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# Construct a right isosceles triangle

Can you build a triangle that is both a right triangle and an isosceles triangle? Created by Sal Khan.

Video transcript

They're asking us to
draw a right triangle. So that means it has to
have a 90-degree angle. But it's also an
isosceles triangle, so that means it has to have
at least two sides equal and has two sides of length 3. So those two sides that
are going to be equal are going to be of
length 3, and it's got to be a right triangle. So let's see if we can do that. So let's try to make this right
over here the right angle. And let's make this side and
this side have length 3, so 3 and then 3 right over there. Let me make sure I get
that right angle right. OK, there you go. So it's a right angle. It's isosceles. At least two sides are equal. And the two sides have length 3. So it seems like we've met
all of our constraints. Now they say, is there
a unique triangle that satisfies this condition? So another way of
rephrasing that, is this the only triangle
that I could have drawn that meets
these conditions? Well. I can't change this angle if I
want to meet these conditions. I can't change
these two lengths. And if you keep
this angle constant and you keep these
two lengths constant, then this point and this
point are going to be there are no matter what. So this is the only side that
can connect those two points. So this is the only triangle
that meets those conditions. You can't have
different side lengths, or you couldn't have different
angles right over here and also meet those conditions. So is there a
unique triangle that satisfies the given conditions? Yes, there's only
one unique triangle.