Vlad Tenev

So this is a triangle, right?

We call it ABC, the three vertices.

So let's say it's isosceles triangle.

which means that these two sides have the same length.

So one kind of interesting fact about isosceles triangles is that it turns out because these two sides have the same length, these angles are also the same.

So what that means, the way you kind of write that is AB equals BC.

implies that

angle BAC equals angle BCA, right?

And if you look at this, I think the interesting thing is that this is kind of a self-contained fact.

You've got these three points.

The only thing you're using in this statement is those points.

You have AB equals BC.

So BAC, which is this angle, is equal to BCA.

But then the question is, how do you prove it?

Like, why is this true?

And the reason it's true requires you to do something that I can, this is like the, there's one creative step here.

And you actually have to construct a new point from scratch.

So you say, okay, I can create a point in between A and C, and I'll call it D.

and this point is the midpoint, right?

It's exactly, I can create a midpoint.