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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 f... | 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 . | can the slope of a function be defined where the function does not exist ? |
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 f... | 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 . | 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 ? |
( 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 f... | 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 . | how did baroque architecture emerge ? |
( 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 f... | 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 f... | 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 , ... | what materials were used to build san carlo alle quattro fontane ? |
( 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 f... | > > 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 exam... | is n't concave and convex for reflections ? |
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 di... | 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 tras... | why ca n't i put than a fourth dot on the pratice ? |
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 di... | 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 . | how do you rotate around a center of origin if there is no center of rotation ? |
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 di... | 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 . | what happens when the x axis is 0 ? |
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... | 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 al... | should n't the blood pressure increase , due to the increase of resistance , caused by the the decraese of blood vessel diameter ? |
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... | 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 . | does inflamation of the blood vessels also include atherosclerosis ? |
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... | 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 g... | would you see symptoms of hypovolemic shock with venous vasculitis ( in other words , inflammation of the veins ) ? |
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... | 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 . | why would the blood pressure reduce when the resistance increases ? |
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 , consu... | 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 ? | so would renting then be considered an investment ? |
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 , consu... | 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... | think about it : when you buy a stock from another person , are you generating wealth for society ? |
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 , consu... | 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 . | how bout if you rent the house to other people , will the hardwood floors and granite create value then ? |
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 , consu... | 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 . | all fall under the term 'investment ' ? |
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 , consu... | 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 . | 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 ? |
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 , consu... | 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 ... | how should we classify purchasing energy saving appliances or solar panels ? |
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 , consu... | 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 retur... | is n't one way to define value what other people would be willing or able to buy ? |
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 , consu... | 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 . | i do n't disagree , but under these assumptions , is food an investment ? |
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 , consu... | 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 . | what value do the bankers create by making `` investments '' ? |
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 , consu... | 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... | would n't buying the granite contribute to labor demand for granite installing , thus fueling the economy ? |
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 , consu... | 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 . | could we not argue that live in a nicer house is as necessary as having a house ? |
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 , consu... | 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 . | for a government , is creating and maintaining a national park ( like carlsbad caverns or the grand canyon ) an investment or consumption ? |
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 , consu... | 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 . | is buying a glove an investment ? |
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 , consu... | 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 . | is it unreasonable to suggest that a nicer house has more potential to appreciate in value and act as a better hedge against inflation ? |
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 , consu... | 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 . | 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 ? |
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 , consu... | 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 ? | about the granite - if it appreciates over time , would n't it be seen as an investment ? |
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 ... | 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 ... | is there a positive correlation between someone with tourette 's and autism ? |
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 ... | 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 othe... | like cipa aka congenital insensitivity to pain with anhidrosis ( which is a disorder that makes you feel no pain } ? |
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 d... | 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 . | would it make sense to take statins just as a preventive measure to slow down the buildup of plaques ? |
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 d... | 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 redu... | what order would you put these interventions in when caring for an mi patient ? |
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 d... | 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 . | how often do doctors use morphine ? |
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 d... | 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 h... | do people who have n't had a heart attack , take the medications listed in the video to help prevent a mi ? |
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 d... | 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... | what dose of aspirin should be administered and when ? |
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 d... | 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 . | when someone 's having heart attack , is it ok to give him 300 mg right away at home ( in non retard form ) ? |
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 d... | 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 . | how are clot-busters actually working and why are they only effective on `` stemi-clots '' ? |
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 d... | 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 ste... | what 's the difference between `` stemi-clots '' and `` nstemi-clots '' /unstable-angina-clots ? |
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 d... | 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 . | what is the `` heart shaped medicine '' called , ? |
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 d... | 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 . t... | i thought that angioplasty had replaced thrombolysis ... ? |
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 d... | 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 infarc... | as a dentist should i operate on someone who has a history of myocardial infarct ? |
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 d... | 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 . | would it be beneficial for a patient to take calcium channel blockers ? |
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 ... | 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 . | can someone explain to me what a rhombus is ? |
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 ... | and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . | so what if the quadrilateral only indicated one pair of parallel sides and one pair of congruent sides ? |
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 '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 . | ( additional information is missing ) is it possible to find out wether or not the quadrilateral is a parallelogram or not ? |
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 ... | 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 . | is n't the second theorem just a converse of the first theorem ? |
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 ... | 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 . | how do you identify the corresponding parts and then label ? |
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 ... | 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 . | is there any difference between the two symbols if we use them to indicate that the measures are equal , like in this case ? |
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 ... | 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 . | is aaa and aas is appropraite property for prooving that the triangles are congruent ? |
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 ... | 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 . | how can we say that angle abd=bdc in the first instance ? |
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 ... | so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . | 2 , why does sal put a line through the parallelogram ? |
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 ... | 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 . | since alternate interior angles are used to find if the lines are parallel , can i still use the converse ? |
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 ... | and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . | 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 ? |
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 '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 . | in a parallelogram , is there an axis of symmetry ? |
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 ... | 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 . | does cpctc ( corresponding parts of conguent triangles are congruent ) include angles or can it only prove sides ? |
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 ... | 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 . | what does the equal sign with the ~ mark on top mean ? |
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 ... | 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 . | is there a reason why the first quadrilateral has arrows and the second one has little lines ? |
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 ... | 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 . | wait , is there a angle-angle-angle theorem or postulate of congruency that can prove triangles congruent ? |
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 ... | 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 . | what would be the theorem for the opposite angles being congruent ? |
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 ... | so this is parallel to that . so we know that ac is parallel to bd by alternate interior angles . and we 're done . | how do you know that the angles are alternate in the second diagram before knowing that they are parrallel ? |
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 ... | that 's the hardest part . draw it . that 's pretty good . | 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 ? |
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 '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 . | i want to ask that why is square a parallelogram ? |
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 ... | 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 . | 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 ? |
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 ... | 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 . | when do you know when to have one transversal or two transversals ? |
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 ... | 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 . | how would you show that if a quadrilateral has opposite angles congruent , the quadrilateral is a parallelogram ? |
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 ... | 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 . | how do you find the exterior length and width of a polygon ? |
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 ... | 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 . | what is the relationship between corresponding sides of a rhombus ? |
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 ... | 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 . | 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 ? |
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 ... | 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 . | 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 ? |
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 ... | 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 . | do you know what these proofs stand for ? |
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 ... | 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 . | by which axiom is abd and bdc equal ? |
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 ... | 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 . | what is the definition of congruent angles ? |
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 ... | 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 . | how is angle < abd congruent to < bdc ? |
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 ... | 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 . | can two angles be congruent ? |
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 ... | 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 . | what 's the total number of diagonals in a 35-sided polygon ? |
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 ... | 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 . | 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 ? |
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 ... | and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . | can anybody think of a counterexample to disprove that a figure is a parallelogram only if opposite sides are congruent ? |
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 ... | 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 . | what is use of asa congruency ? |
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 ... | and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . | what seems to be true about the lengths of the opposite sides of the parallelograms ? |
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 ... | 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 . | how would you prove parallel if the angles are given but not the sides ? |
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 ... | 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 . | could you not use cpctc or corresponding parts of congruent triangles are congruent ? |
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 ... | 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 . | is corresponding angle of congruent triangles the same thing as corresponding parts of congruent triangles are congruent ? |
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 ... | 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 . | what is the theorem for the two triangles ? |
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 ... | 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 . | angles congurence theorem and say the triangles are congruent by asa like in the first proof ? |
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 ... | and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . | 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 ? |
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 ... | 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 . | 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 ? |
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 ... | and then we 're done . we 've proven that opposite sides are congruent . now let 's go the other way . | for the first question would n't the proof prove the theorem that states opposite sides of a parallelogram are congruent ? |
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 ... | 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 . | 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 ? |
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 ... | so i 'll draw it like that . obviously , because it 's the same line . and then we have something interesting . | why is the line sloppy ? |
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 '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 . | why is it that a parallelogram is always congruent but then how can you tell the difference between a parallelogram and a rhombus ? |
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... | 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 . | do we know how the aboriginals first got to australia ? |
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... | 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 . | i wonder why people would kill giant animals if they 're such a wonder today ? |
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... | 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... | 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... | 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... | 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 won... | 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... | 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... | 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 . | what other kinds of species died out because humans came ? |
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... | original -- you know what that means . the first things . the things that were there from the beginning . | were the europeans the first group to introduce sheep to australia ? |
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