Vlad Tenev

If these two points aren't the same, there's a line connecting them that has some length.

And if I have the midpoint, I can connect it to B and then I get two triangles, triangle ABD and triangle BDC.

Now these triangles,

are actually the same triangle because by nature of this being the midpoint, this side is the same as this side, right?

And then they're sharing this side.

And so you have two triangles that are congruent.

They have the same sides.

And what that means is that all of the angles are the same too.

This angle is the same as that angle.

This angle is the same as that angle.

And there you get the fact that

these two angles are the same.

And this problem, by the way, is not just

difficult for some humans, but it was somewhat difficult for AIs too.

It's because the first versions of AI geometry solvers would work with the points.

Let's say we have three points.

You just have A, B, and B, C, and you're not using anything else for the statement.

Where does this point D come from?

That's the genius of it.

You have to know