Why does the pythagorean theorem work?

One of my students today asked my why a^2 + b^2 = c^2

They continued to say why isn't it a + b = c?

Thanks to the help of all of you here, many times I have been prepared to answer these questions. But today I found myself with no other answer than "That is what the formula tells us."

As a teacher and former/current student, I HATE THAT ANSWER.

So I told my student I would find out why and so far you guys here have been a tremendous asset to my classroom and I really appreciate all the time you put in. If anyone can help me out that would be greatly appreciated.