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8
student
well we proved angle ABD and angle DCA
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volunteer
those angles, angles are 90 degrees. So,
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volunteer
um
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volunteer
yeah, we proved ABD and DCA are equal.
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volunteer
are congruent, here, we have proved that, uh, but we are thinking about the reasoning we should give there.
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volunteer
because substitution is not working there, but other reasoning can be used?
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student
But we need to prove how angle A and angle D work to be proved
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student
the first thing I said is already prved
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volunteer
How Uncle A and Uncle D work to be proved.
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student
was given
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volunteer
Um
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student
something with cut by transversal
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volunteer
Yeah, we are doing the same sole A and angle D basically means angle BAD and angle ADC. They are one and the same thing.
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volunteer
So I think you get this message when you write that angle BAD equals angle ADC and new substitution as the reason, so it says that no, it's wrong. Uh, so we are thinking about the correct reason we should give the. Uh, what are the list of reasons do we have
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volunteer
over here?
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volunteer
For the statement that I BAD is equal to an ADC.
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student
these
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volunteer
The these are the same thing. Uh, what was transitive property again. No, I'm sorry, I forgot that.
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volunteer
transitive property.
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student
like if a isqual
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student
if a is equal to e and e is equal to d then a is equal to d
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volunteer
OK, then, yeah, OK, if, yeah, transitive property is basically that
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volunteer
uh A equals E and E equals d, then A equals d. This is exactly what we are trying to say. We are saying that our angle A is equals 90 degree, and then we are saying that angle D is equals is also equal to 90 degrees, and from this we are implying that angle A should be equal to our anger D So yeah, use transitive prope...
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volunteer
Yeah, because when I was, when I was looking here for the reasonings, there was nothing like transitive property. So I was thinking what could be the possible reasoning for this.
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volunteer
Now try transitive reasoning for that.
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student
still no
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volunteer
Still no? Oh my God.
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volunteer
Um
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volunteer
it should work now
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student
its not working yet
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volunteer
Mm.
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volunteer
What notice does it show now?
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student
it shows this
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volunteer
No, you tru use transitive property.
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volunteer
I told you that no, don't you substitution use transitive property.
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student
I did
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student
that's what it gives
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volunteer
to use substitution for congruent, but we are not using substitution. Why does it say substitution then?
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volunteer
This is strange
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volunteer
Uh, now try using this all right angles are congruent.
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volunteer
because now we have proved that both of those are right angles, so maybe it will accept this now.
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student
yes it worked!
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volunteer
OK, yeah. Good.
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volunteer
So, OK, so let's think why the transitive property thing didn't work.
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volunteer
So
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volunteer
so it's basically A equals A E equals t, then we say that a should be equal to D We were saying that angle A equals 90 degrees. Then we said angle D is equals 90 degree. And then we were trying to imply that angle A should be equal to angle angle D
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volunteer
But instead our reasoning uh should have been like 90 degree equals angle.
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volunteer
So this equals this and this again equals this, then we can prove that anguanggu D uh, but, but somehow that should also have, should have worked, but it's fine if it doesn't. So, yeah, I mean, it's OK.
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student
yes
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volunteer
So all right angles are con. So do you understand why it was not working previously because we just assumed that they automatically knew that if it's given that both of these, uh, sides are perpendicular, then the angle should be 90 degrees. So we were wrong with that assumption. We first had to tell them that these an...
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volunteer
uh statement that perpendicular lines form 9 right angles, and then we had to say that all right hungles are congruented. So is the whole problem clear now?
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volunteer
Like, why, why was it not working previously?
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student
yes but its still not finished, like I understand so far
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volunteer
Yeah, yeah, yeah
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volunteer
Uh, yeah, we, it's not finished, but we have written the three statements now. We now, we just now need to write that congruent triangle statement. So just uh write this statement and for the reason, what do you think should be the reason? We have 5 congruency criteria ESA
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volunteer
SSS
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volunteer
S uh SAS AAS.
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volunteer
A is
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volunteer
So we have this angle.
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volunteer
here. We have side and we have angle. So it should be AAS.
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volunteer
uh try to protect this as the last statement, and I think it should work now.
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student
Yes it worked!
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volunteer
OK, yeah, great. Finally, finally.
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volunteer
So do you want me to summarize the whole problem again? I can do that.
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student
yes please! so I can take notes!
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volunteer
Uh, OK. So just give me a minute.
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volunteer
We knew that
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volunteer
um, OK.
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volunteer
So if you wanna take notes
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volunteer
uh, OK, let me just clear this thing.
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volunteer
Uh, these are not important.
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volunteer
OK
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volunteer
So yeah, I'll, I'll write the whole
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volunteer
whole solution for you again.
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volunteer
So the first uh statement we used here was that angle BAD is equal to 90 degree.
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volunteer
Then we use that angle A, D, C is equal to 90-degree.
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volunteer
Uh, and the reasoning for both of these was that uh
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volunteer
perpendicular lines.
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volunteer
make
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volunteer
right angle.
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volunteer
This was our first statement
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volunteer
Then our second statement was that AD is
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volunteer
congruent to AD.
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volunteer
because of the reflexive property.
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volunteer
Then we said that
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volunteer
angle A, B, D equals
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volunteer
angle
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volunteer
ACD.
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volunteer
uh because this is given.
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volunteer
And then from these two statements, we said that
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volunteer
Angle BAD, AD equals angle ADC because
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volunteer
all right angles are
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volunteer
congruent
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volunteer
Uh, just ask me if my handwriting is not very clear.
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volunteer
It's, it's a bit busy, I know.
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volunteer
Uh just ask me if it, if anything is not clear. And then from this we said that by
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volunteer
AAS
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volunteer
triangle
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volunteer
B A D
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volunteer
is congruent to Trale CDA.
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