more for something . but it 's money that 's burned ; it 's not creating more value for society . i continue this in the next video .
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anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation .
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how bout if you rent the house to other people , will the hardwood floors and granite create value then ?
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i 've been wanting to make a video on a couple of terms that people have really thrown around for a while now . and i think it really hits the core of some of the issues we 're dealing with now with the credit debacle but it 's kind of at a deeper level . so the things i want to go over are the ideas of savings , consumption , and investment . and you hear these a lot . everyone obviously says , i 've invested in the stock market or i 've invested in a house and i really want to give you a framework for how i think about these ideas . and frankly , i have n't seen them depicted this way in any economics book , although they 've kind of touched on this , but i think this is really how you should think about these things . so if you save money , and i think we all know what that means , that 's money that you did n't spend , there 's a couple of things that you can do with it . you can either consume your money or you could invest your money . so , let 's just think about a bunch of different situations and think about whether those things are consumption or investment . so let 's say , i have $ 100,000 that i 'm dealing with . so let 's say , i take that $ 100,000 and i build a factory . and i think that that factory is going to be able to produce -- i 'll make up some product -- it 'll be able to produce cars more efficiently and cheaper than any other car factory out there . well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 . in fact , i 'm expecting some type of a return on this investment . and i 've made a bunch of videos on what a return on investment is , and you can usually quantify it . if i take a $ 100,000 and i build this factory and this factory spits out $ 50,000 a year , it 's probably creating at least $ 50,000 a year value , assuming that nothing corrupt is happening in our system . in fact , it 's normally creating more than $ 50,000 a year of value . it may be creating a $ 100,000 a year of value and $ 50,000 of that may be going to the person who 's doing the production and then the other half of the value is actually going to the consumer of whatever this factory is making . and you have to think about it , because if all of the value went to the person who produced the factory then there 's not a huge incentive for someone to use his products anymore . but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment . so building a factory is an investment . now let 's say that i 'm homeless and i have this $ 100,000 . and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs . let 's say build a simple house , and i 'll do that in a neutral color . this is my other use of this $ 100,000 , instead of building a factory , i 'm going to build a simple house . and this house , it provides shelter for me and my family , it allows us that security that now my kids can go to school and they can themselves become more productive citizens . i now have an address . i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ? because i 'm taking this $ 100,000 , that maybe i had or someone gave to me , and it 's generating a return . and what is that return ? well , with a factory , it 's maybe a little easier to quantify . but at minimum , it 's this work that i 'm able to do because i now have a house . because i have the security , i have the address . i have the shelter . i 'm able to relax . it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society . it 's hard to value , maybe i did n't have any job before and now i have a job and i can contribute $ 30,000 a year to society . maybe i 'm working at someone 's factory . maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment . so i also consider this to be an investment . now , my question to you is , let 's say that i already had a house -- so this is an investment . let 's say i already had a house and my family is happy and we have everything we need . we have food on the table and my kids go to school and i 'm able to get a job and all of that exists . but let 's say , i still have a $ 100,000 and i use that $ 100,000 -- i 'll do it in yellow -- to put in some granite counter tops . i have some money left over , let 's say , i 'm going to add a bathroom to my house and i will put the latest hardwood floors , so that my family will be impressed . you can imagine . and maybe i add 2,000 square feet . you normally ca n't get all that for a $ 100,000 but i think you 'll bear with me . so i 'm essentially doing some major home improvements . so my question to you is -- is this an investment or is this consumption ? now , in our everyday world , with most people we deal with , they will call this investment in my house . and why are they saying that ? because they say , by spending a $ 100,000 in the house in this way , that maybe -- if you watch the home and garden channel , they 're doing this all the time -- that if you pour this a $ 100,000 into your house , that maybe the value of your house is going to increase by $ 150,000 . or someone else , all of a sudden , is going to perceive the value of your house as being $ 150,000 . they 'll say , well , you got a $ 50,000 return on investment . i 'd argue that that is not investment . that it 's speculation . you are , essentially , piling money into this stuff -- and i 'll do this in red , consumption is red . what 's happening here truly economically ? when you add granite , or you add an extra bathroom or hardwood floors or this extra 2,000 square feet , is it making anyone who 's living in that house more productive ? is it making you harder working ; is it making you more likely to invent the cure for cancer , or more likely to invent a way of getting cheap energy , or produce more widgets ? no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society . in fact , in no way is this going to contribute to the collective wealth of society . the last two examples i gave contribute to the collective wealth society , some of which you share , and that is your return on the investment . but as a whole , this is an investment into society . and it 's going to make the pie bigger . this right here , does not make the pie bigger . it might make you a little bit happier , make your ego feel a little bit better , let your pride grow , and your self righteousness grow , and show other people that you 've arrived , but it 's not going to increase the wealth of society . and when you say that you 've invested , you are really just saying i 've speculated . what you 're saying is -- by paying this $ 100,000 , you 're going to find , essentially , a greater fool out there . they could have done the same thing , they could have bought your house , spent $ 100,000 and done this , if this is what would have made them happy . but what you 're saying is , essentially , that you 're going to find somebody out there who 's willing to pay $ 150,000 extra for something that should have only cost $ 100,000 . and in fact , if anything , if you use this at all , the value of this is going to go down . so you 're just somehow assuming that the granite counter tops that you choose are going to be the taste that someone else would like or that the hardwood floors are going to be the taste someone else would like . i would actually argue that when you customize your house in this way , you are creating $ 100,000 of consumption to your taste . and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation . one might find some other guy willing to emotionally pay more for something . but it 's money that 's burned ; it 's not creating more value for society . i continue this in the next video .
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well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 .
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all fall under the term 'investment ' ?
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i 've been wanting to make a video on a couple of terms that people have really thrown around for a while now . and i think it really hits the core of some of the issues we 're dealing with now with the credit debacle but it 's kind of at a deeper level . so the things i want to go over are the ideas of savings , consumption , and investment . and you hear these a lot . everyone obviously says , i 've invested in the stock market or i 've invested in a house and i really want to give you a framework for how i think about these ideas . and frankly , i have n't seen them depicted this way in any economics book , although they 've kind of touched on this , but i think this is really how you should think about these things . so if you save money , and i think we all know what that means , that 's money that you did n't spend , there 's a couple of things that you can do with it . you can either consume your money or you could invest your money . so , let 's just think about a bunch of different situations and think about whether those things are consumption or investment . so let 's say , i have $ 100,000 that i 'm dealing with . so let 's say , i take that $ 100,000 and i build a factory . and i think that that factory is going to be able to produce -- i 'll make up some product -- it 'll be able to produce cars more efficiently and cheaper than any other car factory out there . well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 . in fact , i 'm expecting some type of a return on this investment . and i 've made a bunch of videos on what a return on investment is , and you can usually quantify it . if i take a $ 100,000 and i build this factory and this factory spits out $ 50,000 a year , it 's probably creating at least $ 50,000 a year value , assuming that nothing corrupt is happening in our system . in fact , it 's normally creating more than $ 50,000 a year of value . it may be creating a $ 100,000 a year of value and $ 50,000 of that may be going to the person who 's doing the production and then the other half of the value is actually going to the consumer of whatever this factory is making . and you have to think about it , because if all of the value went to the person who produced the factory then there 's not a huge incentive for someone to use his products anymore . but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment . so building a factory is an investment . now let 's say that i 'm homeless and i have this $ 100,000 . and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs . let 's say build a simple house , and i 'll do that in a neutral color . this is my other use of this $ 100,000 , instead of building a factory , i 'm going to build a simple house . and this house , it provides shelter for me and my family , it allows us that security that now my kids can go to school and they can themselves become more productive citizens . i now have an address . i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ? because i 'm taking this $ 100,000 , that maybe i had or someone gave to me , and it 's generating a return . and what is that return ? well , with a factory , it 's maybe a little easier to quantify . but at minimum , it 's this work that i 'm able to do because i now have a house . because i have the security , i have the address . i have the shelter . i 'm able to relax . it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society . it 's hard to value , maybe i did n't have any job before and now i have a job and i can contribute $ 30,000 a year to society . maybe i 'm working at someone 's factory . maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment . so i also consider this to be an investment . now , my question to you is , let 's say that i already had a house -- so this is an investment . let 's say i already had a house and my family is happy and we have everything we need . we have food on the table and my kids go to school and i 'm able to get a job and all of that exists . but let 's say , i still have a $ 100,000 and i use that $ 100,000 -- i 'll do it in yellow -- to put in some granite counter tops . i have some money left over , let 's say , i 'm going to add a bathroom to my house and i will put the latest hardwood floors , so that my family will be impressed . you can imagine . and maybe i add 2,000 square feet . you normally ca n't get all that for a $ 100,000 but i think you 'll bear with me . so i 'm essentially doing some major home improvements . so my question to you is -- is this an investment or is this consumption ? now , in our everyday world , with most people we deal with , they will call this investment in my house . and why are they saying that ? because they say , by spending a $ 100,000 in the house in this way , that maybe -- if you watch the home and garden channel , they 're doing this all the time -- that if you pour this a $ 100,000 into your house , that maybe the value of your house is going to increase by $ 150,000 . or someone else , all of a sudden , is going to perceive the value of your house as being $ 150,000 . they 'll say , well , you got a $ 50,000 return on investment . i 'd argue that that is not investment . that it 's speculation . you are , essentially , piling money into this stuff -- and i 'll do this in red , consumption is red . what 's happening here truly economically ? when you add granite , or you add an extra bathroom or hardwood floors or this extra 2,000 square feet , is it making anyone who 's living in that house more productive ? is it making you harder working ; is it making you more likely to invent the cure for cancer , or more likely to invent a way of getting cheap energy , or produce more widgets ? no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society . in fact , in no way is this going to contribute to the collective wealth of society . the last two examples i gave contribute to the collective wealth society , some of which you share , and that is your return on the investment . but as a whole , this is an investment into society . and it 's going to make the pie bigger . this right here , does not make the pie bigger . it might make you a little bit happier , make your ego feel a little bit better , let your pride grow , and your self righteousness grow , and show other people that you 've arrived , but it 's not going to increase the wealth of society . and when you say that you 've invested , you are really just saying i 've speculated . what you 're saying is -- by paying this $ 100,000 , you 're going to find , essentially , a greater fool out there . they could have done the same thing , they could have bought your house , spent $ 100,000 and done this , if this is what would have made them happy . but what you 're saying is , essentially , that you 're going to find somebody out there who 's willing to pay $ 150,000 extra for something that should have only cost $ 100,000 . and in fact , if anything , if you use this at all , the value of this is going to go down . so you 're just somehow assuming that the granite counter tops that you choose are going to be the taste that someone else would like or that the hardwood floors are going to be the taste someone else would like . i would actually argue that when you customize your house in this way , you are creating $ 100,000 of consumption to your taste . and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation . one might find some other guy willing to emotionally pay more for something . but it 's money that 's burned ; it 's not creating more value for society . i continue this in the next video .
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well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 .
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by consuming the granite , floors , room addition etc does that not produce `` investment '' for the businesses that provided these consumables thereby contributing to the overall economic good of the economy ?
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i 've been wanting to make a video on a couple of terms that people have really thrown around for a while now . and i think it really hits the core of some of the issues we 're dealing with now with the credit debacle but it 's kind of at a deeper level . so the things i want to go over are the ideas of savings , consumption , and investment . and you hear these a lot . everyone obviously says , i 've invested in the stock market or i 've invested in a house and i really want to give you a framework for how i think about these ideas . and frankly , i have n't seen them depicted this way in any economics book , although they 've kind of touched on this , but i think this is really how you should think about these things . so if you save money , and i think we all know what that means , that 's money that you did n't spend , there 's a couple of things that you can do with it . you can either consume your money or you could invest your money . so , let 's just think about a bunch of different situations and think about whether those things are consumption or investment . so let 's say , i have $ 100,000 that i 'm dealing with . so let 's say , i take that $ 100,000 and i build a factory . and i think that that factory is going to be able to produce -- i 'll make up some product -- it 'll be able to produce cars more efficiently and cheaper than any other car factory out there . well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 . in fact , i 'm expecting some type of a return on this investment . and i 've made a bunch of videos on what a return on investment is , and you can usually quantify it . if i take a $ 100,000 and i build this factory and this factory spits out $ 50,000 a year , it 's probably creating at least $ 50,000 a year value , assuming that nothing corrupt is happening in our system . in fact , it 's normally creating more than $ 50,000 a year of value . it may be creating a $ 100,000 a year of value and $ 50,000 of that may be going to the person who 's doing the production and then the other half of the value is actually going to the consumer of whatever this factory is making . and you have to think about it , because if all of the value went to the person who produced the factory then there 's not a huge incentive for someone to use his products anymore . but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment . so building a factory is an investment . now let 's say that i 'm homeless and i have this $ 100,000 . and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs . let 's say build a simple house , and i 'll do that in a neutral color . this is my other use of this $ 100,000 , instead of building a factory , i 'm going to build a simple house . and this house , it provides shelter for me and my family , it allows us that security that now my kids can go to school and they can themselves become more productive citizens . i now have an address . i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ? because i 'm taking this $ 100,000 , that maybe i had or someone gave to me , and it 's generating a return . and what is that return ? well , with a factory , it 's maybe a little easier to quantify . but at minimum , it 's this work that i 'm able to do because i now have a house . because i have the security , i have the address . i have the shelter . i 'm able to relax . it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society . it 's hard to value , maybe i did n't have any job before and now i have a job and i can contribute $ 30,000 a year to society . maybe i 'm working at someone 's factory . maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment . so i also consider this to be an investment . now , my question to you is , let 's say that i already had a house -- so this is an investment . let 's say i already had a house and my family is happy and we have everything we need . we have food on the table and my kids go to school and i 'm able to get a job and all of that exists . but let 's say , i still have a $ 100,000 and i use that $ 100,000 -- i 'll do it in yellow -- to put in some granite counter tops . i have some money left over , let 's say , i 'm going to add a bathroom to my house and i will put the latest hardwood floors , so that my family will be impressed . you can imagine . and maybe i add 2,000 square feet . you normally ca n't get all that for a $ 100,000 but i think you 'll bear with me . so i 'm essentially doing some major home improvements . so my question to you is -- is this an investment or is this consumption ? now , in our everyday world , with most people we deal with , they will call this investment in my house . and why are they saying that ? because they say , by spending a $ 100,000 in the house in this way , that maybe -- if you watch the home and garden channel , they 're doing this all the time -- that if you pour this a $ 100,000 into your house , that maybe the value of your house is going to increase by $ 150,000 . or someone else , all of a sudden , is going to perceive the value of your house as being $ 150,000 . they 'll say , well , you got a $ 50,000 return on investment . i 'd argue that that is not investment . that it 's speculation . you are , essentially , piling money into this stuff -- and i 'll do this in red , consumption is red . what 's happening here truly economically ? when you add granite , or you add an extra bathroom or hardwood floors or this extra 2,000 square feet , is it making anyone who 's living in that house more productive ? is it making you harder working ; is it making you more likely to invent the cure for cancer , or more likely to invent a way of getting cheap energy , or produce more widgets ? no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society . in fact , in no way is this going to contribute to the collective wealth of society . the last two examples i gave contribute to the collective wealth society , some of which you share , and that is your return on the investment . but as a whole , this is an investment into society . and it 's going to make the pie bigger . this right here , does not make the pie bigger . it might make you a little bit happier , make your ego feel a little bit better , let your pride grow , and your self righteousness grow , and show other people that you 've arrived , but it 's not going to increase the wealth of society . and when you say that you 've invested , you are really just saying i 've speculated . what you 're saying is -- by paying this $ 100,000 , you 're going to find , essentially , a greater fool out there . they could have done the same thing , they could have bought your house , spent $ 100,000 and done this , if this is what would have made them happy . but what you 're saying is , essentially , that you 're going to find somebody out there who 's willing to pay $ 150,000 extra for something that should have only cost $ 100,000 . and in fact , if anything , if you use this at all , the value of this is going to go down . so you 're just somehow assuming that the granite counter tops that you choose are going to be the taste that someone else would like or that the hardwood floors are going to be the taste someone else would like . i would actually argue that when you customize your house in this way , you are creating $ 100,000 of consumption to your taste . and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation . one might find some other guy willing to emotionally pay more for something . but it 's money that 's burned ; it 's not creating more value for society . i continue this in the next video .
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no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society .
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how should we classify purchasing energy saving appliances or solar panels ?
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i 've been wanting to make a video on a couple of terms that people have really thrown around for a while now . and i think it really hits the core of some of the issues we 're dealing with now with the credit debacle but it 's kind of at a deeper level . so the things i want to go over are the ideas of savings , consumption , and investment . and you hear these a lot . everyone obviously says , i 've invested in the stock market or i 've invested in a house and i really want to give you a framework for how i think about these ideas . and frankly , i have n't seen them depicted this way in any economics book , although they 've kind of touched on this , but i think this is really how you should think about these things . so if you save money , and i think we all know what that means , that 's money that you did n't spend , there 's a couple of things that you can do with it . you can either consume your money or you could invest your money . so , let 's just think about a bunch of different situations and think about whether those things are consumption or investment . so let 's say , i have $ 100,000 that i 'm dealing with . so let 's say , i take that $ 100,000 and i build a factory . and i think that that factory is going to be able to produce -- i 'll make up some product -- it 'll be able to produce cars more efficiently and cheaper than any other car factory out there . well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 . in fact , i 'm expecting some type of a return on this investment . and i 've made a bunch of videos on what a return on investment is , and you can usually quantify it . if i take a $ 100,000 and i build this factory and this factory spits out $ 50,000 a year , it 's probably creating at least $ 50,000 a year value , assuming that nothing corrupt is happening in our system . in fact , it 's normally creating more than $ 50,000 a year of value . it may be creating a $ 100,000 a year of value and $ 50,000 of that may be going to the person who 's doing the production and then the other half of the value is actually going to the consumer of whatever this factory is making . and you have to think about it , because if all of the value went to the person who produced the factory then there 's not a huge incentive for someone to use his products anymore . but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment . so building a factory is an investment . now let 's say that i 'm homeless and i have this $ 100,000 . and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs . let 's say build a simple house , and i 'll do that in a neutral color . this is my other use of this $ 100,000 , instead of building a factory , i 'm going to build a simple house . and this house , it provides shelter for me and my family , it allows us that security that now my kids can go to school and they can themselves become more productive citizens . i now have an address . i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ? because i 'm taking this $ 100,000 , that maybe i had or someone gave to me , and it 's generating a return . and what is that return ? well , with a factory , it 's maybe a little easier to quantify . but at minimum , it 's this work that i 'm able to do because i now have a house . because i have the security , i have the address . i have the shelter . i 'm able to relax . it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society . it 's hard to value , maybe i did n't have any job before and now i have a job and i can contribute $ 30,000 a year to society . maybe i 'm working at someone 's factory . maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment . so i also consider this to be an investment . now , my question to you is , let 's say that i already had a house -- so this is an investment . let 's say i already had a house and my family is happy and we have everything we need . we have food on the table and my kids go to school and i 'm able to get a job and all of that exists . but let 's say , i still have a $ 100,000 and i use that $ 100,000 -- i 'll do it in yellow -- to put in some granite counter tops . i have some money left over , let 's say , i 'm going to add a bathroom to my house and i will put the latest hardwood floors , so that my family will be impressed . you can imagine . and maybe i add 2,000 square feet . you normally ca n't get all that for a $ 100,000 but i think you 'll bear with me . so i 'm essentially doing some major home improvements . so my question to you is -- is this an investment or is this consumption ? now , in our everyday world , with most people we deal with , they will call this investment in my house . and why are they saying that ? because they say , by spending a $ 100,000 in the house in this way , that maybe -- if you watch the home and garden channel , they 're doing this all the time -- that if you pour this a $ 100,000 into your house , that maybe the value of your house is going to increase by $ 150,000 . or someone else , all of a sudden , is going to perceive the value of your house as being $ 150,000 . they 'll say , well , you got a $ 50,000 return on investment . i 'd argue that that is not investment . that it 's speculation . you are , essentially , piling money into this stuff -- and i 'll do this in red , consumption is red . what 's happening here truly economically ? when you add granite , or you add an extra bathroom or hardwood floors or this extra 2,000 square feet , is it making anyone who 's living in that house more productive ? is it making you harder working ; is it making you more likely to invent the cure for cancer , or more likely to invent a way of getting cheap energy , or produce more widgets ? no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society . in fact , in no way is this going to contribute to the collective wealth of society . the last two examples i gave contribute to the collective wealth society , some of which you share , and that is your return on the investment . but as a whole , this is an investment into society . and it 's going to make the pie bigger . this right here , does not make the pie bigger . it might make you a little bit happier , make your ego feel a little bit better , let your pride grow , and your self righteousness grow , and show other people that you 've arrived , but it 's not going to increase the wealth of society . and when you say that you 've invested , you are really just saying i 've speculated . what you 're saying is -- by paying this $ 100,000 , you 're going to find , essentially , a greater fool out there . they could have done the same thing , they could have bought your house , spent $ 100,000 and done this , if this is what would have made them happy . but what you 're saying is , essentially , that you 're going to find somebody out there who 's willing to pay $ 150,000 extra for something that should have only cost $ 100,000 . and in fact , if anything , if you use this at all , the value of this is going to go down . so you 're just somehow assuming that the granite counter tops that you choose are going to be the taste that someone else would like or that the hardwood floors are going to be the taste someone else would like . i would actually argue that when you customize your house in this way , you are creating $ 100,000 of consumption to your taste . and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation . one might find some other guy willing to emotionally pay more for something . but it 's money that 's burned ; it 's not creating more value for society . i continue this in the next video .
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maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment .
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is n't one way to define value what other people would be willing or able to buy ?
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i 've been wanting to make a video on a couple of terms that people have really thrown around for a while now . and i think it really hits the core of some of the issues we 're dealing with now with the credit debacle but it 's kind of at a deeper level . so the things i want to go over are the ideas of savings , consumption , and investment . and you hear these a lot . everyone obviously says , i 've invested in the stock market or i 've invested in a house and i really want to give you a framework for how i think about these ideas . and frankly , i have n't seen them depicted this way in any economics book , although they 've kind of touched on this , but i think this is really how you should think about these things . so if you save money , and i think we all know what that means , that 's money that you did n't spend , there 's a couple of things that you can do with it . you can either consume your money or you could invest your money . so , let 's just think about a bunch of different situations and think about whether those things are consumption or investment . so let 's say , i have $ 100,000 that i 'm dealing with . so let 's say , i take that $ 100,000 and i build a factory . and i think that that factory is going to be able to produce -- i 'll make up some product -- it 'll be able to produce cars more efficiently and cheaper than any other car factory out there . well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 . in fact , i 'm expecting some type of a return on this investment . and i 've made a bunch of videos on what a return on investment is , and you can usually quantify it . if i take a $ 100,000 and i build this factory and this factory spits out $ 50,000 a year , it 's probably creating at least $ 50,000 a year value , assuming that nothing corrupt is happening in our system . in fact , it 's normally creating more than $ 50,000 a year of value . it may be creating a $ 100,000 a year of value and $ 50,000 of that may be going to the person who 's doing the production and then the other half of the value is actually going to the consumer of whatever this factory is making . and you have to think about it , because if all of the value went to the person who produced the factory then there 's not a huge incentive for someone to use his products anymore . but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment . so building a factory is an investment . now let 's say that i 'm homeless and i have this $ 100,000 . and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs . let 's say build a simple house , and i 'll do that in a neutral color . this is my other use of this $ 100,000 , instead of building a factory , i 'm going to build a simple house . and this house , it provides shelter for me and my family , it allows us that security that now my kids can go to school and they can themselves become more productive citizens . i now have an address . i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ? because i 'm taking this $ 100,000 , that maybe i had or someone gave to me , and it 's generating a return . and what is that return ? well , with a factory , it 's maybe a little easier to quantify . but at minimum , it 's this work that i 'm able to do because i now have a house . because i have the security , i have the address . i have the shelter . i 'm able to relax . it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society . it 's hard to value , maybe i did n't have any job before and now i have a job and i can contribute $ 30,000 a year to society . maybe i 'm working at someone 's factory . maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment . so i also consider this to be an investment . now , my question to you is , let 's say that i already had a house -- so this is an investment . let 's say i already had a house and my family is happy and we have everything we need . we have food on the table and my kids go to school and i 'm able to get a job and all of that exists . but let 's say , i still have a $ 100,000 and i use that $ 100,000 -- i 'll do it in yellow -- to put in some granite counter tops . i have some money left over , let 's say , i 'm going to add a bathroom to my house and i will put the latest hardwood floors , so that my family will be impressed . you can imagine . and maybe i add 2,000 square feet . you normally ca n't get all that for a $ 100,000 but i think you 'll bear with me . so i 'm essentially doing some major home improvements . so my question to you is -- is this an investment or is this consumption ? now , in our everyday world , with most people we deal with , they will call this investment in my house . and why are they saying that ? because they say , by spending a $ 100,000 in the house in this way , that maybe -- if you watch the home and garden channel , they 're doing this all the time -- that if you pour this a $ 100,000 into your house , that maybe the value of your house is going to increase by $ 150,000 . or someone else , all of a sudden , is going to perceive the value of your house as being $ 150,000 . they 'll say , well , you got a $ 50,000 return on investment . i 'd argue that that is not investment . that it 's speculation . you are , essentially , piling money into this stuff -- and i 'll do this in red , consumption is red . what 's happening here truly economically ? when you add granite , or you add an extra bathroom or hardwood floors or this extra 2,000 square feet , is it making anyone who 's living in that house more productive ? is it making you harder working ; is it making you more likely to invent the cure for cancer , or more likely to invent a way of getting cheap energy , or produce more widgets ? no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society . in fact , in no way is this going to contribute to the collective wealth of society . the last two examples i gave contribute to the collective wealth society , some of which you share , and that is your return on the investment . but as a whole , this is an investment into society . and it 's going to make the pie bigger . this right here , does not make the pie bigger . it might make you a little bit happier , make your ego feel a little bit better , let your pride grow , and your self righteousness grow , and show other people that you 've arrived , but it 's not going to increase the wealth of society . and when you say that you 've invested , you are really just saying i 've speculated . what you 're saying is -- by paying this $ 100,000 , you 're going to find , essentially , a greater fool out there . they could have done the same thing , they could have bought your house , spent $ 100,000 and done this , if this is what would have made them happy . but what you 're saying is , essentially , that you 're going to find somebody out there who 's willing to pay $ 150,000 extra for something that should have only cost $ 100,000 . and in fact , if anything , if you use this at all , the value of this is going to go down . so you 're just somehow assuming that the granite counter tops that you choose are going to be the taste that someone else would like or that the hardwood floors are going to be the taste someone else would like . i would actually argue that when you customize your house in this way , you are creating $ 100,000 of consumption to your taste . and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation . one might find some other guy willing to emotionally pay more for something . but it 's money that 's burned ; it 's not creating more value for society . i continue this in the next video .
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and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs .
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i do n't disagree , but under these assumptions , is food an investment ?
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i 've been wanting to make a video on a couple of terms that people have really thrown around for a while now . and i think it really hits the core of some of the issues we 're dealing with now with the credit debacle but it 's kind of at a deeper level . so the things i want to go over are the ideas of savings , consumption , and investment . and you hear these a lot . everyone obviously says , i 've invested in the stock market or i 've invested in a house and i really want to give you a framework for how i think about these ideas . and frankly , i have n't seen them depicted this way in any economics book , although they 've kind of touched on this , but i think this is really how you should think about these things . so if you save money , and i think we all know what that means , that 's money that you did n't spend , there 's a couple of things that you can do with it . you can either consume your money or you could invest your money . so , let 's just think about a bunch of different situations and think about whether those things are consumption or investment . so let 's say , i have $ 100,000 that i 'm dealing with . so let 's say , i take that $ 100,000 and i build a factory . and i think that that factory is going to be able to produce -- i 'll make up some product -- it 'll be able to produce cars more efficiently and cheaper than any other car factory out there . well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 . in fact , i 'm expecting some type of a return on this investment . and i 've made a bunch of videos on what a return on investment is , and you can usually quantify it . if i take a $ 100,000 and i build this factory and this factory spits out $ 50,000 a year , it 's probably creating at least $ 50,000 a year value , assuming that nothing corrupt is happening in our system . in fact , it 's normally creating more than $ 50,000 a year of value . it may be creating a $ 100,000 a year of value and $ 50,000 of that may be going to the person who 's doing the production and then the other half of the value is actually going to the consumer of whatever this factory is making . and you have to think about it , because if all of the value went to the person who produced the factory then there 's not a huge incentive for someone to use his products anymore . but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment . so building a factory is an investment . now let 's say that i 'm homeless and i have this $ 100,000 . and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs . let 's say build a simple house , and i 'll do that in a neutral color . this is my other use of this $ 100,000 , instead of building a factory , i 'm going to build a simple house . and this house , it provides shelter for me and my family , it allows us that security that now my kids can go to school and they can themselves become more productive citizens . i now have an address . i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ? because i 'm taking this $ 100,000 , that maybe i had or someone gave to me , and it 's generating a return . and what is that return ? well , with a factory , it 's maybe a little easier to quantify . but at minimum , it 's this work that i 'm able to do because i now have a house . because i have the security , i have the address . i have the shelter . i 'm able to relax . it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society . it 's hard to value , maybe i did n't have any job before and now i have a job and i can contribute $ 30,000 a year to society . maybe i 'm working at someone 's factory . maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment . so i also consider this to be an investment . now , my question to you is , let 's say that i already had a house -- so this is an investment . let 's say i already had a house and my family is happy and we have everything we need . we have food on the table and my kids go to school and i 'm able to get a job and all of that exists . but let 's say , i still have a $ 100,000 and i use that $ 100,000 -- i 'll do it in yellow -- to put in some granite counter tops . i have some money left over , let 's say , i 'm going to add a bathroom to my house and i will put the latest hardwood floors , so that my family will be impressed . you can imagine . and maybe i add 2,000 square feet . you normally ca n't get all that for a $ 100,000 but i think you 'll bear with me . so i 'm essentially doing some major home improvements . so my question to you is -- is this an investment or is this consumption ? now , in our everyday world , with most people we deal with , they will call this investment in my house . and why are they saying that ? because they say , by spending a $ 100,000 in the house in this way , that maybe -- if you watch the home and garden channel , they 're doing this all the time -- that if you pour this a $ 100,000 into your house , that maybe the value of your house is going to increase by $ 150,000 . or someone else , all of a sudden , is going to perceive the value of your house as being $ 150,000 . they 'll say , well , you got a $ 50,000 return on investment . i 'd argue that that is not investment . that it 's speculation . you are , essentially , piling money into this stuff -- and i 'll do this in red , consumption is red . what 's happening here truly economically ? when you add granite , or you add an extra bathroom or hardwood floors or this extra 2,000 square feet , is it making anyone who 's living in that house more productive ? is it making you harder working ; is it making you more likely to invent the cure for cancer , or more likely to invent a way of getting cheap energy , or produce more widgets ? no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society . in fact , in no way is this going to contribute to the collective wealth of society . the last two examples i gave contribute to the collective wealth society , some of which you share , and that is your return on the investment . but as a whole , this is an investment into society . and it 's going to make the pie bigger . this right here , does not make the pie bigger . it might make you a little bit happier , make your ego feel a little bit better , let your pride grow , and your self righteousness grow , and show other people that you 've arrived , but it 's not going to increase the wealth of society . and when you say that you 've invested , you are really just saying i 've speculated . what you 're saying is -- by paying this $ 100,000 , you 're going to find , essentially , a greater fool out there . they could have done the same thing , they could have bought your house , spent $ 100,000 and done this , if this is what would have made them happy . but what you 're saying is , essentially , that you 're going to find somebody out there who 's willing to pay $ 150,000 extra for something that should have only cost $ 100,000 . and in fact , if anything , if you use this at all , the value of this is going to go down . so you 're just somehow assuming that the granite counter tops that you choose are going to be the taste that someone else would like or that the hardwood floors are going to be the taste someone else would like . i would actually argue that when you customize your house in this way , you are creating $ 100,000 of consumption to your taste . and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation . one might find some other guy willing to emotionally pay more for something . but it 's money that 's burned ; it 's not creating more value for society . i continue this in the next video .
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anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation .
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what value do the bankers create by making `` investments '' ?
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i 've been wanting to make a video on a couple of terms that people have really thrown around for a while now . and i think it really hits the core of some of the issues we 're dealing with now with the credit debacle but it 's kind of at a deeper level . so the things i want to go over are the ideas of savings , consumption , and investment . and you hear these a lot . everyone obviously says , i 've invested in the stock market or i 've invested in a house and i really want to give you a framework for how i think about these ideas . and frankly , i have n't seen them depicted this way in any economics book , although they 've kind of touched on this , but i think this is really how you should think about these things . so if you save money , and i think we all know what that means , that 's money that you did n't spend , there 's a couple of things that you can do with it . you can either consume your money or you could invest your money . so , let 's just think about a bunch of different situations and think about whether those things are consumption or investment . so let 's say , i have $ 100,000 that i 'm dealing with . so let 's say , i take that $ 100,000 and i build a factory . and i think that that factory is going to be able to produce -- i 'll make up some product -- it 'll be able to produce cars more efficiently and cheaper than any other car factory out there . well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 . in fact , i 'm expecting some type of a return on this investment . and i 've made a bunch of videos on what a return on investment is , and you can usually quantify it . if i take a $ 100,000 and i build this factory and this factory spits out $ 50,000 a year , it 's probably creating at least $ 50,000 a year value , assuming that nothing corrupt is happening in our system . in fact , it 's normally creating more than $ 50,000 a year of value . it may be creating a $ 100,000 a year of value and $ 50,000 of that may be going to the person who 's doing the production and then the other half of the value is actually going to the consumer of whatever this factory is making . and you have to think about it , because if all of the value went to the person who produced the factory then there 's not a huge incentive for someone to use his products anymore . but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment . so building a factory is an investment . now let 's say that i 'm homeless and i have this $ 100,000 . and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs . let 's say build a simple house , and i 'll do that in a neutral color . this is my other use of this $ 100,000 , instead of building a factory , i 'm going to build a simple house . and this house , it provides shelter for me and my family , it allows us that security that now my kids can go to school and they can themselves become more productive citizens . i now have an address . i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ? because i 'm taking this $ 100,000 , that maybe i had or someone gave to me , and it 's generating a return . and what is that return ? well , with a factory , it 's maybe a little easier to quantify . but at minimum , it 's this work that i 'm able to do because i now have a house . because i have the security , i have the address . i have the shelter . i 'm able to relax . it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society . it 's hard to value , maybe i did n't have any job before and now i have a job and i can contribute $ 30,000 a year to society . maybe i 'm working at someone 's factory . maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment . so i also consider this to be an investment . now , my question to you is , let 's say that i already had a house -- so this is an investment . let 's say i already had a house and my family is happy and we have everything we need . we have food on the table and my kids go to school and i 'm able to get a job and all of that exists . but let 's say , i still have a $ 100,000 and i use that $ 100,000 -- i 'll do it in yellow -- to put in some granite counter tops . i have some money left over , let 's say , i 'm going to add a bathroom to my house and i will put the latest hardwood floors , so that my family will be impressed . you can imagine . and maybe i add 2,000 square feet . you normally ca n't get all that for a $ 100,000 but i think you 'll bear with me . so i 'm essentially doing some major home improvements . so my question to you is -- is this an investment or is this consumption ? now , in our everyday world , with most people we deal with , they will call this investment in my house . and why are they saying that ? because they say , by spending a $ 100,000 in the house in this way , that maybe -- if you watch the home and garden channel , they 're doing this all the time -- that if you pour this a $ 100,000 into your house , that maybe the value of your house is going to increase by $ 150,000 . or someone else , all of a sudden , is going to perceive the value of your house as being $ 150,000 . they 'll say , well , you got a $ 50,000 return on investment . i 'd argue that that is not investment . that it 's speculation . you are , essentially , piling money into this stuff -- and i 'll do this in red , consumption is red . what 's happening here truly economically ? when you add granite , or you add an extra bathroom or hardwood floors or this extra 2,000 square feet , is it making anyone who 's living in that house more productive ? is it making you harder working ; is it making you more likely to invent the cure for cancer , or more likely to invent a way of getting cheap energy , or produce more widgets ? no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society . in fact , in no way is this going to contribute to the collective wealth of society . the last two examples i gave contribute to the collective wealth society , some of which you share , and that is your return on the investment . but as a whole , this is an investment into society . and it 's going to make the pie bigger . this right here , does not make the pie bigger . it might make you a little bit happier , make your ego feel a little bit better , let your pride grow , and your self righteousness grow , and show other people that you 've arrived , but it 's not going to increase the wealth of society . and when you say that you 've invested , you are really just saying i 've speculated . what you 're saying is -- by paying this $ 100,000 , you 're going to find , essentially , a greater fool out there . they could have done the same thing , they could have bought your house , spent $ 100,000 and done this , if this is what would have made them happy . but what you 're saying is , essentially , that you 're going to find somebody out there who 's willing to pay $ 150,000 extra for something that should have only cost $ 100,000 . and in fact , if anything , if you use this at all , the value of this is going to go down . so you 're just somehow assuming that the granite counter tops that you choose are going to be the taste that someone else would like or that the hardwood floors are going to be the taste someone else would like . i would actually argue that when you customize your house in this way , you are creating $ 100,000 of consumption to your taste . and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation . one might find some other guy willing to emotionally pay more for something . but it 's money that 's burned ; it 's not creating more value for society . i continue this in the next video .
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it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society .
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would n't buying the granite contribute to labor demand for granite installing , thus fueling the economy ?
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i 've been wanting to make a video on a couple of terms that people have really thrown around for a while now . and i think it really hits the core of some of the issues we 're dealing with now with the credit debacle but it 's kind of at a deeper level . so the things i want to go over are the ideas of savings , consumption , and investment . and you hear these a lot . everyone obviously says , i 've invested in the stock market or i 've invested in a house and i really want to give you a framework for how i think about these ideas . and frankly , i have n't seen them depicted this way in any economics book , although they 've kind of touched on this , but i think this is really how you should think about these things . so if you save money , and i think we all know what that means , that 's money that you did n't spend , there 's a couple of things that you can do with it . you can either consume your money or you could invest your money . so , let 's just think about a bunch of different situations and think about whether those things are consumption or investment . so let 's say , i have $ 100,000 that i 'm dealing with . so let 's say , i take that $ 100,000 and i build a factory . and i think that that factory is going to be able to produce -- i 'll make up some product -- it 'll be able to produce cars more efficiently and cheaper than any other car factory out there . well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 . in fact , i 'm expecting some type of a return on this investment . and i 've made a bunch of videos on what a return on investment is , and you can usually quantify it . if i take a $ 100,000 and i build this factory and this factory spits out $ 50,000 a year , it 's probably creating at least $ 50,000 a year value , assuming that nothing corrupt is happening in our system . in fact , it 's normally creating more than $ 50,000 a year of value . it may be creating a $ 100,000 a year of value and $ 50,000 of that may be going to the person who 's doing the production and then the other half of the value is actually going to the consumer of whatever this factory is making . and you have to think about it , because if all of the value went to the person who produced the factory then there 's not a huge incentive for someone to use his products anymore . but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment . so building a factory is an investment . now let 's say that i 'm homeless and i have this $ 100,000 . and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs . let 's say build a simple house , and i 'll do that in a neutral color . this is my other use of this $ 100,000 , instead of building a factory , i 'm going to build a simple house . and this house , it provides shelter for me and my family , it allows us that security that now my kids can go to school and they can themselves become more productive citizens . i now have an address . i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ? because i 'm taking this $ 100,000 , that maybe i had or someone gave to me , and it 's generating a return . and what is that return ? well , with a factory , it 's maybe a little easier to quantify . but at minimum , it 's this work that i 'm able to do because i now have a house . because i have the security , i have the address . i have the shelter . i 'm able to relax . it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society . it 's hard to value , maybe i did n't have any job before and now i have a job and i can contribute $ 30,000 a year to society . maybe i 'm working at someone 's factory . maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment . so i also consider this to be an investment . now , my question to you is , let 's say that i already had a house -- so this is an investment . let 's say i already had a house and my family is happy and we have everything we need . we have food on the table and my kids go to school and i 'm able to get a job and all of that exists . but let 's say , i still have a $ 100,000 and i use that $ 100,000 -- i 'll do it in yellow -- to put in some granite counter tops . i have some money left over , let 's say , i 'm going to add a bathroom to my house and i will put the latest hardwood floors , so that my family will be impressed . you can imagine . and maybe i add 2,000 square feet . you normally ca n't get all that for a $ 100,000 but i think you 'll bear with me . so i 'm essentially doing some major home improvements . so my question to you is -- is this an investment or is this consumption ? now , in our everyday world , with most people we deal with , they will call this investment in my house . and why are they saying that ? because they say , by spending a $ 100,000 in the house in this way , that maybe -- if you watch the home and garden channel , they 're doing this all the time -- that if you pour this a $ 100,000 into your house , that maybe the value of your house is going to increase by $ 150,000 . or someone else , all of a sudden , is going to perceive the value of your house as being $ 150,000 . they 'll say , well , you got a $ 50,000 return on investment . i 'd argue that that is not investment . that it 's speculation . you are , essentially , piling money into this stuff -- and i 'll do this in red , consumption is red . what 's happening here truly economically ? when you add granite , or you add an extra bathroom or hardwood floors or this extra 2,000 square feet , is it making anyone who 's living in that house more productive ? is it making you harder working ; is it making you more likely to invent the cure for cancer , or more likely to invent a way of getting cheap energy , or produce more widgets ? no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society . in fact , in no way is this going to contribute to the collective wealth of society . the last two examples i gave contribute to the collective wealth society , some of which you share , and that is your return on the investment . but as a whole , this is an investment into society . and it 's going to make the pie bigger . this right here , does not make the pie bigger . it might make you a little bit happier , make your ego feel a little bit better , let your pride grow , and your self righteousness grow , and show other people that you 've arrived , but it 's not going to increase the wealth of society . and when you say that you 've invested , you are really just saying i 've speculated . what you 're saying is -- by paying this $ 100,000 , you 're going to find , essentially , a greater fool out there . they could have done the same thing , they could have bought your house , spent $ 100,000 and done this , if this is what would have made them happy . but what you 're saying is , essentially , that you 're going to find somebody out there who 's willing to pay $ 150,000 extra for something that should have only cost $ 100,000 . and in fact , if anything , if you use this at all , the value of this is going to go down . so you 're just somehow assuming that the granite counter tops that you choose are going to be the taste that someone else would like or that the hardwood floors are going to be the taste someone else would like . i would actually argue that when you customize your house in this way , you are creating $ 100,000 of consumption to your taste . and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation . one might find some other guy willing to emotionally pay more for something . but it 's money that 's burned ; it 's not creating more value for society . i continue this in the next video .
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anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation .
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could we not argue that live in a nicer house is as necessary as having a house ?
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i 've been wanting to make a video on a couple of terms that people have really thrown around for a while now . and i think it really hits the core of some of the issues we 're dealing with now with the credit debacle but it 's kind of at a deeper level . so the things i want to go over are the ideas of savings , consumption , and investment . and you hear these a lot . everyone obviously says , i 've invested in the stock market or i 've invested in a house and i really want to give you a framework for how i think about these ideas . and frankly , i have n't seen them depicted this way in any economics book , although they 've kind of touched on this , but i think this is really how you should think about these things . so if you save money , and i think we all know what that means , that 's money that you did n't spend , there 's a couple of things that you can do with it . you can either consume your money or you could invest your money . so , let 's just think about a bunch of different situations and think about whether those things are consumption or investment . so let 's say , i have $ 100,000 that i 'm dealing with . so let 's say , i take that $ 100,000 and i build a factory . and i think that that factory is going to be able to produce -- i 'll make up some product -- it 'll be able to produce cars more efficiently and cheaper than any other car factory out there . well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 . in fact , i 'm expecting some type of a return on this investment . and i 've made a bunch of videos on what a return on investment is , and you can usually quantify it . if i take a $ 100,000 and i build this factory and this factory spits out $ 50,000 a year , it 's probably creating at least $ 50,000 a year value , assuming that nothing corrupt is happening in our system . in fact , it 's normally creating more than $ 50,000 a year of value . it may be creating a $ 100,000 a year of value and $ 50,000 of that may be going to the person who 's doing the production and then the other half of the value is actually going to the consumer of whatever this factory is making . and you have to think about it , because if all of the value went to the person who produced the factory then there 's not a huge incentive for someone to use his products anymore . but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment . so building a factory is an investment . now let 's say that i 'm homeless and i have this $ 100,000 . and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs . let 's say build a simple house , and i 'll do that in a neutral color . this is my other use of this $ 100,000 , instead of building a factory , i 'm going to build a simple house . and this house , it provides shelter for me and my family , it allows us that security that now my kids can go to school and they can themselves become more productive citizens . i now have an address . i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ? because i 'm taking this $ 100,000 , that maybe i had or someone gave to me , and it 's generating a return . and what is that return ? well , with a factory , it 's maybe a little easier to quantify . but at minimum , it 's this work that i 'm able to do because i now have a house . because i have the security , i have the address . i have the shelter . i 'm able to relax . it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society . it 's hard to value , maybe i did n't have any job before and now i have a job and i can contribute $ 30,000 a year to society . maybe i 'm working at someone 's factory . maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment . so i also consider this to be an investment . now , my question to you is , let 's say that i already had a house -- so this is an investment . let 's say i already had a house and my family is happy and we have everything we need . we have food on the table and my kids go to school and i 'm able to get a job and all of that exists . but let 's say , i still have a $ 100,000 and i use that $ 100,000 -- i 'll do it in yellow -- to put in some granite counter tops . i have some money left over , let 's say , i 'm going to add a bathroom to my house and i will put the latest hardwood floors , so that my family will be impressed . you can imagine . and maybe i add 2,000 square feet . you normally ca n't get all that for a $ 100,000 but i think you 'll bear with me . so i 'm essentially doing some major home improvements . so my question to you is -- is this an investment or is this consumption ? now , in our everyday world , with most people we deal with , they will call this investment in my house . and why are they saying that ? because they say , by spending a $ 100,000 in the house in this way , that maybe -- if you watch the home and garden channel , they 're doing this all the time -- that if you pour this a $ 100,000 into your house , that maybe the value of your house is going to increase by $ 150,000 . or someone else , all of a sudden , is going to perceive the value of your house as being $ 150,000 . they 'll say , well , you got a $ 50,000 return on investment . i 'd argue that that is not investment . that it 's speculation . you are , essentially , piling money into this stuff -- and i 'll do this in red , consumption is red . what 's happening here truly economically ? when you add granite , or you add an extra bathroom or hardwood floors or this extra 2,000 square feet , is it making anyone who 's living in that house more productive ? is it making you harder working ; is it making you more likely to invent the cure for cancer , or more likely to invent a way of getting cheap energy , or produce more widgets ? no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society . in fact , in no way is this going to contribute to the collective wealth of society . the last two examples i gave contribute to the collective wealth society , some of which you share , and that is your return on the investment . but as a whole , this is an investment into society . and it 's going to make the pie bigger . this right here , does not make the pie bigger . it might make you a little bit happier , make your ego feel a little bit better , let your pride grow , and your self righteousness grow , and show other people that you 've arrived , but it 's not going to increase the wealth of society . and when you say that you 've invested , you are really just saying i 've speculated . what you 're saying is -- by paying this $ 100,000 , you 're going to find , essentially , a greater fool out there . they could have done the same thing , they could have bought your house , spent $ 100,000 and done this , if this is what would have made them happy . but what you 're saying is , essentially , that you 're going to find somebody out there who 's willing to pay $ 150,000 extra for something that should have only cost $ 100,000 . and in fact , if anything , if you use this at all , the value of this is going to go down . so you 're just somehow assuming that the granite counter tops that you choose are going to be the taste that someone else would like or that the hardwood floors are going to be the taste someone else would like . i would actually argue that when you customize your house in this way , you are creating $ 100,000 of consumption to your taste . and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation . one might find some other guy willing to emotionally pay more for something . but it 's money that 's burned ; it 's not creating more value for society . i continue this in the next video .
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but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment .
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for a government , is creating and maintaining a national park ( like carlsbad caverns or the grand canyon ) an investment or consumption ?
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i 've been wanting to make a video on a couple of terms that people have really thrown around for a while now . and i think it really hits the core of some of the issues we 're dealing with now with the credit debacle but it 's kind of at a deeper level . so the things i want to go over are the ideas of savings , consumption , and investment . and you hear these a lot . everyone obviously says , i 've invested in the stock market or i 've invested in a house and i really want to give you a framework for how i think about these ideas . and frankly , i have n't seen them depicted this way in any economics book , although they 've kind of touched on this , but i think this is really how you should think about these things . so if you save money , and i think we all know what that means , that 's money that you did n't spend , there 's a couple of things that you can do with it . you can either consume your money or you could invest your money . so , let 's just think about a bunch of different situations and think about whether those things are consumption or investment . so let 's say , i have $ 100,000 that i 'm dealing with . so let 's say , i take that $ 100,000 and i build a factory . and i think that that factory is going to be able to produce -- i 'll make up some product -- it 'll be able to produce cars more efficiently and cheaper than any other car factory out there . well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 . in fact , i 'm expecting some type of a return on this investment . and i 've made a bunch of videos on what a return on investment is , and you can usually quantify it . if i take a $ 100,000 and i build this factory and this factory spits out $ 50,000 a year , it 's probably creating at least $ 50,000 a year value , assuming that nothing corrupt is happening in our system . in fact , it 's normally creating more than $ 50,000 a year of value . it may be creating a $ 100,000 a year of value and $ 50,000 of that may be going to the person who 's doing the production and then the other half of the value is actually going to the consumer of whatever this factory is making . and you have to think about it , because if all of the value went to the person who produced the factory then there 's not a huge incentive for someone to use his products anymore . but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment . so building a factory is an investment . now let 's say that i 'm homeless and i have this $ 100,000 . and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs . let 's say build a simple house , and i 'll do that in a neutral color . this is my other use of this $ 100,000 , instead of building a factory , i 'm going to build a simple house . and this house , it provides shelter for me and my family , it allows us that security that now my kids can go to school and they can themselves become more productive citizens . i now have an address . i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ? because i 'm taking this $ 100,000 , that maybe i had or someone gave to me , and it 's generating a return . and what is that return ? well , with a factory , it 's maybe a little easier to quantify . but at minimum , it 's this work that i 'm able to do because i now have a house . because i have the security , i have the address . i have the shelter . i 'm able to relax . it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society . it 's hard to value , maybe i did n't have any job before and now i have a job and i can contribute $ 30,000 a year to society . maybe i 'm working at someone 's factory . maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment . so i also consider this to be an investment . now , my question to you is , let 's say that i already had a house -- so this is an investment . let 's say i already had a house and my family is happy and we have everything we need . we have food on the table and my kids go to school and i 'm able to get a job and all of that exists . but let 's say , i still have a $ 100,000 and i use that $ 100,000 -- i 'll do it in yellow -- to put in some granite counter tops . i have some money left over , let 's say , i 'm going to add a bathroom to my house and i will put the latest hardwood floors , so that my family will be impressed . you can imagine . and maybe i add 2,000 square feet . you normally ca n't get all that for a $ 100,000 but i think you 'll bear with me . so i 'm essentially doing some major home improvements . so my question to you is -- is this an investment or is this consumption ? now , in our everyday world , with most people we deal with , they will call this investment in my house . and why are they saying that ? because they say , by spending a $ 100,000 in the house in this way , that maybe -- if you watch the home and garden channel , they 're doing this all the time -- that if you pour this a $ 100,000 into your house , that maybe the value of your house is going to increase by $ 150,000 . or someone else , all of a sudden , is going to perceive the value of your house as being $ 150,000 . they 'll say , well , you got a $ 50,000 return on investment . i 'd argue that that is not investment . that it 's speculation . you are , essentially , piling money into this stuff -- and i 'll do this in red , consumption is red . what 's happening here truly economically ? when you add granite , or you add an extra bathroom or hardwood floors or this extra 2,000 square feet , is it making anyone who 's living in that house more productive ? is it making you harder working ; is it making you more likely to invent the cure for cancer , or more likely to invent a way of getting cheap energy , or produce more widgets ? no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society . in fact , in no way is this going to contribute to the collective wealth of society . the last two examples i gave contribute to the collective wealth society , some of which you share , and that is your return on the investment . but as a whole , this is an investment into society . and it 's going to make the pie bigger . this right here , does not make the pie bigger . it might make you a little bit happier , make your ego feel a little bit better , let your pride grow , and your self righteousness grow , and show other people that you 've arrived , but it 's not going to increase the wealth of society . and when you say that you 've invested , you are really just saying i 've speculated . what you 're saying is -- by paying this $ 100,000 , you 're going to find , essentially , a greater fool out there . they could have done the same thing , they could have bought your house , spent $ 100,000 and done this , if this is what would have made them happy . but what you 're saying is , essentially , that you 're going to find somebody out there who 's willing to pay $ 150,000 extra for something that should have only cost $ 100,000 . and in fact , if anything , if you use this at all , the value of this is going to go down . so you 're just somehow assuming that the granite counter tops that you choose are going to be the taste that someone else would like or that the hardwood floors are going to be the taste someone else would like . i would actually argue that when you customize your house in this way , you are creating $ 100,000 of consumption to your taste . and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation . one might find some other guy willing to emotionally pay more for something . but it 's money that 's burned ; it 's not creating more value for society . i continue this in the next video .
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well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 .
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is buying a glove an investment ?
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i 've been wanting to make a video on a couple of terms that people have really thrown around for a while now . and i think it really hits the core of some of the issues we 're dealing with now with the credit debacle but it 's kind of at a deeper level . so the things i want to go over are the ideas of savings , consumption , and investment . and you hear these a lot . everyone obviously says , i 've invested in the stock market or i 've invested in a house and i really want to give you a framework for how i think about these ideas . and frankly , i have n't seen them depicted this way in any economics book , although they 've kind of touched on this , but i think this is really how you should think about these things . so if you save money , and i think we all know what that means , that 's money that you did n't spend , there 's a couple of things that you can do with it . you can either consume your money or you could invest your money . so , let 's just think about a bunch of different situations and think about whether those things are consumption or investment . so let 's say , i have $ 100,000 that i 'm dealing with . so let 's say , i take that $ 100,000 and i build a factory . and i think that that factory is going to be able to produce -- i 'll make up some product -- it 'll be able to produce cars more efficiently and cheaper than any other car factory out there . well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 . in fact , i 'm expecting some type of a return on this investment . and i 've made a bunch of videos on what a return on investment is , and you can usually quantify it . if i take a $ 100,000 and i build this factory and this factory spits out $ 50,000 a year , it 's probably creating at least $ 50,000 a year value , assuming that nothing corrupt is happening in our system . in fact , it 's normally creating more than $ 50,000 a year of value . it may be creating a $ 100,000 a year of value and $ 50,000 of that may be going to the person who 's doing the production and then the other half of the value is actually going to the consumer of whatever this factory is making . and you have to think about it , because if all of the value went to the person who produced the factory then there 's not a huge incentive for someone to use his products anymore . but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment . so building a factory is an investment . now let 's say that i 'm homeless and i have this $ 100,000 . and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs . let 's say build a simple house , and i 'll do that in a neutral color . this is my other use of this $ 100,000 , instead of building a factory , i 'm going to build a simple house . and this house , it provides shelter for me and my family , it allows us that security that now my kids can go to school and they can themselves become more productive citizens . i now have an address . i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ? because i 'm taking this $ 100,000 , that maybe i had or someone gave to me , and it 's generating a return . and what is that return ? well , with a factory , it 's maybe a little easier to quantify . but at minimum , it 's this work that i 'm able to do because i now have a house . because i have the security , i have the address . i have the shelter . i 'm able to relax . it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society . it 's hard to value , maybe i did n't have any job before and now i have a job and i can contribute $ 30,000 a year to society . maybe i 'm working at someone 's factory . maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment . so i also consider this to be an investment . now , my question to you is , let 's say that i already had a house -- so this is an investment . let 's say i already had a house and my family is happy and we have everything we need . we have food on the table and my kids go to school and i 'm able to get a job and all of that exists . but let 's say , i still have a $ 100,000 and i use that $ 100,000 -- i 'll do it in yellow -- to put in some granite counter tops . i have some money left over , let 's say , i 'm going to add a bathroom to my house and i will put the latest hardwood floors , so that my family will be impressed . you can imagine . and maybe i add 2,000 square feet . you normally ca n't get all that for a $ 100,000 but i think you 'll bear with me . so i 'm essentially doing some major home improvements . so my question to you is -- is this an investment or is this consumption ? now , in our everyday world , with most people we deal with , they will call this investment in my house . and why are they saying that ? because they say , by spending a $ 100,000 in the house in this way , that maybe -- if you watch the home and garden channel , they 're doing this all the time -- that if you pour this a $ 100,000 into your house , that maybe the value of your house is going to increase by $ 150,000 . or someone else , all of a sudden , is going to perceive the value of your house as being $ 150,000 . they 'll say , well , you got a $ 50,000 return on investment . i 'd argue that that is not investment . that it 's speculation . you are , essentially , piling money into this stuff -- and i 'll do this in red , consumption is red . what 's happening here truly economically ? when you add granite , or you add an extra bathroom or hardwood floors or this extra 2,000 square feet , is it making anyone who 's living in that house more productive ? is it making you harder working ; is it making you more likely to invent the cure for cancer , or more likely to invent a way of getting cheap energy , or produce more widgets ? no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society . in fact , in no way is this going to contribute to the collective wealth of society . the last two examples i gave contribute to the collective wealth society , some of which you share , and that is your return on the investment . but as a whole , this is an investment into society . and it 's going to make the pie bigger . this right here , does not make the pie bigger . it might make you a little bit happier , make your ego feel a little bit better , let your pride grow , and your self righteousness grow , and show other people that you 've arrived , but it 's not going to increase the wealth of society . and when you say that you 've invested , you are really just saying i 've speculated . what you 're saying is -- by paying this $ 100,000 , you 're going to find , essentially , a greater fool out there . they could have done the same thing , they could have bought your house , spent $ 100,000 and done this , if this is what would have made them happy . but what you 're saying is , essentially , that you 're going to find somebody out there who 's willing to pay $ 150,000 extra for something that should have only cost $ 100,000 . and in fact , if anything , if you use this at all , the value of this is going to go down . so you 're just somehow assuming that the granite counter tops that you choose are going to be the taste that someone else would like or that the hardwood floors are going to be the taste someone else would like . i would actually argue that when you customize your house in this way , you are creating $ 100,000 of consumption to your taste . and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation . one might find some other guy willing to emotionally pay more for something . but it 's money that 's burned ; it 's not creating more value for society . i continue this in the next video .
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anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation .
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is it unreasonable to suggest that a nicer house has more potential to appreciate in value and act as a better hedge against inflation ?
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i 've been wanting to make a video on a couple of terms that people have really thrown around for a while now . and i think it really hits the core of some of the issues we 're dealing with now with the credit debacle but it 's kind of at a deeper level . so the things i want to go over are the ideas of savings , consumption , and investment . and you hear these a lot . everyone obviously says , i 've invested in the stock market or i 've invested in a house and i really want to give you a framework for how i think about these ideas . and frankly , i have n't seen them depicted this way in any economics book , although they 've kind of touched on this , but i think this is really how you should think about these things . so if you save money , and i think we all know what that means , that 's money that you did n't spend , there 's a couple of things that you can do with it . you can either consume your money or you could invest your money . so , let 's just think about a bunch of different situations and think about whether those things are consumption or investment . so let 's say , i have $ 100,000 that i 'm dealing with . so let 's say , i take that $ 100,000 and i build a factory . and i think that that factory is going to be able to produce -- i 'll make up some product -- it 'll be able to produce cars more efficiently and cheaper than any other car factory out there . well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 . in fact , i 'm expecting some type of a return on this investment . and i 've made a bunch of videos on what a return on investment is , and you can usually quantify it . if i take a $ 100,000 and i build this factory and this factory spits out $ 50,000 a year , it 's probably creating at least $ 50,000 a year value , assuming that nothing corrupt is happening in our system . in fact , it 's normally creating more than $ 50,000 a year of value . it may be creating a $ 100,000 a year of value and $ 50,000 of that may be going to the person who 's doing the production and then the other half of the value is actually going to the consumer of whatever this factory is making . and you have to think about it , because if all of the value went to the person who produced the factory then there 's not a huge incentive for someone to use his products anymore . but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment . so building a factory is an investment . now let 's say that i 'm homeless and i have this $ 100,000 . and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs . let 's say build a simple house , and i 'll do that in a neutral color . this is my other use of this $ 100,000 , instead of building a factory , i 'm going to build a simple house . and this house , it provides shelter for me and my family , it allows us that security that now my kids can go to school and they can themselves become more productive citizens . i now have an address . i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ? because i 'm taking this $ 100,000 , that maybe i had or someone gave to me , and it 's generating a return . and what is that return ? well , with a factory , it 's maybe a little easier to quantify . but at minimum , it 's this work that i 'm able to do because i now have a house . because i have the security , i have the address . i have the shelter . i 'm able to relax . it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society . it 's hard to value , maybe i did n't have any job before and now i have a job and i can contribute $ 30,000 a year to society . maybe i 'm working at someone 's factory . maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment . so i also consider this to be an investment . now , my question to you is , let 's say that i already had a house -- so this is an investment . let 's say i already had a house and my family is happy and we have everything we need . we have food on the table and my kids go to school and i 'm able to get a job and all of that exists . but let 's say , i still have a $ 100,000 and i use that $ 100,000 -- i 'll do it in yellow -- to put in some granite counter tops . i have some money left over , let 's say , i 'm going to add a bathroom to my house and i will put the latest hardwood floors , so that my family will be impressed . you can imagine . and maybe i add 2,000 square feet . you normally ca n't get all that for a $ 100,000 but i think you 'll bear with me . so i 'm essentially doing some major home improvements . so my question to you is -- is this an investment or is this consumption ? now , in our everyday world , with most people we deal with , they will call this investment in my house . and why are they saying that ? because they say , by spending a $ 100,000 in the house in this way , that maybe -- if you watch the home and garden channel , they 're doing this all the time -- that if you pour this a $ 100,000 into your house , that maybe the value of your house is going to increase by $ 150,000 . or someone else , all of a sudden , is going to perceive the value of your house as being $ 150,000 . they 'll say , well , you got a $ 50,000 return on investment . i 'd argue that that is not investment . that it 's speculation . you are , essentially , piling money into this stuff -- and i 'll do this in red , consumption is red . what 's happening here truly economically ? when you add granite , or you add an extra bathroom or hardwood floors or this extra 2,000 square feet , is it making anyone who 's living in that house more productive ? is it making you harder working ; is it making you more likely to invent the cure for cancer , or more likely to invent a way of getting cheap energy , or produce more widgets ? no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society . in fact , in no way is this going to contribute to the collective wealth of society . the last two examples i gave contribute to the collective wealth society , some of which you share , and that is your return on the investment . but as a whole , this is an investment into society . and it 's going to make the pie bigger . this right here , does not make the pie bigger . it might make you a little bit happier , make your ego feel a little bit better , let your pride grow , and your self righteousness grow , and show other people that you 've arrived , but it 's not going to increase the wealth of society . and when you say that you 've invested , you are really just saying i 've speculated . what you 're saying is -- by paying this $ 100,000 , you 're going to find , essentially , a greater fool out there . they could have done the same thing , they could have bought your house , spent $ 100,000 and done this , if this is what would have made them happy . but what you 're saying is , essentially , that you 're going to find somebody out there who 's willing to pay $ 150,000 extra for something that should have only cost $ 100,000 . and in fact , if anything , if you use this at all , the value of this is going to go down . so you 're just somehow assuming that the granite counter tops that you choose are going to be the taste that someone else would like or that the hardwood floors are going to be the taste someone else would like . i would actually argue that when you customize your house in this way , you are creating $ 100,000 of consumption to your taste . and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation . one might find some other guy willing to emotionally pay more for something . but it 's money that 's burned ; it 's not creating more value for society . i continue this in the next video .
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and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs .
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could n't we have just as easily asked , or stated , are n't the so called investments made by corporations just methods of increasing executive compensation , with no intrinsic value to anyone else ?
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i 've been wanting to make a video on a couple of terms that people have really thrown around for a while now . and i think it really hits the core of some of the issues we 're dealing with now with the credit debacle but it 's kind of at a deeper level . so the things i want to go over are the ideas of savings , consumption , and investment . and you hear these a lot . everyone obviously says , i 've invested in the stock market or i 've invested in a house and i really want to give you a framework for how i think about these ideas . and frankly , i have n't seen them depicted this way in any economics book , although they 've kind of touched on this , but i think this is really how you should think about these things . so if you save money , and i think we all know what that means , that 's money that you did n't spend , there 's a couple of things that you can do with it . you can either consume your money or you could invest your money . so , let 's just think about a bunch of different situations and think about whether those things are consumption or investment . so let 's say , i have $ 100,000 that i 'm dealing with . so let 's say , i take that $ 100,000 and i build a factory . and i think that that factory is going to be able to produce -- i 'll make up some product -- it 'll be able to produce cars more efficiently and cheaper than any other car factory out there . well , i think we 'd all agree that this is an investment . and why is it an investment ? because i 'm taking this $ 100,000 and i 'm putting it to some use that is creating , hopefully , more value than my original $ 100,000 . in fact , i 'm expecting some type of a return on this investment . and i 've made a bunch of videos on what a return on investment is , and you can usually quantify it . if i take a $ 100,000 and i build this factory and this factory spits out $ 50,000 a year , it 's probably creating at least $ 50,000 a year value , assuming that nothing corrupt is happening in our system . in fact , it 's normally creating more than $ 50,000 a year of value . it may be creating a $ 100,000 a year of value and $ 50,000 of that may be going to the person who 's doing the production and then the other half of the value is actually going to the consumer of whatever this factory is making . and you have to think about it , because if all of the value went to the person who produced the factory then there 's not a huge incentive for someone to use his products anymore . but anyway , that 's not the topic of discussion . we 're just trying to get at a mental framework on what consumption is versus investment . so i think we all agree that if i were to build a factory that this is -- let 's say i 'll do everything in green as investment . so building a factory is an investment . now let 's say that i 'm homeless and i have this $ 100,000 . and because i 'm homeless , i do n't have a place to go and eat dinner and rest and relax . because i do n't have that , i ca n't get a job and i ca n't become a productive member of society . so maybe , i 'm going to use this $ 100,000 to buy a simple house that meets all of my needs . let 's say build a simple house , and i 'll do that in a neutral color . this is my other use of this $ 100,000 , instead of building a factory , i 'm going to build a simple house . and this house , it provides shelter for me and my family , it allows us that security that now my kids can go to school and they can themselves become more productive citizens . i now have an address . i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ? because i 'm taking this $ 100,000 , that maybe i had or someone gave to me , and it 's generating a return . and what is that return ? well , with a factory , it 's maybe a little easier to quantify . but at minimum , it 's this work that i 'm able to do because i now have a house . because i have the security , i have the address . i have the shelter . i 'm able to relax . it 's that security and it 's also the return that probably my kids are going to be able to now contribute to society . maybe if they grew up homeless , they would have never been able to contribute . and now that they have a roof over their head , and are able to go to school , et cetera , they are going to be able to give some economic value back to society . it 's hard to value , maybe i did n't have any job before and now i have a job and i can contribute $ 30,000 a year to society . maybe i 'm working at someone 's factory . maybe i 'm providing some other -- maybe i 'm a farmer now . whatever , i 'm providing some source of value . and maybe my kids -- if they never got an education , they would have maybe added $ 10,000 of value per year to people and now they can add $ 20,000 of value . so that difference would also be some of the return on this investment . so i also consider this to be an investment . now , my question to you is , let 's say that i already had a house -- so this is an investment . let 's say i already had a house and my family is happy and we have everything we need . we have food on the table and my kids go to school and i 'm able to get a job and all of that exists . but let 's say , i still have a $ 100,000 and i use that $ 100,000 -- i 'll do it in yellow -- to put in some granite counter tops . i have some money left over , let 's say , i 'm going to add a bathroom to my house and i will put the latest hardwood floors , so that my family will be impressed . you can imagine . and maybe i add 2,000 square feet . you normally ca n't get all that for a $ 100,000 but i think you 'll bear with me . so i 'm essentially doing some major home improvements . so my question to you is -- is this an investment or is this consumption ? now , in our everyday world , with most people we deal with , they will call this investment in my house . and why are they saying that ? because they say , by spending a $ 100,000 in the house in this way , that maybe -- if you watch the home and garden channel , they 're doing this all the time -- that if you pour this a $ 100,000 into your house , that maybe the value of your house is going to increase by $ 150,000 . or someone else , all of a sudden , is going to perceive the value of your house as being $ 150,000 . they 'll say , well , you got a $ 50,000 return on investment . i 'd argue that that is not investment . that it 's speculation . you are , essentially , piling money into this stuff -- and i 'll do this in red , consumption is red . what 's happening here truly economically ? when you add granite , or you add an extra bathroom or hardwood floors or this extra 2,000 square feet , is it making anyone who 's living in that house more productive ? is it making you harder working ; is it making you more likely to invent the cure for cancer , or more likely to invent a way of getting cheap energy , or produce more widgets ? no , it 's just , if anything , providing more things for you to have to take care of , that you 're not going to be able to focus as much on your work . or more energy is going to have to be extended to maintain this type of place , to heat and cool a 2,000 square foot house . so if anything , by actually pouring the $ 100,000 here , you 're actually creating something that is going to suck more out of society . in fact , in no way is this going to contribute to the collective wealth of society . the last two examples i gave contribute to the collective wealth society , some of which you share , and that is your return on the investment . but as a whole , this is an investment into society . and it 's going to make the pie bigger . this right here , does not make the pie bigger . it might make you a little bit happier , make your ego feel a little bit better , let your pride grow , and your self righteousness grow , and show other people that you 've arrived , but it 's not going to increase the wealth of society . and when you say that you 've invested , you are really just saying i 've speculated . what you 're saying is -- by paying this $ 100,000 , you 're going to find , essentially , a greater fool out there . they could have done the same thing , they could have bought your house , spent $ 100,000 and done this , if this is what would have made them happy . but what you 're saying is , essentially , that you 're going to find somebody out there who 's willing to pay $ 150,000 extra for something that should have only cost $ 100,000 . and in fact , if anything , if you use this at all , the value of this is going to go down . so you 're just somehow assuming that the granite counter tops that you choose are going to be the taste that someone else would like or that the hardwood floors are going to be the taste someone else would like . i would actually argue that when you customize your house in this way , you are creating $ 100,000 of consumption to your taste . and i 'd be surprised if someone else , truly , is willing to pay more than $ 100,000 unless they 're being , in some way , irrational or they can finance this because it 's part of the mortgage . anyway , this is , i think , just the big picture : investment adds value to society . a simple house adds value to society . consumption is something where people might call it an investment because it 's kind of speculation . one might find some other guy willing to emotionally pay more for something . but it 's money that 's burned ; it 's not creating more value for society . i continue this in the next video .
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i have a place to take a shower , that allows me to go get a job and i can now create value for society as a whole , instead of being on the corner and begging for money from people . i would argue that this is also an investment . why is it ?
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about the granite - if it appreciates over time , would n't it be seen as an investment ?
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so you may have heard of tourette 's or tourette syndrome before , and it 's possible that when you think about tourette 's , you might picture what 's been kinda popularized in tv shows and movies , which is that people with tourette 's have these kind of verbal outbursts . and while this is possible in someone with tourette 's , this popularized image of tourette 's is actually not all that common . so if this is n't exactly what tourette 's is always like , then what is tourette 's ? tourette 's is a disorder that causes the person to make sudden , really brief , unwanted movements and sounds . and just before these unwanted movements or sounds occur , the person actually feels this urge to make them . kinda like that feeling you get when you have an itch that you really wan na scratch . or like that feeling we get just before we 're about to sneeze . and just like itching and sneezing , right after doing these things , the person feels a sense of relief . so an example of an unusual or unwanted movement could be something like unnecessary blinking or facial expressions , or maybe shrugging the shoulders or kicking . and an unusual unwanted sound could be something like grunting or repeating words , or maybe swearing . and there 's actually a word to describe these movements and sounds . they 're called `` tics . '' so tourette 's is actually a particular type of tic disorders . there are a few different types of tic disorders , and what makes tourette 's different from the other types is that someone with tourette 's has both of these types of tics . so the movements and the sounds . they might not occur together at exactly the same time , but the person does occasionally have both movement and sound tics . and something that 's really unique to tourette 's and helps set it apart from other movement disorders is that many people are able to find ways to suppress their tics . so in other words , with effort , they 're able to kind of push away that urge to engage in a tic behavior . but often they 'll need to release the urge in another way , maybe by performing a different movement or sound that is more appropriate while they 're in public , maybe like blinking or shrugging the shoulders . or , maybe they 'll need to release the urge later on by actually engaging in the tic , but this time in privacy . so you might have been able to guess from the examples that we put down here , these examples of possible tics , that tourette 's can look pretty different between different people . and that 's definitely the case . tourette 's is actually a spectrum disorder , which means that someone with tourette 's can fall anywhere along a spectrum that ranges from mild to severe , where mild would mean that the person 's tics , the unwanted movements and sounds that they make , are n't really noticeable and do n't really impact their life . so maybe every so often they blink unnecessarily or clear their throat , something that you might not even notice . and on the severe end of the spectrum , the tics that the person has would be really debilitating . so maybe their tics involve really noticeable head-jerking or saying obscene words . these sorts of tics could really impact the person 's day to day life , especially if they occur frequently . so tourette 's is a disorder that crops up in childhood , usually around the age of about six to seven years old . and while we have n't completely figured out what causes tourette 's , we do have some clues about the cause . so , for example , we know that a lot of people with tourette 's have parents who also have tourette 's . and we also know that boys are about three times more likely to be affected than girls . so both of these things suggest that there 's probably a genetic cause involved , something going on in the genes that are being passed down from the parents to their kids . and we also have a clue about where in the brain we think things might be going awry . so we know that in the brains of people with tourette 's , there 's a particular neural circuit that does n't quite function properly . so bear with me here , this is a bit of a complex name , but we 'll go through it in a sec . so the cortico-striatal-thalamic-cortico circuit is what 's not quite functioning properly . so `` cortico '' here stands for the cortex of the brain , and `` striatal '' stands for striatum , which is part of the basal ganglia here . and `` thalamic '' stands for thalamus . so these structures normally chat to each other to coordinate our movements . so in someone with tourette 's where this circuit is n't able to function properly , that might explain why movements ca n't really be prevented like they normally would be and the person ends up with tics . so even though we think we might know what 's going on in the brains of people with tourette 's , we do n't currently have a way to actually see this . we do n't have a brain scan or a blood test to look for and diagnose tourette 's . so instead , tourette 's is diagnosed by looking for the movement and vocal tics in children that we suspect might have the disorder . now , once we determine that someone does indeed have tourette 's , what do we do to treat it ? well , it turns out that for a lot of people with tourette 's , the disorder is on the mild end of the spectrum here and the tics often actually disappear or at least improve significantly once the child reaches adulthood . so for these people , we do n't usually really need any medications to manage the tourette 's , and instead one of the main things that we usually do is something called habit reversal therapy . remember how we mentioned that people with tourette 's can often find a way to suppress their tics ? with habit reversal training , the idea here is to help the child learn to recognize those urges that happen just before a tic is about to occur , and then try to help them find a new habit that they can use to help relieve that urge without performing the tic . so maybe their tic is kicking . and when they start to feel that urge that would normally be relieved by kicking , we get them to itch their nose instead , and try to relieve the urge through this movement . so even though we 're kinda trading one example of a tic for another , itching the nose is much more subtle and something that the person can probably do in public to relieve the urge they feel before a tic comes on . now , for some people , they 're on the far end of the spectrum . so their tourette 's is more severe , and it does impact their daily living . so when this is the case , we might need something more than habit reversal training to manage the tics . now when someone has an involuntary sound that they make , or maybe a movement that just happens to be in a really specific part of the body , one way that we might be able to deal with this is by going directly to the problematic body part . so maybe if it 's a movement , let 's say that it 's a hand jerk , we could try to stop that from occurring by preventing the messages that neurons send to that particular muscle to tell it to move . and funny enough , we can actually do this with botox . so when we inject botox into the hand here that jerks during a tic , that blocks some of the signals coming from the neurons that send messages to the hand to make it active . so after the injection of botox , the hand ca n't really be as active anymore for a few months until the botox wears off . so the tic may not be as noticeable , or it may not even occur . now , sometimes the tics may not be so localized . they might be more widespread . so we might need something that acts in a little bit more of a widespread way than botox does . so when this is the case , rather than going to the muscles involved in the tics , we might need to head back up to the source , the brain , and try something that will reduce these movements in a more global way . and it turns out that we have these particular medications called antidopaminergic medications that we can use . so dopaminergic here is referring to dopamine , a chemical that neurons can use to initiate movements in muscles . so these antidopaminergic medications they prevent dopamine in the brain from activating the muscles so much . so all these extra movements do n't really get initiated , and the person 's tics hopefully get decreased or go away . and it turns out that quite a few kids with tourette 's also have other disorders that co-occur with their tourette 's . disorders like attention deficit hyperactivity disorder , or also known as adhd , and obsessive compulsive disorder , also known as ocd . so for kids with tourette 's that also have one of these other disorders , they may need to go on a medication or have some sort of therapy to help them manage these disorders as well as their tourette 's .
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so you may have heard of tourette 's or tourette syndrome before , and it 's possible that when you think about tourette 's , you might picture what 's been kinda popularized in tv shows and movies , which is that people with tourette 's have these kind of verbal outbursts . and while this is possible in someone with tourette 's , this popularized image of tourette 's is actually not all that common . so if this is n't exactly what tourette 's is always like , then what is tourette 's ?
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is there a positive correlation between someone with tourette 's and autism ?
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so you may have heard of tourette 's or tourette syndrome before , and it 's possible that when you think about tourette 's , you might picture what 's been kinda popularized in tv shows and movies , which is that people with tourette 's have these kind of verbal outbursts . and while this is possible in someone with tourette 's , this popularized image of tourette 's is actually not all that common . so if this is n't exactly what tourette 's is always like , then what is tourette 's ? tourette 's is a disorder that causes the person to make sudden , really brief , unwanted movements and sounds . and just before these unwanted movements or sounds occur , the person actually feels this urge to make them . kinda like that feeling you get when you have an itch that you really wan na scratch . or like that feeling we get just before we 're about to sneeze . and just like itching and sneezing , right after doing these things , the person feels a sense of relief . so an example of an unusual or unwanted movement could be something like unnecessary blinking or facial expressions , or maybe shrugging the shoulders or kicking . and an unusual unwanted sound could be something like grunting or repeating words , or maybe swearing . and there 's actually a word to describe these movements and sounds . they 're called `` tics . '' so tourette 's is actually a particular type of tic disorders . there are a few different types of tic disorders , and what makes tourette 's different from the other types is that someone with tourette 's has both of these types of tics . so the movements and the sounds . they might not occur together at exactly the same time , but the person does occasionally have both movement and sound tics . and something that 's really unique to tourette 's and helps set it apart from other movement disorders is that many people are able to find ways to suppress their tics . so in other words , with effort , they 're able to kind of push away that urge to engage in a tic behavior . but often they 'll need to release the urge in another way , maybe by performing a different movement or sound that is more appropriate while they 're in public , maybe like blinking or shrugging the shoulders . or , maybe they 'll need to release the urge later on by actually engaging in the tic , but this time in privacy . so you might have been able to guess from the examples that we put down here , these examples of possible tics , that tourette 's can look pretty different between different people . and that 's definitely the case . tourette 's is actually a spectrum disorder , which means that someone with tourette 's can fall anywhere along a spectrum that ranges from mild to severe , where mild would mean that the person 's tics , the unwanted movements and sounds that they make , are n't really noticeable and do n't really impact their life . so maybe every so often they blink unnecessarily or clear their throat , something that you might not even notice . and on the severe end of the spectrum , the tics that the person has would be really debilitating . so maybe their tics involve really noticeable head-jerking or saying obscene words . these sorts of tics could really impact the person 's day to day life , especially if they occur frequently . so tourette 's is a disorder that crops up in childhood , usually around the age of about six to seven years old . and while we have n't completely figured out what causes tourette 's , we do have some clues about the cause . so , for example , we know that a lot of people with tourette 's have parents who also have tourette 's . and we also know that boys are about three times more likely to be affected than girls . so both of these things suggest that there 's probably a genetic cause involved , something going on in the genes that are being passed down from the parents to their kids . and we also have a clue about where in the brain we think things might be going awry . so we know that in the brains of people with tourette 's , there 's a particular neural circuit that does n't quite function properly . so bear with me here , this is a bit of a complex name , but we 'll go through it in a sec . so the cortico-striatal-thalamic-cortico circuit is what 's not quite functioning properly . so `` cortico '' here stands for the cortex of the brain , and `` striatal '' stands for striatum , which is part of the basal ganglia here . and `` thalamic '' stands for thalamus . so these structures normally chat to each other to coordinate our movements . so in someone with tourette 's where this circuit is n't able to function properly , that might explain why movements ca n't really be prevented like they normally would be and the person ends up with tics . so even though we think we might know what 's going on in the brains of people with tourette 's , we do n't currently have a way to actually see this . we do n't have a brain scan or a blood test to look for and diagnose tourette 's . so instead , tourette 's is diagnosed by looking for the movement and vocal tics in children that we suspect might have the disorder . now , once we determine that someone does indeed have tourette 's , what do we do to treat it ? well , it turns out that for a lot of people with tourette 's , the disorder is on the mild end of the spectrum here and the tics often actually disappear or at least improve significantly once the child reaches adulthood . so for these people , we do n't usually really need any medications to manage the tourette 's , and instead one of the main things that we usually do is something called habit reversal therapy . remember how we mentioned that people with tourette 's can often find a way to suppress their tics ? with habit reversal training , the idea here is to help the child learn to recognize those urges that happen just before a tic is about to occur , and then try to help them find a new habit that they can use to help relieve that urge without performing the tic . so maybe their tic is kicking . and when they start to feel that urge that would normally be relieved by kicking , we get them to itch their nose instead , and try to relieve the urge through this movement . so even though we 're kinda trading one example of a tic for another , itching the nose is much more subtle and something that the person can probably do in public to relieve the urge they feel before a tic comes on . now , for some people , they 're on the far end of the spectrum . so their tourette 's is more severe , and it does impact their daily living . so when this is the case , we might need something more than habit reversal training to manage the tics . now when someone has an involuntary sound that they make , or maybe a movement that just happens to be in a really specific part of the body , one way that we might be able to deal with this is by going directly to the problematic body part . so maybe if it 's a movement , let 's say that it 's a hand jerk , we could try to stop that from occurring by preventing the messages that neurons send to that particular muscle to tell it to move . and funny enough , we can actually do this with botox . so when we inject botox into the hand here that jerks during a tic , that blocks some of the signals coming from the neurons that send messages to the hand to make it active . so after the injection of botox , the hand ca n't really be as active anymore for a few months until the botox wears off . so the tic may not be as noticeable , or it may not even occur . now , sometimes the tics may not be so localized . they might be more widespread . so we might need something that acts in a little bit more of a widespread way than botox does . so when this is the case , rather than going to the muscles involved in the tics , we might need to head back up to the source , the brain , and try something that will reduce these movements in a more global way . and it turns out that we have these particular medications called antidopaminergic medications that we can use . so dopaminergic here is referring to dopamine , a chemical that neurons can use to initiate movements in muscles . so these antidopaminergic medications they prevent dopamine in the brain from activating the muscles so much . so all these extra movements do n't really get initiated , and the person 's tics hopefully get decreased or go away . and it turns out that quite a few kids with tourette 's also have other disorders that co-occur with their tourette 's . disorders like attention deficit hyperactivity disorder , or also known as adhd , and obsessive compulsive disorder , also known as ocd . so for kids with tourette 's that also have one of these other disorders , they may need to go on a medication or have some sort of therapy to help them manage these disorders as well as their tourette 's .
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and it turns out that quite a few kids with tourette 's also have other disorders that co-occur with their tourette 's . disorders like attention deficit hyperactivity disorder , or also known as adhd , and obsessive compulsive disorder , also known as ocd . so for kids with tourette 's that also have one of these other disorders , they may need to go on a medication or have some sort of therapy to help them manage these disorders as well as their tourette 's .
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like cipa aka congenital insensitivity to pain with anhidrosis ( which is a disorder that makes you feel no pain } ?
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the main idea in treating myocardial infarcts is to limit the damage that happens to your heart , and to minimize complications that might crop up . the treatment has to address the clot that caused the myocardial infarct in the first place . and it has to restore the balance between the myocardial oxygen supply and demand . so there are some treatment aspects that are common to all of the types of acute coronary syndromes . but there 's some really important differences in the approach to patients who present with a stemi , or an st elevation myocardial infarct ; compared to unstable angina and n stemi , non-st elevation myocardial infarct . and we 'll talk about those . unstable angina and n stemi 's they 're usually treated in the same way . whereas stemi 's are treated a little bit differently because they 're more serious . so what happens ? well any patient who comes to a hospital with a suspected heart attack , with a suspected myocardial infarct , will first be admitted to an intensive care setting . they would be under continuous ecg monitoring for arrhythmias , or abnormal heart rhythms . remember the ecg would also give a really good idea of what type of heart attack they might have had . they 'd be made to lie down in bed to prevent their heart from working to hard . thus , minimizing their heart muscles oxygen demand . they might be given supplemental oxygen , if it turned out that they were n't carrying enough oxygen in their blood stream . and they might be given morphine and that 's to reduce the amount of chest pain that they 're feeling . and to also reduce the amount of anxiety that they might be feeling . and hopefully by doing that , by reducing their anxiety they 'd reduce their heart rate and even further reduce the amount of oxygen that their heart needed . really importantly , they 'd be given aspirin too . and the aspirin would reduce the development of the clot that might be causing their symptoms , that might be causing their myocardial infarct . this aspirin is actually one of the most important interventions in reducing mortality in patients with all forms of acute coronary syndrome . okay , so all that stuff happens right away on an immediate basis . then we have to think about sort of getting rid of that clot that caused their heart attack . and allowing blood to flow back into that area that was deprived of blood . so getting rid of that clot and allowing blood back into that part of the heart is called reperfusion . and that 's the next goal . if a patient comes in and the ecg trace has determined that they have a stemi , an st elevation myocardial infarct and they presented to the hospital within about two hours of the onset of their symptoms . they might be given a medication to break down their clot , in a process called thrombolysis , or thrombolysis . thrombo refers to the blood clot and lysis refers to break down . this is actually what 's being referred to when you hear of clot busters . unfortunately , no relation to ghostbusters . so if this mediation 's given early enough , there 's a really high chance of restoring blood flow to the damaged part of the heart . and that actually really reduces the tissue damage that the heart would experience . again , just to reiterate this is only for patients with stemi 's , not unstable angina or n stemi 's . and that 's because the type of clots that are being busted up with clot busters , they 're only found in stemi 's and not in n stemi 's . so everything that we 've talked is really part of the acute management of someone who presents with an acute coronary syndrome . so all this stuff will happen in the hospital right away . then the patient will be put on medications at the hospital that they 'll then have to continue for the rest of their life . and the reason for this is because taking these medications for the rest of their lives , this has been shown in clinical trials to reduce mortality , so that 's the rate of death attributed to having had a previous heart attack . among other positive affects , they 've also been shown to reduce the chance of you having another heart attack . so again , these are medications that you 'll start in hospital after the sort of acute management . and then you 'll need to be on them indefinitely . so what are these drugs ? well , there 's drugs that try to restore that oxygen supply and demand balance . so drugs like beta blockers , beta blockers work by making the heart beat slower , so fewer beats per minute . and it also makes the heart beat with a reduced force . so over all this reduces the heart 's oxygen demand , because if the muscles not working as hard it needs less oxygen . another group of drugs you might get are nitrates . nitrates are vasodilators , so they open up your blood vessels . they dilate your blood vessels to improve your blood flow . you 'd also be given more medications to prevent the development of more clots that could block off your coronary vessels . so you 're already on aspirin , but you might also be given one called heparin or warfarin . and what these do is they prevent your clotting cascade from happening as easily . so they slow down the growth of , first of all the clot that might have caused your myocardial infarct , and second any further clots that you might develop down the track . you 'd probably be given a statin . statin 's reduce your blood cholesterol level . and so they decrease progression of atherosclerotic buildup in your coronary arteries . remember plaques are filled with cholesterol , so you 'd probably be given a statin to take indefinitely . finally , you might be given an ace inhibitor . ace inhibitor 's reduce blood pressure and actually studies have shown that ace inhibitors can reduce negative structural changes that can happen in your heart after myocardial infarct . so those are the major , sort of treatments with medications that you get after having a myocardial infarct .
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statin 's reduce your blood cholesterol level . and so they decrease progression of atherosclerotic buildup in your coronary arteries . remember plaques are filled with cholesterol , so you 'd probably be given a statin to take indefinitely . finally , you might be given an ace inhibitor .
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would it make sense to take statins just as a preventive measure to slow down the buildup of plaques ?
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the main idea in treating myocardial infarcts is to limit the damage that happens to your heart , and to minimize complications that might crop up . the treatment has to address the clot that caused the myocardial infarct in the first place . and it has to restore the balance between the myocardial oxygen supply and demand . so there are some treatment aspects that are common to all of the types of acute coronary syndromes . but there 's some really important differences in the approach to patients who present with a stemi , or an st elevation myocardial infarct ; compared to unstable angina and n stemi , non-st elevation myocardial infarct . and we 'll talk about those . unstable angina and n stemi 's they 're usually treated in the same way . whereas stemi 's are treated a little bit differently because they 're more serious . so what happens ? well any patient who comes to a hospital with a suspected heart attack , with a suspected myocardial infarct , will first be admitted to an intensive care setting . they would be under continuous ecg monitoring for arrhythmias , or abnormal heart rhythms . remember the ecg would also give a really good idea of what type of heart attack they might have had . they 'd be made to lie down in bed to prevent their heart from working to hard . thus , minimizing their heart muscles oxygen demand . they might be given supplemental oxygen , if it turned out that they were n't carrying enough oxygen in their blood stream . and they might be given morphine and that 's to reduce the amount of chest pain that they 're feeling . and to also reduce the amount of anxiety that they might be feeling . and hopefully by doing that , by reducing their anxiety they 'd reduce their heart rate and even further reduce the amount of oxygen that their heart needed . really importantly , they 'd be given aspirin too . and the aspirin would reduce the development of the clot that might be causing their symptoms , that might be causing their myocardial infarct . this aspirin is actually one of the most important interventions in reducing mortality in patients with all forms of acute coronary syndrome . okay , so all that stuff happens right away on an immediate basis . then we have to think about sort of getting rid of that clot that caused their heart attack . and allowing blood to flow back into that area that was deprived of blood . so getting rid of that clot and allowing blood back into that part of the heart is called reperfusion . and that 's the next goal . if a patient comes in and the ecg trace has determined that they have a stemi , an st elevation myocardial infarct and they presented to the hospital within about two hours of the onset of their symptoms . they might be given a medication to break down their clot , in a process called thrombolysis , or thrombolysis . thrombo refers to the blood clot and lysis refers to break down . this is actually what 's being referred to when you hear of clot busters . unfortunately , no relation to ghostbusters . so if this mediation 's given early enough , there 's a really high chance of restoring blood flow to the damaged part of the heart . and that actually really reduces the tissue damage that the heart would experience . again , just to reiterate this is only for patients with stemi 's , not unstable angina or n stemi 's . and that 's because the type of clots that are being busted up with clot busters , they 're only found in stemi 's and not in n stemi 's . so everything that we 've talked is really part of the acute management of someone who presents with an acute coronary syndrome . so all this stuff will happen in the hospital right away . then the patient will be put on medications at the hospital that they 'll then have to continue for the rest of their life . and the reason for this is because taking these medications for the rest of their lives , this has been shown in clinical trials to reduce mortality , so that 's the rate of death attributed to having had a previous heart attack . among other positive affects , they 've also been shown to reduce the chance of you having another heart attack . so again , these are medications that you 'll start in hospital after the sort of acute management . and then you 'll need to be on them indefinitely . so what are these drugs ? well , there 's drugs that try to restore that oxygen supply and demand balance . so drugs like beta blockers , beta blockers work by making the heart beat slower , so fewer beats per minute . and it also makes the heart beat with a reduced force . so over all this reduces the heart 's oxygen demand , because if the muscles not working as hard it needs less oxygen . another group of drugs you might get are nitrates . nitrates are vasodilators , so they open up your blood vessels . they dilate your blood vessels to improve your blood flow . you 'd also be given more medications to prevent the development of more clots that could block off your coronary vessels . so you 're already on aspirin , but you might also be given one called heparin or warfarin . and what these do is they prevent your clotting cascade from happening as easily . so they slow down the growth of , first of all the clot that might have caused your myocardial infarct , and second any further clots that you might develop down the track . you 'd probably be given a statin . statin 's reduce your blood cholesterol level . and so they decrease progression of atherosclerotic buildup in your coronary arteries . remember plaques are filled with cholesterol , so you 'd probably be given a statin to take indefinitely . finally , you might be given an ace inhibitor . ace inhibitor 's reduce blood pressure and actually studies have shown that ace inhibitors can reduce negative structural changes that can happen in your heart after myocardial infarct . so those are the major , sort of treatments with medications that you get after having a myocardial infarct .
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so all this stuff will happen in the hospital right away . then the patient will be put on medications at the hospital that they 'll then have to continue for the rest of their life . and the reason for this is because taking these medications for the rest of their lives , this has been shown in clinical trials to reduce mortality , so that 's the rate of death attributed to having had a previous heart attack .
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what order would you put these interventions in when caring for an mi patient ?
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the main idea in treating myocardial infarcts is to limit the damage that happens to your heart , and to minimize complications that might crop up . the treatment has to address the clot that caused the myocardial infarct in the first place . and it has to restore the balance between the myocardial oxygen supply and demand . so there are some treatment aspects that are common to all of the types of acute coronary syndromes . but there 's some really important differences in the approach to patients who present with a stemi , or an st elevation myocardial infarct ; compared to unstable angina and n stemi , non-st elevation myocardial infarct . and we 'll talk about those . unstable angina and n stemi 's they 're usually treated in the same way . whereas stemi 's are treated a little bit differently because they 're more serious . so what happens ? well any patient who comes to a hospital with a suspected heart attack , with a suspected myocardial infarct , will first be admitted to an intensive care setting . they would be under continuous ecg monitoring for arrhythmias , or abnormal heart rhythms . remember the ecg would also give a really good idea of what type of heart attack they might have had . they 'd be made to lie down in bed to prevent their heart from working to hard . thus , minimizing their heart muscles oxygen demand . they might be given supplemental oxygen , if it turned out that they were n't carrying enough oxygen in their blood stream . and they might be given morphine and that 's to reduce the amount of chest pain that they 're feeling . and to also reduce the amount of anxiety that they might be feeling . and hopefully by doing that , by reducing their anxiety they 'd reduce their heart rate and even further reduce the amount of oxygen that their heart needed . really importantly , they 'd be given aspirin too . and the aspirin would reduce the development of the clot that might be causing their symptoms , that might be causing their myocardial infarct . this aspirin is actually one of the most important interventions in reducing mortality in patients with all forms of acute coronary syndrome . okay , so all that stuff happens right away on an immediate basis . then we have to think about sort of getting rid of that clot that caused their heart attack . and allowing blood to flow back into that area that was deprived of blood . so getting rid of that clot and allowing blood back into that part of the heart is called reperfusion . and that 's the next goal . if a patient comes in and the ecg trace has determined that they have a stemi , an st elevation myocardial infarct and they presented to the hospital within about two hours of the onset of their symptoms . they might be given a medication to break down their clot , in a process called thrombolysis , or thrombolysis . thrombo refers to the blood clot and lysis refers to break down . this is actually what 's being referred to when you hear of clot busters . unfortunately , no relation to ghostbusters . so if this mediation 's given early enough , there 's a really high chance of restoring blood flow to the damaged part of the heart . and that actually really reduces the tissue damage that the heart would experience . again , just to reiterate this is only for patients with stemi 's , not unstable angina or n stemi 's . and that 's because the type of clots that are being busted up with clot busters , they 're only found in stemi 's and not in n stemi 's . so everything that we 've talked is really part of the acute management of someone who presents with an acute coronary syndrome . so all this stuff will happen in the hospital right away . then the patient will be put on medications at the hospital that they 'll then have to continue for the rest of their life . and the reason for this is because taking these medications for the rest of their lives , this has been shown in clinical trials to reduce mortality , so that 's the rate of death attributed to having had a previous heart attack . among other positive affects , they 've also been shown to reduce the chance of you having another heart attack . so again , these are medications that you 'll start in hospital after the sort of acute management . and then you 'll need to be on them indefinitely . so what are these drugs ? well , there 's drugs that try to restore that oxygen supply and demand balance . so drugs like beta blockers , beta blockers work by making the heart beat slower , so fewer beats per minute . and it also makes the heart beat with a reduced force . so over all this reduces the heart 's oxygen demand , because if the muscles not working as hard it needs less oxygen . another group of drugs you might get are nitrates . nitrates are vasodilators , so they open up your blood vessels . they dilate your blood vessels to improve your blood flow . you 'd also be given more medications to prevent the development of more clots that could block off your coronary vessels . so you 're already on aspirin , but you might also be given one called heparin or warfarin . and what these do is they prevent your clotting cascade from happening as easily . so they slow down the growth of , first of all the clot that might have caused your myocardial infarct , and second any further clots that you might develop down the track . you 'd probably be given a statin . statin 's reduce your blood cholesterol level . and so they decrease progression of atherosclerotic buildup in your coronary arteries . remember plaques are filled with cholesterol , so you 'd probably be given a statin to take indefinitely . finally , you might be given an ace inhibitor . ace inhibitor 's reduce blood pressure and actually studies have shown that ace inhibitors can reduce negative structural changes that can happen in your heart after myocardial infarct . so those are the major , sort of treatments with medications that you get after having a myocardial infarct .
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they might be given supplemental oxygen , if it turned out that they were n't carrying enough oxygen in their blood stream . and they might be given morphine and that 's to reduce the amount of chest pain that they 're feeling . and to also reduce the amount of anxiety that they might be feeling .
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how often do doctors use morphine ?
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the main idea in treating myocardial infarcts is to limit the damage that happens to your heart , and to minimize complications that might crop up . the treatment has to address the clot that caused the myocardial infarct in the first place . and it has to restore the balance between the myocardial oxygen supply and demand . so there are some treatment aspects that are common to all of the types of acute coronary syndromes . but there 's some really important differences in the approach to patients who present with a stemi , or an st elevation myocardial infarct ; compared to unstable angina and n stemi , non-st elevation myocardial infarct . and we 'll talk about those . unstable angina and n stemi 's they 're usually treated in the same way . whereas stemi 's are treated a little bit differently because they 're more serious . so what happens ? well any patient who comes to a hospital with a suspected heart attack , with a suspected myocardial infarct , will first be admitted to an intensive care setting . they would be under continuous ecg monitoring for arrhythmias , or abnormal heart rhythms . remember the ecg would also give a really good idea of what type of heart attack they might have had . they 'd be made to lie down in bed to prevent their heart from working to hard . thus , minimizing their heart muscles oxygen demand . they might be given supplemental oxygen , if it turned out that they were n't carrying enough oxygen in their blood stream . and they might be given morphine and that 's to reduce the amount of chest pain that they 're feeling . and to also reduce the amount of anxiety that they might be feeling . and hopefully by doing that , by reducing their anxiety they 'd reduce their heart rate and even further reduce the amount of oxygen that their heart needed . really importantly , they 'd be given aspirin too . and the aspirin would reduce the development of the clot that might be causing their symptoms , that might be causing their myocardial infarct . this aspirin is actually one of the most important interventions in reducing mortality in patients with all forms of acute coronary syndrome . okay , so all that stuff happens right away on an immediate basis . then we have to think about sort of getting rid of that clot that caused their heart attack . and allowing blood to flow back into that area that was deprived of blood . so getting rid of that clot and allowing blood back into that part of the heart is called reperfusion . and that 's the next goal . if a patient comes in and the ecg trace has determined that they have a stemi , an st elevation myocardial infarct and they presented to the hospital within about two hours of the onset of their symptoms . they might be given a medication to break down their clot , in a process called thrombolysis , or thrombolysis . thrombo refers to the blood clot and lysis refers to break down . this is actually what 's being referred to when you hear of clot busters . unfortunately , no relation to ghostbusters . so if this mediation 's given early enough , there 's a really high chance of restoring blood flow to the damaged part of the heart . and that actually really reduces the tissue damage that the heart would experience . again , just to reiterate this is only for patients with stemi 's , not unstable angina or n stemi 's . and that 's because the type of clots that are being busted up with clot busters , they 're only found in stemi 's and not in n stemi 's . so everything that we 've talked is really part of the acute management of someone who presents with an acute coronary syndrome . so all this stuff will happen in the hospital right away . then the patient will be put on medications at the hospital that they 'll then have to continue for the rest of their life . and the reason for this is because taking these medications for the rest of their lives , this has been shown in clinical trials to reduce mortality , so that 's the rate of death attributed to having had a previous heart attack . among other positive affects , they 've also been shown to reduce the chance of you having another heart attack . so again , these are medications that you 'll start in hospital after the sort of acute management . and then you 'll need to be on them indefinitely . so what are these drugs ? well , there 's drugs that try to restore that oxygen supply and demand balance . so drugs like beta blockers , beta blockers work by making the heart beat slower , so fewer beats per minute . and it also makes the heart beat with a reduced force . so over all this reduces the heart 's oxygen demand , because if the muscles not working as hard it needs less oxygen . another group of drugs you might get are nitrates . nitrates are vasodilators , so they open up your blood vessels . they dilate your blood vessels to improve your blood flow . you 'd also be given more medications to prevent the development of more clots that could block off your coronary vessels . so you 're already on aspirin , but you might also be given one called heparin or warfarin . and what these do is they prevent your clotting cascade from happening as easily . so they slow down the growth of , first of all the clot that might have caused your myocardial infarct , and second any further clots that you might develop down the track . you 'd probably be given a statin . statin 's reduce your blood cholesterol level . and so they decrease progression of atherosclerotic buildup in your coronary arteries . remember plaques are filled with cholesterol , so you 'd probably be given a statin to take indefinitely . finally , you might be given an ace inhibitor . ace inhibitor 's reduce blood pressure and actually studies have shown that ace inhibitors can reduce negative structural changes that can happen in your heart after myocardial infarct . so those are the major , sort of treatments with medications that you get after having a myocardial infarct .
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then the patient will be put on medications at the hospital that they 'll then have to continue for the rest of their life . and the reason for this is because taking these medications for the rest of their lives , this has been shown in clinical trials to reduce mortality , so that 's the rate of death attributed to having had a previous heart attack . among other positive affects , they 've also been shown to reduce the chance of you having another heart attack . so again , these are medications that you 'll start in hospital after the sort of acute management .
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do people who have n't had a heart attack , take the medications listed in the video to help prevent a mi ?
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the main idea in treating myocardial infarcts is to limit the damage that happens to your heart , and to minimize complications that might crop up . the treatment has to address the clot that caused the myocardial infarct in the first place . and it has to restore the balance between the myocardial oxygen supply and demand . so there are some treatment aspects that are common to all of the types of acute coronary syndromes . but there 's some really important differences in the approach to patients who present with a stemi , or an st elevation myocardial infarct ; compared to unstable angina and n stemi , non-st elevation myocardial infarct . and we 'll talk about those . unstable angina and n stemi 's they 're usually treated in the same way . whereas stemi 's are treated a little bit differently because they 're more serious . so what happens ? well any patient who comes to a hospital with a suspected heart attack , with a suspected myocardial infarct , will first be admitted to an intensive care setting . they would be under continuous ecg monitoring for arrhythmias , or abnormal heart rhythms . remember the ecg would also give a really good idea of what type of heart attack they might have had . they 'd be made to lie down in bed to prevent their heart from working to hard . thus , minimizing their heart muscles oxygen demand . they might be given supplemental oxygen , if it turned out that they were n't carrying enough oxygen in their blood stream . and they might be given morphine and that 's to reduce the amount of chest pain that they 're feeling . and to also reduce the amount of anxiety that they might be feeling . and hopefully by doing that , by reducing their anxiety they 'd reduce their heart rate and even further reduce the amount of oxygen that their heart needed . really importantly , they 'd be given aspirin too . and the aspirin would reduce the development of the clot that might be causing their symptoms , that might be causing their myocardial infarct . this aspirin is actually one of the most important interventions in reducing mortality in patients with all forms of acute coronary syndrome . okay , so all that stuff happens right away on an immediate basis . then we have to think about sort of getting rid of that clot that caused their heart attack . and allowing blood to flow back into that area that was deprived of blood . so getting rid of that clot and allowing blood back into that part of the heart is called reperfusion . and that 's the next goal . if a patient comes in and the ecg trace has determined that they have a stemi , an st elevation myocardial infarct and they presented to the hospital within about two hours of the onset of their symptoms . they might be given a medication to break down their clot , in a process called thrombolysis , or thrombolysis . thrombo refers to the blood clot and lysis refers to break down . this is actually what 's being referred to when you hear of clot busters . unfortunately , no relation to ghostbusters . so if this mediation 's given early enough , there 's a really high chance of restoring blood flow to the damaged part of the heart . and that actually really reduces the tissue damage that the heart would experience . again , just to reiterate this is only for patients with stemi 's , not unstable angina or n stemi 's . and that 's because the type of clots that are being busted up with clot busters , they 're only found in stemi 's and not in n stemi 's . so everything that we 've talked is really part of the acute management of someone who presents with an acute coronary syndrome . so all this stuff will happen in the hospital right away . then the patient will be put on medications at the hospital that they 'll then have to continue for the rest of their life . and the reason for this is because taking these medications for the rest of their lives , this has been shown in clinical trials to reduce mortality , so that 's the rate of death attributed to having had a previous heart attack . among other positive affects , they 've also been shown to reduce the chance of you having another heart attack . so again , these are medications that you 'll start in hospital after the sort of acute management . and then you 'll need to be on them indefinitely . so what are these drugs ? well , there 's drugs that try to restore that oxygen supply and demand balance . so drugs like beta blockers , beta blockers work by making the heart beat slower , so fewer beats per minute . and it also makes the heart beat with a reduced force . so over all this reduces the heart 's oxygen demand , because if the muscles not working as hard it needs less oxygen . another group of drugs you might get are nitrates . nitrates are vasodilators , so they open up your blood vessels . they dilate your blood vessels to improve your blood flow . you 'd also be given more medications to prevent the development of more clots that could block off your coronary vessels . so you 're already on aspirin , but you might also be given one called heparin or warfarin . and what these do is they prevent your clotting cascade from happening as easily . so they slow down the growth of , first of all the clot that might have caused your myocardial infarct , and second any further clots that you might develop down the track . you 'd probably be given a statin . statin 's reduce your blood cholesterol level . and so they decrease progression of atherosclerotic buildup in your coronary arteries . remember plaques are filled with cholesterol , so you 'd probably be given a statin to take indefinitely . finally , you might be given an ace inhibitor . ace inhibitor 's reduce blood pressure and actually studies have shown that ace inhibitors can reduce negative structural changes that can happen in your heart after myocardial infarct . so those are the major , sort of treatments with medications that you get after having a myocardial infarct .
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and hopefully by doing that , by reducing their anxiety they 'd reduce their heart rate and even further reduce the amount of oxygen that their heart needed . really importantly , they 'd be given aspirin too . and the aspirin would reduce the development of the clot that might be causing their symptoms , that might be causing their myocardial infarct .
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what dose of aspirin should be administered and when ?
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the main idea in treating myocardial infarcts is to limit the damage that happens to your heart , and to minimize complications that might crop up . the treatment has to address the clot that caused the myocardial infarct in the first place . and it has to restore the balance between the myocardial oxygen supply and demand . so there are some treatment aspects that are common to all of the types of acute coronary syndromes . but there 's some really important differences in the approach to patients who present with a stemi , or an st elevation myocardial infarct ; compared to unstable angina and n stemi , non-st elevation myocardial infarct . and we 'll talk about those . unstable angina and n stemi 's they 're usually treated in the same way . whereas stemi 's are treated a little bit differently because they 're more serious . so what happens ? well any patient who comes to a hospital with a suspected heart attack , with a suspected myocardial infarct , will first be admitted to an intensive care setting . they would be under continuous ecg monitoring for arrhythmias , or abnormal heart rhythms . remember the ecg would also give a really good idea of what type of heart attack they might have had . they 'd be made to lie down in bed to prevent their heart from working to hard . thus , minimizing their heart muscles oxygen demand . they might be given supplemental oxygen , if it turned out that they were n't carrying enough oxygen in their blood stream . and they might be given morphine and that 's to reduce the amount of chest pain that they 're feeling . and to also reduce the amount of anxiety that they might be feeling . and hopefully by doing that , by reducing their anxiety they 'd reduce their heart rate and even further reduce the amount of oxygen that their heart needed . really importantly , they 'd be given aspirin too . and the aspirin would reduce the development of the clot that might be causing their symptoms , that might be causing their myocardial infarct . this aspirin is actually one of the most important interventions in reducing mortality in patients with all forms of acute coronary syndrome . okay , so all that stuff happens right away on an immediate basis . then we have to think about sort of getting rid of that clot that caused their heart attack . and allowing blood to flow back into that area that was deprived of blood . so getting rid of that clot and allowing blood back into that part of the heart is called reperfusion . and that 's the next goal . if a patient comes in and the ecg trace has determined that they have a stemi , an st elevation myocardial infarct and they presented to the hospital within about two hours of the onset of their symptoms . they might be given a medication to break down their clot , in a process called thrombolysis , or thrombolysis . thrombo refers to the blood clot and lysis refers to break down . this is actually what 's being referred to when you hear of clot busters . unfortunately , no relation to ghostbusters . so if this mediation 's given early enough , there 's a really high chance of restoring blood flow to the damaged part of the heart . and that actually really reduces the tissue damage that the heart would experience . again , just to reiterate this is only for patients with stemi 's , not unstable angina or n stemi 's . and that 's because the type of clots that are being busted up with clot busters , they 're only found in stemi 's and not in n stemi 's . so everything that we 've talked is really part of the acute management of someone who presents with an acute coronary syndrome . so all this stuff will happen in the hospital right away . then the patient will be put on medications at the hospital that they 'll then have to continue for the rest of their life . and the reason for this is because taking these medications for the rest of their lives , this has been shown in clinical trials to reduce mortality , so that 's the rate of death attributed to having had a previous heart attack . among other positive affects , they 've also been shown to reduce the chance of you having another heart attack . so again , these are medications that you 'll start in hospital after the sort of acute management . and then you 'll need to be on them indefinitely . so what are these drugs ? well , there 's drugs that try to restore that oxygen supply and demand balance . so drugs like beta blockers , beta blockers work by making the heart beat slower , so fewer beats per minute . and it also makes the heart beat with a reduced force . so over all this reduces the heart 's oxygen demand , because if the muscles not working as hard it needs less oxygen . another group of drugs you might get are nitrates . nitrates are vasodilators , so they open up your blood vessels . they dilate your blood vessels to improve your blood flow . you 'd also be given more medications to prevent the development of more clots that could block off your coronary vessels . so you 're already on aspirin , but you might also be given one called heparin or warfarin . and what these do is they prevent your clotting cascade from happening as easily . so they slow down the growth of , first of all the clot that might have caused your myocardial infarct , and second any further clots that you might develop down the track . you 'd probably be given a statin . statin 's reduce your blood cholesterol level . and so they decrease progression of atherosclerotic buildup in your coronary arteries . remember plaques are filled with cholesterol , so you 'd probably be given a statin to take indefinitely . finally , you might be given an ace inhibitor . ace inhibitor 's reduce blood pressure and actually studies have shown that ace inhibitors can reduce negative structural changes that can happen in your heart after myocardial infarct . so those are the major , sort of treatments with medications that you get after having a myocardial infarct .
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they would be under continuous ecg monitoring for arrhythmias , or abnormal heart rhythms . remember the ecg would also give a really good idea of what type of heart attack they might have had . they 'd be made to lie down in bed to prevent their heart from working to hard .
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when someone 's having heart attack , is it ok to give him 300 mg right away at home ( in non retard form ) ?
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the main idea in treating myocardial infarcts is to limit the damage that happens to your heart , and to minimize complications that might crop up . the treatment has to address the clot that caused the myocardial infarct in the first place . and it has to restore the balance between the myocardial oxygen supply and demand . so there are some treatment aspects that are common to all of the types of acute coronary syndromes . but there 's some really important differences in the approach to patients who present with a stemi , or an st elevation myocardial infarct ; compared to unstable angina and n stemi , non-st elevation myocardial infarct . and we 'll talk about those . unstable angina and n stemi 's they 're usually treated in the same way . whereas stemi 's are treated a little bit differently because they 're more serious . so what happens ? well any patient who comes to a hospital with a suspected heart attack , with a suspected myocardial infarct , will first be admitted to an intensive care setting . they would be under continuous ecg monitoring for arrhythmias , or abnormal heart rhythms . remember the ecg would also give a really good idea of what type of heart attack they might have had . they 'd be made to lie down in bed to prevent their heart from working to hard . thus , minimizing their heart muscles oxygen demand . they might be given supplemental oxygen , if it turned out that they were n't carrying enough oxygen in their blood stream . and they might be given morphine and that 's to reduce the amount of chest pain that they 're feeling . and to also reduce the amount of anxiety that they might be feeling . and hopefully by doing that , by reducing their anxiety they 'd reduce their heart rate and even further reduce the amount of oxygen that their heart needed . really importantly , they 'd be given aspirin too . and the aspirin would reduce the development of the clot that might be causing their symptoms , that might be causing their myocardial infarct . this aspirin is actually one of the most important interventions in reducing mortality in patients with all forms of acute coronary syndrome . okay , so all that stuff happens right away on an immediate basis . then we have to think about sort of getting rid of that clot that caused their heart attack . and allowing blood to flow back into that area that was deprived of blood . so getting rid of that clot and allowing blood back into that part of the heart is called reperfusion . and that 's the next goal . if a patient comes in and the ecg trace has determined that they have a stemi , an st elevation myocardial infarct and they presented to the hospital within about two hours of the onset of their symptoms . they might be given a medication to break down their clot , in a process called thrombolysis , or thrombolysis . thrombo refers to the blood clot and lysis refers to break down . this is actually what 's being referred to when you hear of clot busters . unfortunately , no relation to ghostbusters . so if this mediation 's given early enough , there 's a really high chance of restoring blood flow to the damaged part of the heart . and that actually really reduces the tissue damage that the heart would experience . again , just to reiterate this is only for patients with stemi 's , not unstable angina or n stemi 's . and that 's because the type of clots that are being busted up with clot busters , they 're only found in stemi 's and not in n stemi 's . so everything that we 've talked is really part of the acute management of someone who presents with an acute coronary syndrome . so all this stuff will happen in the hospital right away . then the patient will be put on medications at the hospital that they 'll then have to continue for the rest of their life . and the reason for this is because taking these medications for the rest of their lives , this has been shown in clinical trials to reduce mortality , so that 's the rate of death attributed to having had a previous heart attack . among other positive affects , they 've also been shown to reduce the chance of you having another heart attack . so again , these are medications that you 'll start in hospital after the sort of acute management . and then you 'll need to be on them indefinitely . so what are these drugs ? well , there 's drugs that try to restore that oxygen supply and demand balance . so drugs like beta blockers , beta blockers work by making the heart beat slower , so fewer beats per minute . and it also makes the heart beat with a reduced force . so over all this reduces the heart 's oxygen demand , because if the muscles not working as hard it needs less oxygen . another group of drugs you might get are nitrates . nitrates are vasodilators , so they open up your blood vessels . they dilate your blood vessels to improve your blood flow . you 'd also be given more medications to prevent the development of more clots that could block off your coronary vessels . so you 're already on aspirin , but you might also be given one called heparin or warfarin . and what these do is they prevent your clotting cascade from happening as easily . so they slow down the growth of , first of all the clot that might have caused your myocardial infarct , and second any further clots that you might develop down the track . you 'd probably be given a statin . statin 's reduce your blood cholesterol level . and so they decrease progression of atherosclerotic buildup in your coronary arteries . remember plaques are filled with cholesterol , so you 'd probably be given a statin to take indefinitely . finally , you might be given an ace inhibitor . ace inhibitor 's reduce blood pressure and actually studies have shown that ace inhibitors can reduce negative structural changes that can happen in your heart after myocardial infarct . so those are the major , sort of treatments with medications that you get after having a myocardial infarct .
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thrombo refers to the blood clot and lysis refers to break down . this is actually what 's being referred to when you hear of clot busters . unfortunately , no relation to ghostbusters .
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how are clot-busters actually working and why are they only effective on `` stemi-clots '' ?
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the main idea in treating myocardial infarcts is to limit the damage that happens to your heart , and to minimize complications that might crop up . the treatment has to address the clot that caused the myocardial infarct in the first place . and it has to restore the balance between the myocardial oxygen supply and demand . so there are some treatment aspects that are common to all of the types of acute coronary syndromes . but there 's some really important differences in the approach to patients who present with a stemi , or an st elevation myocardial infarct ; compared to unstable angina and n stemi , non-st elevation myocardial infarct . and we 'll talk about those . unstable angina and n stemi 's they 're usually treated in the same way . whereas stemi 's are treated a little bit differently because they 're more serious . so what happens ? well any patient who comes to a hospital with a suspected heart attack , with a suspected myocardial infarct , will first be admitted to an intensive care setting . they would be under continuous ecg monitoring for arrhythmias , or abnormal heart rhythms . remember the ecg would also give a really good idea of what type of heart attack they might have had . they 'd be made to lie down in bed to prevent their heart from working to hard . thus , minimizing their heart muscles oxygen demand . they might be given supplemental oxygen , if it turned out that they were n't carrying enough oxygen in their blood stream . and they might be given morphine and that 's to reduce the amount of chest pain that they 're feeling . and to also reduce the amount of anxiety that they might be feeling . and hopefully by doing that , by reducing their anxiety they 'd reduce their heart rate and even further reduce the amount of oxygen that their heart needed . really importantly , they 'd be given aspirin too . and the aspirin would reduce the development of the clot that might be causing their symptoms , that might be causing their myocardial infarct . this aspirin is actually one of the most important interventions in reducing mortality in patients with all forms of acute coronary syndrome . okay , so all that stuff happens right away on an immediate basis . then we have to think about sort of getting rid of that clot that caused their heart attack . and allowing blood to flow back into that area that was deprived of blood . so getting rid of that clot and allowing blood back into that part of the heart is called reperfusion . and that 's the next goal . if a patient comes in and the ecg trace has determined that they have a stemi , an st elevation myocardial infarct and they presented to the hospital within about two hours of the onset of their symptoms . they might be given a medication to break down their clot , in a process called thrombolysis , or thrombolysis . thrombo refers to the blood clot and lysis refers to break down . this is actually what 's being referred to when you hear of clot busters . unfortunately , no relation to ghostbusters . so if this mediation 's given early enough , there 's a really high chance of restoring blood flow to the damaged part of the heart . and that actually really reduces the tissue damage that the heart would experience . again , just to reiterate this is only for patients with stemi 's , not unstable angina or n stemi 's . and that 's because the type of clots that are being busted up with clot busters , they 're only found in stemi 's and not in n stemi 's . so everything that we 've talked is really part of the acute management of someone who presents with an acute coronary syndrome . so all this stuff will happen in the hospital right away . then the patient will be put on medications at the hospital that they 'll then have to continue for the rest of their life . and the reason for this is because taking these medications for the rest of their lives , this has been shown in clinical trials to reduce mortality , so that 's the rate of death attributed to having had a previous heart attack . among other positive affects , they 've also been shown to reduce the chance of you having another heart attack . so again , these are medications that you 'll start in hospital after the sort of acute management . and then you 'll need to be on them indefinitely . so what are these drugs ? well , there 's drugs that try to restore that oxygen supply and demand balance . so drugs like beta blockers , beta blockers work by making the heart beat slower , so fewer beats per minute . and it also makes the heart beat with a reduced force . so over all this reduces the heart 's oxygen demand , because if the muscles not working as hard it needs less oxygen . another group of drugs you might get are nitrates . nitrates are vasodilators , so they open up your blood vessels . they dilate your blood vessels to improve your blood flow . you 'd also be given more medications to prevent the development of more clots that could block off your coronary vessels . so you 're already on aspirin , but you might also be given one called heparin or warfarin . and what these do is they prevent your clotting cascade from happening as easily . so they slow down the growth of , first of all the clot that might have caused your myocardial infarct , and second any further clots that you might develop down the track . you 'd probably be given a statin . statin 's reduce your blood cholesterol level . and so they decrease progression of atherosclerotic buildup in your coronary arteries . remember plaques are filled with cholesterol , so you 'd probably be given a statin to take indefinitely . finally , you might be given an ace inhibitor . ace inhibitor 's reduce blood pressure and actually studies have shown that ace inhibitors can reduce negative structural changes that can happen in your heart after myocardial infarct . so those are the major , sort of treatments with medications that you get after having a myocardial infarct .
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and that actually really reduces the tissue damage that the heart would experience . again , just to reiterate this is only for patients with stemi 's , not unstable angina or n stemi 's . and that 's because the type of clots that are being busted up with clot busters , they 're only found in stemi 's and not in n stemi 's .
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what 's the difference between `` stemi-clots '' and `` nstemi-clots '' /unstable-angina-clots ?
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the main idea in treating myocardial infarcts is to limit the damage that happens to your heart , and to minimize complications that might crop up . the treatment has to address the clot that caused the myocardial infarct in the first place . and it has to restore the balance between the myocardial oxygen supply and demand . so there are some treatment aspects that are common to all of the types of acute coronary syndromes . but there 's some really important differences in the approach to patients who present with a stemi , or an st elevation myocardial infarct ; compared to unstable angina and n stemi , non-st elevation myocardial infarct . and we 'll talk about those . unstable angina and n stemi 's they 're usually treated in the same way . whereas stemi 's are treated a little bit differently because they 're more serious . so what happens ? well any patient who comes to a hospital with a suspected heart attack , with a suspected myocardial infarct , will first be admitted to an intensive care setting . they would be under continuous ecg monitoring for arrhythmias , or abnormal heart rhythms . remember the ecg would also give a really good idea of what type of heart attack they might have had . they 'd be made to lie down in bed to prevent their heart from working to hard . thus , minimizing their heart muscles oxygen demand . they might be given supplemental oxygen , if it turned out that they were n't carrying enough oxygen in their blood stream . and they might be given morphine and that 's to reduce the amount of chest pain that they 're feeling . and to also reduce the amount of anxiety that they might be feeling . and hopefully by doing that , by reducing their anxiety they 'd reduce their heart rate and even further reduce the amount of oxygen that their heart needed . really importantly , they 'd be given aspirin too . and the aspirin would reduce the development of the clot that might be causing their symptoms , that might be causing their myocardial infarct . this aspirin is actually one of the most important interventions in reducing mortality in patients with all forms of acute coronary syndrome . okay , so all that stuff happens right away on an immediate basis . then we have to think about sort of getting rid of that clot that caused their heart attack . and allowing blood to flow back into that area that was deprived of blood . so getting rid of that clot and allowing blood back into that part of the heart is called reperfusion . and that 's the next goal . if a patient comes in and the ecg trace has determined that they have a stemi , an st elevation myocardial infarct and they presented to the hospital within about two hours of the onset of their symptoms . they might be given a medication to break down their clot , in a process called thrombolysis , or thrombolysis . thrombo refers to the blood clot and lysis refers to break down . this is actually what 's being referred to when you hear of clot busters . unfortunately , no relation to ghostbusters . so if this mediation 's given early enough , there 's a really high chance of restoring blood flow to the damaged part of the heart . and that actually really reduces the tissue damage that the heart would experience . again , just to reiterate this is only for patients with stemi 's , not unstable angina or n stemi 's . and that 's because the type of clots that are being busted up with clot busters , they 're only found in stemi 's and not in n stemi 's . so everything that we 've talked is really part of the acute management of someone who presents with an acute coronary syndrome . so all this stuff will happen in the hospital right away . then the patient will be put on medications at the hospital that they 'll then have to continue for the rest of their life . and the reason for this is because taking these medications for the rest of their lives , this has been shown in clinical trials to reduce mortality , so that 's the rate of death attributed to having had a previous heart attack . among other positive affects , they 've also been shown to reduce the chance of you having another heart attack . so again , these are medications that you 'll start in hospital after the sort of acute management . and then you 'll need to be on them indefinitely . so what are these drugs ? well , there 's drugs that try to restore that oxygen supply and demand balance . so drugs like beta blockers , beta blockers work by making the heart beat slower , so fewer beats per minute . and it also makes the heart beat with a reduced force . so over all this reduces the heart 's oxygen demand , because if the muscles not working as hard it needs less oxygen . another group of drugs you might get are nitrates . nitrates are vasodilators , so they open up your blood vessels . they dilate your blood vessels to improve your blood flow . you 'd also be given more medications to prevent the development of more clots that could block off your coronary vessels . so you 're already on aspirin , but you might also be given one called heparin or warfarin . and what these do is they prevent your clotting cascade from happening as easily . so they slow down the growth of , first of all the clot that might have caused your myocardial infarct , and second any further clots that you might develop down the track . you 'd probably be given a statin . statin 's reduce your blood cholesterol level . and so they decrease progression of atherosclerotic buildup in your coronary arteries . remember plaques are filled with cholesterol , so you 'd probably be given a statin to take indefinitely . finally , you might be given an ace inhibitor . ace inhibitor 's reduce blood pressure and actually studies have shown that ace inhibitors can reduce negative structural changes that can happen in your heart after myocardial infarct . so those are the major , sort of treatments with medications that you get after having a myocardial infarct .
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and allowing blood to flow back into that area that was deprived of blood . so getting rid of that clot and allowing blood back into that part of the heart is called reperfusion . and that 's the next goal .
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what is the `` heart shaped medicine '' called , ?
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the main idea in treating myocardial infarcts is to limit the damage that happens to your heart , and to minimize complications that might crop up . the treatment has to address the clot that caused the myocardial infarct in the first place . and it has to restore the balance between the myocardial oxygen supply and demand . so there are some treatment aspects that are common to all of the types of acute coronary syndromes . but there 's some really important differences in the approach to patients who present with a stemi , or an st elevation myocardial infarct ; compared to unstable angina and n stemi , non-st elevation myocardial infarct . and we 'll talk about those . unstable angina and n stemi 's they 're usually treated in the same way . whereas stemi 's are treated a little bit differently because they 're more serious . so what happens ? well any patient who comes to a hospital with a suspected heart attack , with a suspected myocardial infarct , will first be admitted to an intensive care setting . they would be under continuous ecg monitoring for arrhythmias , or abnormal heart rhythms . remember the ecg would also give a really good idea of what type of heart attack they might have had . they 'd be made to lie down in bed to prevent their heart from working to hard . thus , minimizing their heart muscles oxygen demand . they might be given supplemental oxygen , if it turned out that they were n't carrying enough oxygen in their blood stream . and they might be given morphine and that 's to reduce the amount of chest pain that they 're feeling . and to also reduce the amount of anxiety that they might be feeling . and hopefully by doing that , by reducing their anxiety they 'd reduce their heart rate and even further reduce the amount of oxygen that their heart needed . really importantly , they 'd be given aspirin too . and the aspirin would reduce the development of the clot that might be causing their symptoms , that might be causing their myocardial infarct . this aspirin is actually one of the most important interventions in reducing mortality in patients with all forms of acute coronary syndrome . okay , so all that stuff happens right away on an immediate basis . then we have to think about sort of getting rid of that clot that caused their heart attack . and allowing blood to flow back into that area that was deprived of blood . so getting rid of that clot and allowing blood back into that part of the heart is called reperfusion . and that 's the next goal . if a patient comes in and the ecg trace has determined that they have a stemi , an st elevation myocardial infarct and they presented to the hospital within about two hours of the onset of their symptoms . they might be given a medication to break down their clot , in a process called thrombolysis , or thrombolysis . thrombo refers to the blood clot and lysis refers to break down . this is actually what 's being referred to when you hear of clot busters . unfortunately , no relation to ghostbusters . so if this mediation 's given early enough , there 's a really high chance of restoring blood flow to the damaged part of the heart . and that actually really reduces the tissue damage that the heart would experience . again , just to reiterate this is only for patients with stemi 's , not unstable angina or n stemi 's . and that 's because the type of clots that are being busted up with clot busters , they 're only found in stemi 's and not in n stemi 's . so everything that we 've talked is really part of the acute management of someone who presents with an acute coronary syndrome . so all this stuff will happen in the hospital right away . then the patient will be put on medications at the hospital that they 'll then have to continue for the rest of their life . and the reason for this is because taking these medications for the rest of their lives , this has been shown in clinical trials to reduce mortality , so that 's the rate of death attributed to having had a previous heart attack . among other positive affects , they 've also been shown to reduce the chance of you having another heart attack . so again , these are medications that you 'll start in hospital after the sort of acute management . and then you 'll need to be on them indefinitely . so what are these drugs ? well , there 's drugs that try to restore that oxygen supply and demand balance . so drugs like beta blockers , beta blockers work by making the heart beat slower , so fewer beats per minute . and it also makes the heart beat with a reduced force . so over all this reduces the heart 's oxygen demand , because if the muscles not working as hard it needs less oxygen . another group of drugs you might get are nitrates . nitrates are vasodilators , so they open up your blood vessels . they dilate your blood vessels to improve your blood flow . you 'd also be given more medications to prevent the development of more clots that could block off your coronary vessels . so you 're already on aspirin , but you might also be given one called heparin or warfarin . and what these do is they prevent your clotting cascade from happening as easily . so they slow down the growth of , first of all the clot that might have caused your myocardial infarct , and second any further clots that you might develop down the track . you 'd probably be given a statin . statin 's reduce your blood cholesterol level . and so they decrease progression of atherosclerotic buildup in your coronary arteries . remember plaques are filled with cholesterol , so you 'd probably be given a statin to take indefinitely . finally , you might be given an ace inhibitor . ace inhibitor 's reduce blood pressure and actually studies have shown that ace inhibitors can reduce negative structural changes that can happen in your heart after myocardial infarct . so those are the major , sort of treatments with medications that you get after having a myocardial infarct .
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if a patient comes in and the ecg trace has determined that they have a stemi , an st elevation myocardial infarct and they presented to the hospital within about two hours of the onset of their symptoms . they might be given a medication to break down their clot , in a process called thrombolysis , or thrombolysis . thrombo refers to the blood clot and lysis refers to break down .
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i thought that angioplasty had replaced thrombolysis ... ?
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the main idea in treating myocardial infarcts is to limit the damage that happens to your heart , and to minimize complications that might crop up . the treatment has to address the clot that caused the myocardial infarct in the first place . and it has to restore the balance between the myocardial oxygen supply and demand . so there are some treatment aspects that are common to all of the types of acute coronary syndromes . but there 's some really important differences in the approach to patients who present with a stemi , or an st elevation myocardial infarct ; compared to unstable angina and n stemi , non-st elevation myocardial infarct . and we 'll talk about those . unstable angina and n stemi 's they 're usually treated in the same way . whereas stemi 's are treated a little bit differently because they 're more serious . so what happens ? well any patient who comes to a hospital with a suspected heart attack , with a suspected myocardial infarct , will first be admitted to an intensive care setting . they would be under continuous ecg monitoring for arrhythmias , or abnormal heart rhythms . remember the ecg would also give a really good idea of what type of heart attack they might have had . they 'd be made to lie down in bed to prevent their heart from working to hard . thus , minimizing their heart muscles oxygen demand . they might be given supplemental oxygen , if it turned out that they were n't carrying enough oxygen in their blood stream . and they might be given morphine and that 's to reduce the amount of chest pain that they 're feeling . and to also reduce the amount of anxiety that they might be feeling . and hopefully by doing that , by reducing their anxiety they 'd reduce their heart rate and even further reduce the amount of oxygen that their heart needed . really importantly , they 'd be given aspirin too . and the aspirin would reduce the development of the clot that might be causing their symptoms , that might be causing their myocardial infarct . this aspirin is actually one of the most important interventions in reducing mortality in patients with all forms of acute coronary syndrome . okay , so all that stuff happens right away on an immediate basis . then we have to think about sort of getting rid of that clot that caused their heart attack . and allowing blood to flow back into that area that was deprived of blood . so getting rid of that clot and allowing blood back into that part of the heart is called reperfusion . and that 's the next goal . if a patient comes in and the ecg trace has determined that they have a stemi , an st elevation myocardial infarct and they presented to the hospital within about two hours of the onset of their symptoms . they might be given a medication to break down their clot , in a process called thrombolysis , or thrombolysis . thrombo refers to the blood clot and lysis refers to break down . this is actually what 's being referred to when you hear of clot busters . unfortunately , no relation to ghostbusters . so if this mediation 's given early enough , there 's a really high chance of restoring blood flow to the damaged part of the heart . and that actually really reduces the tissue damage that the heart would experience . again , just to reiterate this is only for patients with stemi 's , not unstable angina or n stemi 's . and that 's because the type of clots that are being busted up with clot busters , they 're only found in stemi 's and not in n stemi 's . so everything that we 've talked is really part of the acute management of someone who presents with an acute coronary syndrome . so all this stuff will happen in the hospital right away . then the patient will be put on medications at the hospital that they 'll then have to continue for the rest of their life . and the reason for this is because taking these medications for the rest of their lives , this has been shown in clinical trials to reduce mortality , so that 's the rate of death attributed to having had a previous heart attack . among other positive affects , they 've also been shown to reduce the chance of you having another heart attack . so again , these are medications that you 'll start in hospital after the sort of acute management . and then you 'll need to be on them indefinitely . so what are these drugs ? well , there 's drugs that try to restore that oxygen supply and demand balance . so drugs like beta blockers , beta blockers work by making the heart beat slower , so fewer beats per minute . and it also makes the heart beat with a reduced force . so over all this reduces the heart 's oxygen demand , because if the muscles not working as hard it needs less oxygen . another group of drugs you might get are nitrates . nitrates are vasodilators , so they open up your blood vessels . they dilate your blood vessels to improve your blood flow . you 'd also be given more medications to prevent the development of more clots that could block off your coronary vessels . so you 're already on aspirin , but you might also be given one called heparin or warfarin . and what these do is they prevent your clotting cascade from happening as easily . so they slow down the growth of , first of all the clot that might have caused your myocardial infarct , and second any further clots that you might develop down the track . you 'd probably be given a statin . statin 's reduce your blood cholesterol level . and so they decrease progression of atherosclerotic buildup in your coronary arteries . remember plaques are filled with cholesterol , so you 'd probably be given a statin to take indefinitely . finally , you might be given an ace inhibitor . ace inhibitor 's reduce blood pressure and actually studies have shown that ace inhibitors can reduce negative structural changes that can happen in your heart after myocardial infarct . so those are the major , sort of treatments with medications that you get after having a myocardial infarct .
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so there are some treatment aspects that are common to all of the types of acute coronary syndromes . but there 's some really important differences in the approach to patients who present with a stemi , or an st elevation myocardial infarct ; compared to unstable angina and n stemi , non-st elevation myocardial infarct . and we 'll talk about those .
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as a dentist should i operate on someone who has a history of myocardial infarct ?
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the main idea in treating myocardial infarcts is to limit the damage that happens to your heart , and to minimize complications that might crop up . the treatment has to address the clot that caused the myocardial infarct in the first place . and it has to restore the balance between the myocardial oxygen supply and demand . so there are some treatment aspects that are common to all of the types of acute coronary syndromes . but there 's some really important differences in the approach to patients who present with a stemi , or an st elevation myocardial infarct ; compared to unstable angina and n stemi , non-st elevation myocardial infarct . and we 'll talk about those . unstable angina and n stemi 's they 're usually treated in the same way . whereas stemi 's are treated a little bit differently because they 're more serious . so what happens ? well any patient who comes to a hospital with a suspected heart attack , with a suspected myocardial infarct , will first be admitted to an intensive care setting . they would be under continuous ecg monitoring for arrhythmias , or abnormal heart rhythms . remember the ecg would also give a really good idea of what type of heart attack they might have had . they 'd be made to lie down in bed to prevent their heart from working to hard . thus , minimizing their heart muscles oxygen demand . they might be given supplemental oxygen , if it turned out that they were n't carrying enough oxygen in their blood stream . and they might be given morphine and that 's to reduce the amount of chest pain that they 're feeling . and to also reduce the amount of anxiety that they might be feeling . and hopefully by doing that , by reducing their anxiety they 'd reduce their heart rate and even further reduce the amount of oxygen that their heart needed . really importantly , they 'd be given aspirin too . and the aspirin would reduce the development of the clot that might be causing their symptoms , that might be causing their myocardial infarct . this aspirin is actually one of the most important interventions in reducing mortality in patients with all forms of acute coronary syndrome . okay , so all that stuff happens right away on an immediate basis . then we have to think about sort of getting rid of that clot that caused their heart attack . and allowing blood to flow back into that area that was deprived of blood . so getting rid of that clot and allowing blood back into that part of the heart is called reperfusion . and that 's the next goal . if a patient comes in and the ecg trace has determined that they have a stemi , an st elevation myocardial infarct and they presented to the hospital within about two hours of the onset of their symptoms . they might be given a medication to break down their clot , in a process called thrombolysis , or thrombolysis . thrombo refers to the blood clot and lysis refers to break down . this is actually what 's being referred to when you hear of clot busters . unfortunately , no relation to ghostbusters . so if this mediation 's given early enough , there 's a really high chance of restoring blood flow to the damaged part of the heart . and that actually really reduces the tissue damage that the heart would experience . again , just to reiterate this is only for patients with stemi 's , not unstable angina or n stemi 's . and that 's because the type of clots that are being busted up with clot busters , they 're only found in stemi 's and not in n stemi 's . so everything that we 've talked is really part of the acute management of someone who presents with an acute coronary syndrome . so all this stuff will happen in the hospital right away . then the patient will be put on medications at the hospital that they 'll then have to continue for the rest of their life . and the reason for this is because taking these medications for the rest of their lives , this has been shown in clinical trials to reduce mortality , so that 's the rate of death attributed to having had a previous heart attack . among other positive affects , they 've also been shown to reduce the chance of you having another heart attack . so again , these are medications that you 'll start in hospital after the sort of acute management . and then you 'll need to be on them indefinitely . so what are these drugs ? well , there 's drugs that try to restore that oxygen supply and demand balance . so drugs like beta blockers , beta blockers work by making the heart beat slower , so fewer beats per minute . and it also makes the heart beat with a reduced force . so over all this reduces the heart 's oxygen demand , because if the muscles not working as hard it needs less oxygen . another group of drugs you might get are nitrates . nitrates are vasodilators , so they open up your blood vessels . they dilate your blood vessels to improve your blood flow . you 'd also be given more medications to prevent the development of more clots that could block off your coronary vessels . so you 're already on aspirin , but you might also be given one called heparin or warfarin . and what these do is they prevent your clotting cascade from happening as easily . so they slow down the growth of , first of all the clot that might have caused your myocardial infarct , and second any further clots that you might develop down the track . you 'd probably be given a statin . statin 's reduce your blood cholesterol level . and so they decrease progression of atherosclerotic buildup in your coronary arteries . remember plaques are filled with cholesterol , so you 'd probably be given a statin to take indefinitely . finally , you might be given an ace inhibitor . ace inhibitor 's reduce blood pressure and actually studies have shown that ace inhibitors can reduce negative structural changes that can happen in your heart after myocardial infarct . so those are the major , sort of treatments with medications that you get after having a myocardial infarct .
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well , there 's drugs that try to restore that oxygen supply and demand balance . so drugs like beta blockers , beta blockers work by making the heart beat slower , so fewer beats per minute . and it also makes the heart beat with a reduced force .
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would it be beneficial for a patient to take calcium channel blockers ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length .
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can someone explain to me what a rhombus is ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way .
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so what if the quadrilateral only indicated one pair of parallel sides and one pair of congruent sides ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse .
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( additional information is missing ) is it possible to find out wether or not the quadrilateral is a parallelogram or not ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc .
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is n't the second theorem just a converse of the first theorem ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that .
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how do you identify the corresponding parts and then label ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent .
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is there any difference between the two symbols if we use them to indicate that the measures are equal , like in this case ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time .
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is aaa and aas is appropraite property for prooving that the triangles are congruent ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc .
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how can we say that angle abd=bdc in the first instance ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting .
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2 , why does sal put a line through the parallelogram ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this .
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since alternate interior angles are used to find if the lines are parallel , can i still use the converse ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way .
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how would you prove that a quadrilateral is a parallelogram if the opposite sides are congruent and you did n't know that they were parallel ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse .
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in a parallelogram , is there an axis of symmetry ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time .
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does cpctc ( corresponding parts of conguent triangles are congruent ) include angles or can it only prove sides ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles .
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what does the equal sign with the ~ mark on top mean ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc .
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is there a reason why the first quadrilateral has arrows and the second one has little lines ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles .
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wait , is there a angle-angle-angle theorem or postulate of congruency that can prove triangles congruent ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time .
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what would be the theorem for the opposite angles being congruent ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done .
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how do you know that the angles are alternate in the second diagram before knowing that they are parrallel ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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that 's the hardest part . draw it . that 's pretty good .
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is there a reason ( in a 2 column proof ) for being able to draw a transversal in a parallelogram that would spilt the parallelogram into two triangles ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse .
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i want to ask that why is square a parallelogram ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions .
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i ask myself this constantly because i do n't see it anywhere , if you are trying to prove a quadrilateral is a parallelogram given that opposite sides are parallel , does that means it 's a parallelogram ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this .
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when do you know when to have one transversal or two transversals ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time .
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how would you show that if a quadrilateral has opposite angles congruent , the quadrilateral is a parallelogram ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions .
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how do you find the exterior length and width of a polygon ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that .
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what is the relationship between corresponding sides of a rhombus ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time .
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my question is , when speaking of the congruence of angles , is it necessary to specify the vertices of the two angles in an order that reflects their location in the corresponding triangles of which they are a part ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc .
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i noticed 4 that lines a , b and c in the first parallelogram are connected to d and in the second parallelogram a , b and d are connected to c. dose this mean there from the same point or dose the lines connecting them make it impossible ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc .
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do you know what these proofs stand for ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc .
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by which axiom is abd and bdc equal ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time .
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what is the definition of congruent angles ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc .
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how is angle < abd congruent to < bdc ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time .
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can two angles be congruent ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length .
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what 's the total number of diagonals in a 35-sided polygon ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc .
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so if we were to draw a diagonal in a given diagram and our reason would be it is a transversal of parallel lines , that would be fine ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way .
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can anybody think of a counterexample to disprove that a figure is a parallelogram only if opposite sides are congruent ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right .
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what is use of asa congruency ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way .
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what seems to be true about the lengths of the opposite sides of the parallelograms ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic .
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how would you prove parallel if the angles are given but not the sides ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time .
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could you not use cpctc or corresponding parts of congruent triangles are congruent ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time .
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is corresponding angle of congruent triangles the same thing as corresponding parts of congruent triangles are congruent ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle .
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what is the theorem for the two triangles ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time .
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angles congurence theorem and say the triangles are congruent by asa like in the first proof ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way .
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if sal meant opposite sides of a parallelogram then its already implied that the opposite sides are parallel , or is he referring to two pairs of opposite sides that are only congruent to their opposite side ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time .
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would n't ou be able to say `` congruent parts of congruent triangles are congruent '' ( cpctc/cpct ) instead of corresponding sides of congruent triangles are congruent ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way .
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for the first question would n't the proof prove the theorem that states opposite sides of a parallelogram are congruent ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time .
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for the second question , would n't the proof prove the theorem that states if both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting .
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why is the line sloppy ?
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what we 're going to prove in this video is a couple of fairly straightforward parallelogram-related proofs . and this first one , we 're going to say , hey , if we have this parallelogram abcd , let 's prove that the opposite sides have the same length . so prove that ab is equal to dc and that ad is equal to bc . so let me draw a diagonal here . and this diagonal , depending on how you view it , is intersecting two sets of parallel lines . so you could also consider it to be a transversal . actually , let me draw it a little bit neater than that . i can do a better job . nope . that 's not any better . that is about as good as i can do . so if we view db , this diagonal db -- we can view it as a transversal for the parallel lines ab and dc . and if you view it that way , you can pick out that angle abd is going to be congruent -- so angle abd . that 's that angle right there -- is going to be congruent to angle bdc , because they are alternate interior angles . you have a transversal -- parallel lines . so we know that angle abd is going to be congruent to angle bdc . now , you could also view this diagonal , db -- you could view it as a transversal of these two parallel lines , of the other pair of parallel lines , ad and bc . and if you look at it that way , then you immediately see that angle dbc right over here is going to be congruent to angle adb for the exact same reason . they are alternate interior angles of a transversal intersecting these two parallel lines . so i could write this . this is alternate interior angles are congruent when you have a transversal intersecting two parallel lines . and we also see that both of these triangles , triangle adb and triangle cdb , both share this side over here . it 's obviously equal to itself . now , why is this useful ? well , you might realize that we 've just shown that both of these triangles , they have this pink angle . then they have this side in common . and then they have the green angle . pink angle , side in common , and then the green angle . so we 've just shown by angle-side-angle that these two triangles are congruent . so let me write this down . we have shown that triangle -- i 'll go from non-labeled to pink to green -- adb is congruent to triangle -- non-labeled to pink to green -- cbd . and this comes out of angle-side-angle congruency . well , what does that do for us ? well , if two triangles are congruent , then all of the corresponding features of the two triangles are going to be congruent . in particular , side dc on this bottom triangle corresponds to side ba on that top triangle . so they need to be congruent . so we get dc is going to be equal to ba . and that 's because they are corresponding sides of congruent triangles . so this is going to be equal to that . and by that exact same logic , ad corresponds to cb . ad is equal to cb . and for the exact same reason -- corresponding sides of congruent triangles . and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse . so let 's draw a diagonal here , since we know a lot about triangles . so let me draw . there we go . that 's the hardest part . draw it . that 's pretty good . all right . so we obviously know that cb is going to be equal to itself . so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . we 've split this quadrilateral into two triangles , triangle acb and triangle dbc . and notice , all three sides of these two triangles are equal to each other . so we know by side-side-side that they are congruent . so we know that triangle a -- and we 're starting at a , and then i 'm going to the one-hash side . so acb is congruent to triangle dbc . and this is by side-side-side congruency . well , what does that do for us ? well , it tells us that all of the corresponding angles are going to be congruent . so for example , angle abc is going to be -- so let me mark that . you can say abc is going to be congruent to dcb . and you could say , by corresponding angles congruent of congruent triangles . i 'm just using some shorthand here to save some time . so abc is going to be congruent to dcb , so these two angles are going to be congruent . well , this is interesting , because here you have a line . and it 's intersecting ab and cd . and we clearly see that these things that could be alternate interior angles are congruent . and because we have these congruent alternate interior angles , we know that ab must be parallel to cd . so this must be parallel to that . so we know that ab is parallel to cd by alternate interior angles of a transversal intersecting parallel lines . now , we can use that exact same logic . we also know that angle -- let me get this right . angle acb is congruent to angle dbc . and we know that by corresponding angles congruent of congruent triangles . so we 're just saying this angle is equal to that angle . well , once again , these could be alternate interior angles . they look like they could be . this is a transversal . and here 's two lines here , which we 're not sure whether they 're parallel . but because the alternate interior angles are congruent , we know that they are parallel . so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . so what we 've done is -- it 's interesting . we 've shown if you have a parallelogram , opposite sides have the same length . and if opposite sides have the same length , then you have a parallelogram . and so we 've actually proven it in both directions . and so we can actually make what you call an `` if and only if '' statement . you could say opposite sides of a quadrilateral are parallel if and only if their lengths are equal . and you say if and only if . so if they are parallel , then you could say their lengths are equal . and only if their lengths are equal are they parallel . we 've proven it in both directions .
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let 's say that we have some type of a quadrilateral , and we know that the opposite sides are congruent . can we prove to ourselves that this is a parallelogram ? well , it 's kind of the same proof in reverse .
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why is it that a parallelogram is always congruent but then how can you tell the difference between a parallelogram and a rhombus ?
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farming , as we now associate the word , has been around for about 7,000 to 10,000 years . and when we think of farming , we imagine a farmer planting seeds , and later harvesting the crops . or maybe having cattle that they can allow to graze , and then using that cattle for either meat , or milk , or wool . but there 's actually a different type of farming that predates this association with i guess what we could call the traditional form of farming . and it predates it by several tens of thousands of years . and we believe that it started with the original inhabitants of australia . and what they did is -- and this is why we call it farming -- and because if you think about farming in the most general sense , it 's really humans using technology to manipulate their environment so it becomes more suitable for humans . so it becomes more suitable for things that humans might want to eat , or get milk from , or whatever . and this type of farming is called firestick farming . and i think you can already imagine what it might involve . it involves using fire , which is really a form of technology -- or it can be a form of technology -- using fire to make the environment more suitable for human activity . and so what the original australians did -- the indigenous australians , or sometimes referred to as the aboriginal australians . and if you 're wondering where the word aboriginal comes from , you might recognize some parts of it . original -- you know what that means . the first things . the things that were there from the beginning . and then you have ab , which is latin for from . so this is literally from the beginning . so when you say aboriginal australians , you 're really saying the australians that were there from the beginning . and so what they would do is , is that we believe if you go back 50,000 or 60,000 years before the first aboriginal australians settled australia , australia had much more forest . it still has forest . this is a modern picture , obviously , of an australian forest . but what they did is that they set up controlled burns . and what these controlled burns did is that they cleared away a lot of the forest . they cleared away a lot of the brush that 's over here , and it made it much more suitable for grassland to develop . and the reason why they liked grassland -- so let 's make a little cycle here of what they did . so they have controlled burns . controlled fires . those controlled fires helped promote grassland . and then once you have grassland , that made the environment more suitable for animals that the original human settlers could essentially live off of . that they could hunt , that they could potentially eat their meat . and so , for example , things like kangaroos . and these supported the human population , which obviously , would then do the controlled burns . and you see here -- so we could have started off with something like this . someone provides a controlled burn . and they were actually pretty scientific about how they did it . they would n't just go at the end of summer , when everything was hot , and ready to just blow up , and then start a fire that they could n't control . they would often do these in seasons knowing that it had a certain level of moisture in the air , it was n't too hot . and to a large degree , by doing these controlled burns , not only did it provide an environment -- kind of do this firestick farming -- not only did it provide an environment that was suitable for things like kangaroos , some type of things that humans could eat -- but it also prevented major fires . and you still see forest rangers doing this type of thing . and there 's some reason to believe that what the original australians did , on some level , was more nuanced and more fine-tuned than even what we do , in a modern sense , in controlled burns . so these controlled fires also prevented major uncontrollable fires . because what happens is if you do n't have these controlled fires , then you have brush building up , year after year after year . you have stuff building up . and then , when the fires do occur , the uncontrolled fires are less likely to be started during the winter , when the air is cool or when there might be some moisture . they 're more likely to occur in the dry season . so you have all this stuff build up . and then when the fire does happen , it happens in the driest season . and then what happens with all of the stuff built up in the dry season , it just becomes uncontrollable . one of the byproducts -- or actually there are several byproducts of this firestick farming -- we believe , is a lot of the grassland in australia now might have been more forested before . and even when the first european settlers came in the late 1700s , they were kind of surprised when they went into what is now sydney harbor and they said , wow , look at all the grassland here . it almost looks like park space . and then they would let their sheep graze there . and they were surprised -- because they had driven out the original inhabitants . and then they were surprised when forests just started to grow up in that grassland . and it was because the original australians were actually controlling that forest growth to make it more inhabitable for things like kangaroos . and then when the english settlers came , they started to have their sheep graze in those grasslands . and it also was responsible for the disappearance , we think , of many major -- i guess , for lack of a better word -- megafauna . so really large animals that inhabited australia , for really millions of years , until humans showed up . and this is one of them . it 's just neat to look at them . this is called diprotodon optatum . or , another way to think of it , the giant wombat . and there 's fossils of the giant wombat around 40,000 , 50,000 years ago . but they disappeared with humans showing up . and there 's multiple ways that you can think about why they disappeared . they might have -- and this is probably the case -- they might have been more dependent on the forest habitat . or this was a more favorable habitat for them than the grasslands . maybe because they ate leaves that were high up . or another thing is , once the forest habitat goes away , they were actually also easier to hunt down . or either way you think about it , they might have just been hunted by humans . but we do see that with humans coming to the australian continent , you start to see the disappearance -- and this is n't the only one -- but there were several major species of megafauna , of super large animals , that disappeared at that time period .
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and if you 're wondering where the word aboriginal comes from , you might recognize some parts of it . original -- you know what that means . the first things . the things that were there from the beginning .
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do we know how the aboriginals first got to australia ?
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farming , as we now associate the word , has been around for about 7,000 to 10,000 years . and when we think of farming , we imagine a farmer planting seeds , and later harvesting the crops . or maybe having cattle that they can allow to graze , and then using that cattle for either meat , or milk , or wool . but there 's actually a different type of farming that predates this association with i guess what we could call the traditional form of farming . and it predates it by several tens of thousands of years . and we believe that it started with the original inhabitants of australia . and what they did is -- and this is why we call it farming -- and because if you think about farming in the most general sense , it 's really humans using technology to manipulate their environment so it becomes more suitable for humans . so it becomes more suitable for things that humans might want to eat , or get milk from , or whatever . and this type of farming is called firestick farming . and i think you can already imagine what it might involve . it involves using fire , which is really a form of technology -- or it can be a form of technology -- using fire to make the environment more suitable for human activity . and so what the original australians did -- the indigenous australians , or sometimes referred to as the aboriginal australians . and if you 're wondering where the word aboriginal comes from , you might recognize some parts of it . original -- you know what that means . the first things . the things that were there from the beginning . and then you have ab , which is latin for from . so this is literally from the beginning . so when you say aboriginal australians , you 're really saying the australians that were there from the beginning . and so what they would do is , is that we believe if you go back 50,000 or 60,000 years before the first aboriginal australians settled australia , australia had much more forest . it still has forest . this is a modern picture , obviously , of an australian forest . but what they did is that they set up controlled burns . and what these controlled burns did is that they cleared away a lot of the forest . they cleared away a lot of the brush that 's over here , and it made it much more suitable for grassland to develop . and the reason why they liked grassland -- so let 's make a little cycle here of what they did . so they have controlled burns . controlled fires . those controlled fires helped promote grassland . and then once you have grassland , that made the environment more suitable for animals that the original human settlers could essentially live off of . that they could hunt , that they could potentially eat their meat . and so , for example , things like kangaroos . and these supported the human population , which obviously , would then do the controlled burns . and you see here -- so we could have started off with something like this . someone provides a controlled burn . and they were actually pretty scientific about how they did it . they would n't just go at the end of summer , when everything was hot , and ready to just blow up , and then start a fire that they could n't control . they would often do these in seasons knowing that it had a certain level of moisture in the air , it was n't too hot . and to a large degree , by doing these controlled burns , not only did it provide an environment -- kind of do this firestick farming -- not only did it provide an environment that was suitable for things like kangaroos , some type of things that humans could eat -- but it also prevented major fires . and you still see forest rangers doing this type of thing . and there 's some reason to believe that what the original australians did , on some level , was more nuanced and more fine-tuned than even what we do , in a modern sense , in controlled burns . so these controlled fires also prevented major uncontrollable fires . because what happens is if you do n't have these controlled fires , then you have brush building up , year after year after year . you have stuff building up . and then , when the fires do occur , the uncontrolled fires are less likely to be started during the winter , when the air is cool or when there might be some moisture . they 're more likely to occur in the dry season . so you have all this stuff build up . and then when the fire does happen , it happens in the driest season . and then what happens with all of the stuff built up in the dry season , it just becomes uncontrollable . one of the byproducts -- or actually there are several byproducts of this firestick farming -- we believe , is a lot of the grassland in australia now might have been more forested before . and even when the first european settlers came in the late 1700s , they were kind of surprised when they went into what is now sydney harbor and they said , wow , look at all the grassland here . it almost looks like park space . and then they would let their sheep graze there . and they were surprised -- because they had driven out the original inhabitants . and then they were surprised when forests just started to grow up in that grassland . and it was because the original australians were actually controlling that forest growth to make it more inhabitable for things like kangaroos . and then when the english settlers came , they started to have their sheep graze in those grasslands . and it also was responsible for the disappearance , we think , of many major -- i guess , for lack of a better word -- megafauna . so really large animals that inhabited australia , for really millions of years , until humans showed up . and this is one of them . it 's just neat to look at them . this is called diprotodon optatum . or , another way to think of it , the giant wombat . and there 's fossils of the giant wombat around 40,000 , 50,000 years ago . but they disappeared with humans showing up . and there 's multiple ways that you can think about why they disappeared . they might have -- and this is probably the case -- they might have been more dependent on the forest habitat . or this was a more favorable habitat for them than the grasslands . maybe because they ate leaves that were high up . or another thing is , once the forest habitat goes away , they were actually also easier to hunt down . or either way you think about it , they might have just been hunted by humans . but we do see that with humans coming to the australian continent , you start to see the disappearance -- and this is n't the only one -- but there were several major species of megafauna , of super large animals , that disappeared at that time period .
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it almost looks like park space . and then they would let their sheep graze there . and they were surprised -- because they had driven out the original inhabitants .
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i wonder why people would kill giant animals if they 're such a wonder today ?
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farming , as we now associate the word , has been around for about 7,000 to 10,000 years . and when we think of farming , we imagine a farmer planting seeds , and later harvesting the crops . or maybe having cattle that they can allow to graze , and then using that cattle for either meat , or milk , or wool . but there 's actually a different type of farming that predates this association with i guess what we could call the traditional form of farming . and it predates it by several tens of thousands of years . and we believe that it started with the original inhabitants of australia . and what they did is -- and this is why we call it farming -- and because if you think about farming in the most general sense , it 's really humans using technology to manipulate their environment so it becomes more suitable for humans . so it becomes more suitable for things that humans might want to eat , or get milk from , or whatever . and this type of farming is called firestick farming . and i think you can already imagine what it might involve . it involves using fire , which is really a form of technology -- or it can be a form of technology -- using fire to make the environment more suitable for human activity . and so what the original australians did -- the indigenous australians , or sometimes referred to as the aboriginal australians . and if you 're wondering where the word aboriginal comes from , you might recognize some parts of it . original -- you know what that means . the first things . the things that were there from the beginning . and then you have ab , which is latin for from . so this is literally from the beginning . so when you say aboriginal australians , you 're really saying the australians that were there from the beginning . and so what they would do is , is that we believe if you go back 50,000 or 60,000 years before the first aboriginal australians settled australia , australia had much more forest . it still has forest . this is a modern picture , obviously , of an australian forest . but what they did is that they set up controlled burns . and what these controlled burns did is that they cleared away a lot of the forest . they cleared away a lot of the brush that 's over here , and it made it much more suitable for grassland to develop . and the reason why they liked grassland -- so let 's make a little cycle here of what they did . so they have controlled burns . controlled fires . those controlled fires helped promote grassland . and then once you have grassland , that made the environment more suitable for animals that the original human settlers could essentially live off of . that they could hunt , that they could potentially eat their meat . and so , for example , things like kangaroos . and these supported the human population , which obviously , would then do the controlled burns . and you see here -- so we could have started off with something like this . someone provides a controlled burn . and they were actually pretty scientific about how they did it . they would n't just go at the end of summer , when everything was hot , and ready to just blow up , and then start a fire that they could n't control . they would often do these in seasons knowing that it had a certain level of moisture in the air , it was n't too hot . and to a large degree , by doing these controlled burns , not only did it provide an environment -- kind of do this firestick farming -- not only did it provide an environment that was suitable for things like kangaroos , some type of things that humans could eat -- but it also prevented major fires . and you still see forest rangers doing this type of thing . and there 's some reason to believe that what the original australians did , on some level , was more nuanced and more fine-tuned than even what we do , in a modern sense , in controlled burns . so these controlled fires also prevented major uncontrollable fires . because what happens is if you do n't have these controlled fires , then you have brush building up , year after year after year . you have stuff building up . and then , when the fires do occur , the uncontrolled fires are less likely to be started during the winter , when the air is cool or when there might be some moisture . they 're more likely to occur in the dry season . so you have all this stuff build up . and then when the fire does happen , it happens in the driest season . and then what happens with all of the stuff built up in the dry season , it just becomes uncontrollable . one of the byproducts -- or actually there are several byproducts of this firestick farming -- we believe , is a lot of the grassland in australia now might have been more forested before . and even when the first european settlers came in the late 1700s , they were kind of surprised when they went into what is now sydney harbor and they said , wow , look at all the grassland here . it almost looks like park space . and then they would let their sheep graze there . and they were surprised -- because they had driven out the original inhabitants . and then they were surprised when forests just started to grow up in that grassland . and it was because the original australians were actually controlling that forest growth to make it more inhabitable for things like kangaroos . and then when the english settlers came , they started to have their sheep graze in those grasslands . and it also was responsible for the disappearance , we think , of many major -- i guess , for lack of a better word -- megafauna . so really large animals that inhabited australia , for really millions of years , until humans showed up . and this is one of them . it 's just neat to look at them . this is called diprotodon optatum . or , another way to think of it , the giant wombat . and there 's fossils of the giant wombat around 40,000 , 50,000 years ago . but they disappeared with humans showing up . and there 's multiple ways that you can think about why they disappeared . they might have -- and this is probably the case -- they might have been more dependent on the forest habitat . or this was a more favorable habitat for them than the grasslands . maybe because they ate leaves that were high up . or another thing is , once the forest habitat goes away , they were actually also easier to hunt down . or either way you think about it , they might have just been hunted by humans . but we do see that with humans coming to the australian continent , you start to see the disappearance -- and this is n't the only one -- but there were several major species of megafauna , of super large animals , that disappeared at that time period .
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so they have controlled burns . controlled fires . those controlled fires helped promote grassland .
|
what do modern forest rangers do controlled fires for ?
|
farming , as we now associate the word , has been around for about 7,000 to 10,000 years . and when we think of farming , we imagine a farmer planting seeds , and later harvesting the crops . or maybe having cattle that they can allow to graze , and then using that cattle for either meat , or milk , or wool . but there 's actually a different type of farming that predates this association with i guess what we could call the traditional form of farming . and it predates it by several tens of thousands of years . and we believe that it started with the original inhabitants of australia . and what they did is -- and this is why we call it farming -- and because if you think about farming in the most general sense , it 's really humans using technology to manipulate their environment so it becomes more suitable for humans . so it becomes more suitable for things that humans might want to eat , or get milk from , or whatever . and this type of farming is called firestick farming . and i think you can already imagine what it might involve . it involves using fire , which is really a form of technology -- or it can be a form of technology -- using fire to make the environment more suitable for human activity . and so what the original australians did -- the indigenous australians , or sometimes referred to as the aboriginal australians . and if you 're wondering where the word aboriginal comes from , you might recognize some parts of it . original -- you know what that means . the first things . the things that were there from the beginning . and then you have ab , which is latin for from . so this is literally from the beginning . so when you say aboriginal australians , you 're really saying the australians that were there from the beginning . and so what they would do is , is that we believe if you go back 50,000 or 60,000 years before the first aboriginal australians settled australia , australia had much more forest . it still has forest . this is a modern picture , obviously , of an australian forest . but what they did is that they set up controlled burns . and what these controlled burns did is that they cleared away a lot of the forest . they cleared away a lot of the brush that 's over here , and it made it much more suitable for grassland to develop . and the reason why they liked grassland -- so let 's make a little cycle here of what they did . so they have controlled burns . controlled fires . those controlled fires helped promote grassland . and then once you have grassland , that made the environment more suitable for animals that the original human settlers could essentially live off of . that they could hunt , that they could potentially eat their meat . and so , for example , things like kangaroos . and these supported the human population , which obviously , would then do the controlled burns . and you see here -- so we could have started off with something like this . someone provides a controlled burn . and they were actually pretty scientific about how they did it . they would n't just go at the end of summer , when everything was hot , and ready to just blow up , and then start a fire that they could n't control . they would often do these in seasons knowing that it had a certain level of moisture in the air , it was n't too hot . and to a large degree , by doing these controlled burns , not only did it provide an environment -- kind of do this firestick farming -- not only did it provide an environment that was suitable for things like kangaroos , some type of things that humans could eat -- but it also prevented major fires . and you still see forest rangers doing this type of thing . and there 's some reason to believe that what the original australians did , on some level , was more nuanced and more fine-tuned than even what we do , in a modern sense , in controlled burns . so these controlled fires also prevented major uncontrollable fires . because what happens is if you do n't have these controlled fires , then you have brush building up , year after year after year . you have stuff building up . and then , when the fires do occur , the uncontrolled fires are less likely to be started during the winter , when the air is cool or when there might be some moisture . they 're more likely to occur in the dry season . so you have all this stuff build up . and then when the fire does happen , it happens in the driest season . and then what happens with all of the stuff built up in the dry season , it just becomes uncontrollable . one of the byproducts -- or actually there are several byproducts of this firestick farming -- we believe , is a lot of the grassland in australia now might have been more forested before . and even when the first european settlers came in the late 1700s , they were kind of surprised when they went into what is now sydney harbor and they said , wow , look at all the grassland here . it almost looks like park space . and then they would let their sheep graze there . and they were surprised -- because they had driven out the original inhabitants . and then they were surprised when forests just started to grow up in that grassland . and it was because the original australians were actually controlling that forest growth to make it more inhabitable for things like kangaroos . and then when the english settlers came , they started to have their sheep graze in those grasslands . and it also was responsible for the disappearance , we think , of many major -- i guess , for lack of a better word -- megafauna . so really large animals that inhabited australia , for really millions of years , until humans showed up . and this is one of them . it 's just neat to look at them . this is called diprotodon optatum . or , another way to think of it , the giant wombat . and there 's fossils of the giant wombat around 40,000 , 50,000 years ago . but they disappeared with humans showing up . and there 's multiple ways that you can think about why they disappeared . they might have -- and this is probably the case -- they might have been more dependent on the forest habitat . or this was a more favorable habitat for them than the grasslands . maybe because they ate leaves that were high up . or another thing is , once the forest habitat goes away , they were actually also easier to hunt down . or either way you think about it , they might have just been hunted by humans . but we do see that with humans coming to the australian continent , you start to see the disappearance -- and this is n't the only one -- but there were several major species of megafauna , of super large animals , that disappeared at that time period .
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so they have controlled burns . controlled fires . those controlled fires helped promote grassland .
|
and why would people set fires on their lands ?
|
farming , as we now associate the word , has been around for about 7,000 to 10,000 years . and when we think of farming , we imagine a farmer planting seeds , and later harvesting the crops . or maybe having cattle that they can allow to graze , and then using that cattle for either meat , or milk , or wool . but there 's actually a different type of farming that predates this association with i guess what we could call the traditional form of farming . and it predates it by several tens of thousands of years . and we believe that it started with the original inhabitants of australia . and what they did is -- and this is why we call it farming -- and because if you think about farming in the most general sense , it 's really humans using technology to manipulate their environment so it becomes more suitable for humans . so it becomes more suitable for things that humans might want to eat , or get milk from , or whatever . and this type of farming is called firestick farming . and i think you can already imagine what it might involve . it involves using fire , which is really a form of technology -- or it can be a form of technology -- using fire to make the environment more suitable for human activity . and so what the original australians did -- the indigenous australians , or sometimes referred to as the aboriginal australians . and if you 're wondering where the word aboriginal comes from , you might recognize some parts of it . original -- you know what that means . the first things . the things that were there from the beginning . and then you have ab , which is latin for from . so this is literally from the beginning . so when you say aboriginal australians , you 're really saying the australians that were there from the beginning . and so what they would do is , is that we believe if you go back 50,000 or 60,000 years before the first aboriginal australians settled australia , australia had much more forest . it still has forest . this is a modern picture , obviously , of an australian forest . but what they did is that they set up controlled burns . and what these controlled burns did is that they cleared away a lot of the forest . they cleared away a lot of the brush that 's over here , and it made it much more suitable for grassland to develop . and the reason why they liked grassland -- so let 's make a little cycle here of what they did . so they have controlled burns . controlled fires . those controlled fires helped promote grassland . and then once you have grassland , that made the environment more suitable for animals that the original human settlers could essentially live off of . that they could hunt , that they could potentially eat their meat . and so , for example , things like kangaroos . and these supported the human population , which obviously , would then do the controlled burns . and you see here -- so we could have started off with something like this . someone provides a controlled burn . and they were actually pretty scientific about how they did it . they would n't just go at the end of summer , when everything was hot , and ready to just blow up , and then start a fire that they could n't control . they would often do these in seasons knowing that it had a certain level of moisture in the air , it was n't too hot . and to a large degree , by doing these controlled burns , not only did it provide an environment -- kind of do this firestick farming -- not only did it provide an environment that was suitable for things like kangaroos , some type of things that humans could eat -- but it also prevented major fires . and you still see forest rangers doing this type of thing . and there 's some reason to believe that what the original australians did , on some level , was more nuanced and more fine-tuned than even what we do , in a modern sense , in controlled burns . so these controlled fires also prevented major uncontrollable fires . because what happens is if you do n't have these controlled fires , then you have brush building up , year after year after year . you have stuff building up . and then , when the fires do occur , the uncontrolled fires are less likely to be started during the winter , when the air is cool or when there might be some moisture . they 're more likely to occur in the dry season . so you have all this stuff build up . and then when the fire does happen , it happens in the driest season . and then what happens with all of the stuff built up in the dry season , it just becomes uncontrollable . one of the byproducts -- or actually there are several byproducts of this firestick farming -- we believe , is a lot of the grassland in australia now might have been more forested before . and even when the first european settlers came in the late 1700s , they were kind of surprised when they went into what is now sydney harbor and they said , wow , look at all the grassland here . it almost looks like park space . and then they would let their sheep graze there . and they were surprised -- because they had driven out the original inhabitants . and then they were surprised when forests just started to grow up in that grassland . and it was because the original australians were actually controlling that forest growth to make it more inhabitable for things like kangaroos . and then when the english settlers came , they started to have their sheep graze in those grasslands . and it also was responsible for the disappearance , we think , of many major -- i guess , for lack of a better word -- megafauna . so really large animals that inhabited australia , for really millions of years , until humans showed up . and this is one of them . it 's just neat to look at them . this is called diprotodon optatum . or , another way to think of it , the giant wombat . and there 's fossils of the giant wombat around 40,000 , 50,000 years ago . but they disappeared with humans showing up . and there 's multiple ways that you can think about why they disappeared . they might have -- and this is probably the case -- they might have been more dependent on the forest habitat . or this was a more favorable habitat for them than the grasslands . maybe because they ate leaves that were high up . or another thing is , once the forest habitat goes away , they were actually also easier to hunt down . or either way you think about it , they might have just been hunted by humans . but we do see that with humans coming to the australian continent , you start to see the disappearance -- and this is n't the only one -- but there were several major species of megafauna , of super large animals , that disappeared at that time period .
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so they have controlled burns . controlled fires . those controlled fires helped promote grassland .
|
how were the fires controlled ?
|
farming , as we now associate the word , has been around for about 7,000 to 10,000 years . and when we think of farming , we imagine a farmer planting seeds , and later harvesting the crops . or maybe having cattle that they can allow to graze , and then using that cattle for either meat , or milk , or wool . but there 's actually a different type of farming that predates this association with i guess what we could call the traditional form of farming . and it predates it by several tens of thousands of years . and we believe that it started with the original inhabitants of australia . and what they did is -- and this is why we call it farming -- and because if you think about farming in the most general sense , it 's really humans using technology to manipulate their environment so it becomes more suitable for humans . so it becomes more suitable for things that humans might want to eat , or get milk from , or whatever . and this type of farming is called firestick farming . and i think you can already imagine what it might involve . it involves using fire , which is really a form of technology -- or it can be a form of technology -- using fire to make the environment more suitable for human activity . and so what the original australians did -- the indigenous australians , or sometimes referred to as the aboriginal australians . and if you 're wondering where the word aboriginal comes from , you might recognize some parts of it . original -- you know what that means . the first things . the things that were there from the beginning . and then you have ab , which is latin for from . so this is literally from the beginning . so when you say aboriginal australians , you 're really saying the australians that were there from the beginning . and so what they would do is , is that we believe if you go back 50,000 or 60,000 years before the first aboriginal australians settled australia , australia had much more forest . it still has forest . this is a modern picture , obviously , of an australian forest . but what they did is that they set up controlled burns . and what these controlled burns did is that they cleared away a lot of the forest . they cleared away a lot of the brush that 's over here , and it made it much more suitable for grassland to develop . and the reason why they liked grassland -- so let 's make a little cycle here of what they did . so they have controlled burns . controlled fires . those controlled fires helped promote grassland . and then once you have grassland , that made the environment more suitable for animals that the original human settlers could essentially live off of . that they could hunt , that they could potentially eat their meat . and so , for example , things like kangaroos . and these supported the human population , which obviously , would then do the controlled burns . and you see here -- so we could have started off with something like this . someone provides a controlled burn . and they were actually pretty scientific about how they did it . they would n't just go at the end of summer , when everything was hot , and ready to just blow up , and then start a fire that they could n't control . they would often do these in seasons knowing that it had a certain level of moisture in the air , it was n't too hot . and to a large degree , by doing these controlled burns , not only did it provide an environment -- kind of do this firestick farming -- not only did it provide an environment that was suitable for things like kangaroos , some type of things that humans could eat -- but it also prevented major fires . and you still see forest rangers doing this type of thing . and there 's some reason to believe that what the original australians did , on some level , was more nuanced and more fine-tuned than even what we do , in a modern sense , in controlled burns . so these controlled fires also prevented major uncontrollable fires . because what happens is if you do n't have these controlled fires , then you have brush building up , year after year after year . you have stuff building up . and then , when the fires do occur , the uncontrolled fires are less likely to be started during the winter , when the air is cool or when there might be some moisture . they 're more likely to occur in the dry season . so you have all this stuff build up . and then when the fire does happen , it happens in the driest season . and then what happens with all of the stuff built up in the dry season , it just becomes uncontrollable . one of the byproducts -- or actually there are several byproducts of this firestick farming -- we believe , is a lot of the grassland in australia now might have been more forested before . and even when the first european settlers came in the late 1700s , they were kind of surprised when they went into what is now sydney harbor and they said , wow , look at all the grassland here . it almost looks like park space . and then they would let their sheep graze there . and they were surprised -- because they had driven out the original inhabitants . and then they were surprised when forests just started to grow up in that grassland . and it was because the original australians were actually controlling that forest growth to make it more inhabitable for things like kangaroos . and then when the english settlers came , they started to have their sheep graze in those grasslands . and it also was responsible for the disappearance , we think , of many major -- i guess , for lack of a better word -- megafauna . so really large animals that inhabited australia , for really millions of years , until humans showed up . and this is one of them . it 's just neat to look at them . this is called diprotodon optatum . or , another way to think of it , the giant wombat . and there 's fossils of the giant wombat around 40,000 , 50,000 years ago . but they disappeared with humans showing up . and there 's multiple ways that you can think about why they disappeared . they might have -- and this is probably the case -- they might have been more dependent on the forest habitat . or this was a more favorable habitat for them than the grasslands . maybe because they ate leaves that were high up . or another thing is , once the forest habitat goes away , they were actually also easier to hunt down . or either way you think about it , they might have just been hunted by humans . but we do see that with humans coming to the australian continent , you start to see the disappearance -- and this is n't the only one -- but there were several major species of megafauna , of super large animals , that disappeared at that time period .
|
it involves using fire , which is really a form of technology -- or it can be a form of technology -- using fire to make the environment more suitable for human activity . and so what the original australians did -- the indigenous australians , or sometimes referred to as the aboriginal australians . and if you 're wondering where the word aboriginal comes from , you might recognize some parts of it .
|
how did we come to know that the aboriginal australians used scientific ways before starting a forest fire ?
|
farming , as we now associate the word , has been around for about 7,000 to 10,000 years . and when we think of farming , we imagine a farmer planting seeds , and later harvesting the crops . or maybe having cattle that they can allow to graze , and then using that cattle for either meat , or milk , or wool . but there 's actually a different type of farming that predates this association with i guess what we could call the traditional form of farming . and it predates it by several tens of thousands of years . and we believe that it started with the original inhabitants of australia . and what they did is -- and this is why we call it farming -- and because if you think about farming in the most general sense , it 's really humans using technology to manipulate their environment so it becomes more suitable for humans . so it becomes more suitable for things that humans might want to eat , or get milk from , or whatever . and this type of farming is called firestick farming . and i think you can already imagine what it might involve . it involves using fire , which is really a form of technology -- or it can be a form of technology -- using fire to make the environment more suitable for human activity . and so what the original australians did -- the indigenous australians , or sometimes referred to as the aboriginal australians . and if you 're wondering where the word aboriginal comes from , you might recognize some parts of it . original -- you know what that means . the first things . the things that were there from the beginning . and then you have ab , which is latin for from . so this is literally from the beginning . so when you say aboriginal australians , you 're really saying the australians that were there from the beginning . and so what they would do is , is that we believe if you go back 50,000 or 60,000 years before the first aboriginal australians settled australia , australia had much more forest . it still has forest . this is a modern picture , obviously , of an australian forest . but what they did is that they set up controlled burns . and what these controlled burns did is that they cleared away a lot of the forest . they cleared away a lot of the brush that 's over here , and it made it much more suitable for grassland to develop . and the reason why they liked grassland -- so let 's make a little cycle here of what they did . so they have controlled burns . controlled fires . those controlled fires helped promote grassland . and then once you have grassland , that made the environment more suitable for animals that the original human settlers could essentially live off of . that they could hunt , that they could potentially eat their meat . and so , for example , things like kangaroos . and these supported the human population , which obviously , would then do the controlled burns . and you see here -- so we could have started off with something like this . someone provides a controlled burn . and they were actually pretty scientific about how they did it . they would n't just go at the end of summer , when everything was hot , and ready to just blow up , and then start a fire that they could n't control . they would often do these in seasons knowing that it had a certain level of moisture in the air , it was n't too hot . and to a large degree , by doing these controlled burns , not only did it provide an environment -- kind of do this firestick farming -- not only did it provide an environment that was suitable for things like kangaroos , some type of things that humans could eat -- but it also prevented major fires . and you still see forest rangers doing this type of thing . and there 's some reason to believe that what the original australians did , on some level , was more nuanced and more fine-tuned than even what we do , in a modern sense , in controlled burns . so these controlled fires also prevented major uncontrollable fires . because what happens is if you do n't have these controlled fires , then you have brush building up , year after year after year . you have stuff building up . and then , when the fires do occur , the uncontrolled fires are less likely to be started during the winter , when the air is cool or when there might be some moisture . they 're more likely to occur in the dry season . so you have all this stuff build up . and then when the fire does happen , it happens in the driest season . and then what happens with all of the stuff built up in the dry season , it just becomes uncontrollable . one of the byproducts -- or actually there are several byproducts of this firestick farming -- we believe , is a lot of the grassland in australia now might have been more forested before . and even when the first european settlers came in the late 1700s , they were kind of surprised when they went into what is now sydney harbor and they said , wow , look at all the grassland here . it almost looks like park space . and then they would let their sheep graze there . and they were surprised -- because they had driven out the original inhabitants . and then they were surprised when forests just started to grow up in that grassland . and it was because the original australians were actually controlling that forest growth to make it more inhabitable for things like kangaroos . and then when the english settlers came , they started to have their sheep graze in those grasslands . and it also was responsible for the disappearance , we think , of many major -- i guess , for lack of a better word -- megafauna . so really large animals that inhabited australia , for really millions of years , until humans showed up . and this is one of them . it 's just neat to look at them . this is called diprotodon optatum . or , another way to think of it , the giant wombat . and there 's fossils of the giant wombat around 40,000 , 50,000 years ago . but they disappeared with humans showing up . and there 's multiple ways that you can think about why they disappeared . they might have -- and this is probably the case -- they might have been more dependent on the forest habitat . or this was a more favorable habitat for them than the grasslands . maybe because they ate leaves that were high up . or another thing is , once the forest habitat goes away , they were actually also easier to hunt down . or either way you think about it , they might have just been hunted by humans . but we do see that with humans coming to the australian continent , you start to see the disappearance -- and this is n't the only one -- but there were several major species of megafauna , of super large animals , that disappeared at that time period .
|
so it becomes more suitable for things that humans might want to eat , or get milk from , or whatever . and this type of farming is called firestick farming . and i think you can already imagine what it might involve .
|
there were no cameras when the aboriginal australians did firestick farming , so how did sal get that picture ?
|
farming , as we now associate the word , has been around for about 7,000 to 10,000 years . and when we think of farming , we imagine a farmer planting seeds , and later harvesting the crops . or maybe having cattle that they can allow to graze , and then using that cattle for either meat , or milk , or wool . but there 's actually a different type of farming that predates this association with i guess what we could call the traditional form of farming . and it predates it by several tens of thousands of years . and we believe that it started with the original inhabitants of australia . and what they did is -- and this is why we call it farming -- and because if you think about farming in the most general sense , it 's really humans using technology to manipulate their environment so it becomes more suitable for humans . so it becomes more suitable for things that humans might want to eat , or get milk from , or whatever . and this type of farming is called firestick farming . and i think you can already imagine what it might involve . it involves using fire , which is really a form of technology -- or it can be a form of technology -- using fire to make the environment more suitable for human activity . and so what the original australians did -- the indigenous australians , or sometimes referred to as the aboriginal australians . and if you 're wondering where the word aboriginal comes from , you might recognize some parts of it . original -- you know what that means . the first things . the things that were there from the beginning . and then you have ab , which is latin for from . so this is literally from the beginning . so when you say aboriginal australians , you 're really saying the australians that were there from the beginning . and so what they would do is , is that we believe if you go back 50,000 or 60,000 years before the first aboriginal australians settled australia , australia had much more forest . it still has forest . this is a modern picture , obviously , of an australian forest . but what they did is that they set up controlled burns . and what these controlled burns did is that they cleared away a lot of the forest . they cleared away a lot of the brush that 's over here , and it made it much more suitable for grassland to develop . and the reason why they liked grassland -- so let 's make a little cycle here of what they did . so they have controlled burns . controlled fires . those controlled fires helped promote grassland . and then once you have grassland , that made the environment more suitable for animals that the original human settlers could essentially live off of . that they could hunt , that they could potentially eat their meat . and so , for example , things like kangaroos . and these supported the human population , which obviously , would then do the controlled burns . and you see here -- so we could have started off with something like this . someone provides a controlled burn . and they were actually pretty scientific about how they did it . they would n't just go at the end of summer , when everything was hot , and ready to just blow up , and then start a fire that they could n't control . they would often do these in seasons knowing that it had a certain level of moisture in the air , it was n't too hot . and to a large degree , by doing these controlled burns , not only did it provide an environment -- kind of do this firestick farming -- not only did it provide an environment that was suitable for things like kangaroos , some type of things that humans could eat -- but it also prevented major fires . and you still see forest rangers doing this type of thing . and there 's some reason to believe that what the original australians did , on some level , was more nuanced and more fine-tuned than even what we do , in a modern sense , in controlled burns . so these controlled fires also prevented major uncontrollable fires . because what happens is if you do n't have these controlled fires , then you have brush building up , year after year after year . you have stuff building up . and then , when the fires do occur , the uncontrolled fires are less likely to be started during the winter , when the air is cool or when there might be some moisture . they 're more likely to occur in the dry season . so you have all this stuff build up . and then when the fire does happen , it happens in the driest season . and then what happens with all of the stuff built up in the dry season , it just becomes uncontrollable . one of the byproducts -- or actually there are several byproducts of this firestick farming -- we believe , is a lot of the grassland in australia now might have been more forested before . and even when the first european settlers came in the late 1700s , they were kind of surprised when they went into what is now sydney harbor and they said , wow , look at all the grassland here . it almost looks like park space . and then they would let their sheep graze there . and they were surprised -- because they had driven out the original inhabitants . and then they were surprised when forests just started to grow up in that grassland . and it was because the original australians were actually controlling that forest growth to make it more inhabitable for things like kangaroos . and then when the english settlers came , they started to have their sheep graze in those grasslands . and it also was responsible for the disappearance , we think , of many major -- i guess , for lack of a better word -- megafauna . so really large animals that inhabited australia , for really millions of years , until humans showed up . and this is one of them . it 's just neat to look at them . this is called diprotodon optatum . or , another way to think of it , the giant wombat . and there 's fossils of the giant wombat around 40,000 , 50,000 years ago . but they disappeared with humans showing up . and there 's multiple ways that you can think about why they disappeared . they might have -- and this is probably the case -- they might have been more dependent on the forest habitat . or this was a more favorable habitat for them than the grasslands . maybe because they ate leaves that were high up . or another thing is , once the forest habitat goes away , they were actually also easier to hunt down . or either way you think about it , they might have just been hunted by humans . but we do see that with humans coming to the australian continent , you start to see the disappearance -- and this is n't the only one -- but there were several major species of megafauna , of super large animals , that disappeared at that time period .
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and there 's fossils of the giant wombat around 40,000 , 50,000 years ago . but they disappeared with humans showing up . and there 's multiple ways that you can think about why they disappeared .
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what other kinds of species died out because humans came ?
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farming , as we now associate the word , has been around for about 7,000 to 10,000 years . and when we think of farming , we imagine a farmer planting seeds , and later harvesting the crops . or maybe having cattle that they can allow to graze , and then using that cattle for either meat , or milk , or wool . but there 's actually a different type of farming that predates this association with i guess what we could call the traditional form of farming . and it predates it by several tens of thousands of years . and we believe that it started with the original inhabitants of australia . and what they did is -- and this is why we call it farming -- and because if you think about farming in the most general sense , it 's really humans using technology to manipulate their environment so it becomes more suitable for humans . so it becomes more suitable for things that humans might want to eat , or get milk from , or whatever . and this type of farming is called firestick farming . and i think you can already imagine what it might involve . it involves using fire , which is really a form of technology -- or it can be a form of technology -- using fire to make the environment more suitable for human activity . and so what the original australians did -- the indigenous australians , or sometimes referred to as the aboriginal australians . and if you 're wondering where the word aboriginal comes from , you might recognize some parts of it . original -- you know what that means . the first things . the things that were there from the beginning . and then you have ab , which is latin for from . so this is literally from the beginning . so when you say aboriginal australians , you 're really saying the australians that were there from the beginning . and so what they would do is , is that we believe if you go back 50,000 or 60,000 years before the first aboriginal australians settled australia , australia had much more forest . it still has forest . this is a modern picture , obviously , of an australian forest . but what they did is that they set up controlled burns . and what these controlled burns did is that they cleared away a lot of the forest . they cleared away a lot of the brush that 's over here , and it made it much more suitable for grassland to develop . and the reason why they liked grassland -- so let 's make a little cycle here of what they did . so they have controlled burns . controlled fires . those controlled fires helped promote grassland . and then once you have grassland , that made the environment more suitable for animals that the original human settlers could essentially live off of . that they could hunt , that they could potentially eat their meat . and so , for example , things like kangaroos . and these supported the human population , which obviously , would then do the controlled burns . and you see here -- so we could have started off with something like this . someone provides a controlled burn . and they were actually pretty scientific about how they did it . they would n't just go at the end of summer , when everything was hot , and ready to just blow up , and then start a fire that they could n't control . they would often do these in seasons knowing that it had a certain level of moisture in the air , it was n't too hot . and to a large degree , by doing these controlled burns , not only did it provide an environment -- kind of do this firestick farming -- not only did it provide an environment that was suitable for things like kangaroos , some type of things that humans could eat -- but it also prevented major fires . and you still see forest rangers doing this type of thing . and there 's some reason to believe that what the original australians did , on some level , was more nuanced and more fine-tuned than even what we do , in a modern sense , in controlled burns . so these controlled fires also prevented major uncontrollable fires . because what happens is if you do n't have these controlled fires , then you have brush building up , year after year after year . you have stuff building up . and then , when the fires do occur , the uncontrolled fires are less likely to be started during the winter , when the air is cool or when there might be some moisture . they 're more likely to occur in the dry season . so you have all this stuff build up . and then when the fire does happen , it happens in the driest season . and then what happens with all of the stuff built up in the dry season , it just becomes uncontrollable . one of the byproducts -- or actually there are several byproducts of this firestick farming -- we believe , is a lot of the grassland in australia now might have been more forested before . and even when the first european settlers came in the late 1700s , they were kind of surprised when they went into what is now sydney harbor and they said , wow , look at all the grassland here . it almost looks like park space . and then they would let their sheep graze there . and they were surprised -- because they had driven out the original inhabitants . and then they were surprised when forests just started to grow up in that grassland . and it was because the original australians were actually controlling that forest growth to make it more inhabitable for things like kangaroos . and then when the english settlers came , they started to have their sheep graze in those grasslands . and it also was responsible for the disappearance , we think , of many major -- i guess , for lack of a better word -- megafauna . so really large animals that inhabited australia , for really millions of years , until humans showed up . and this is one of them . it 's just neat to look at them . this is called diprotodon optatum . or , another way to think of it , the giant wombat . and there 's fossils of the giant wombat around 40,000 , 50,000 years ago . but they disappeared with humans showing up . and there 's multiple ways that you can think about why they disappeared . they might have -- and this is probably the case -- they might have been more dependent on the forest habitat . or this was a more favorable habitat for them than the grasslands . maybe because they ate leaves that were high up . or another thing is , once the forest habitat goes away , they were actually also easier to hunt down . or either way you think about it , they might have just been hunted by humans . but we do see that with humans coming to the australian continent , you start to see the disappearance -- and this is n't the only one -- but there were several major species of megafauna , of super large animals , that disappeared at that time period .
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original -- you know what that means . the first things . the things that were there from the beginning .
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were the europeans the first group to introduce sheep to australia ?
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