Why the Pythagorean Theorem Is True
A simple proof of why c² = a² + b²
If you’ve ever taken a geometry class, the one thing you’re likely to still remember from it is the relationship among the sides of a right triangle.
a² + b² = c²
I remember learning this fact in school. It’s was easy to remember, so I liked the theorem well enough.
What always bothered me though, is that nobody would give any explanation as to why it was true.
The standard drawing fails to enlighten
The teacher would go on to show what that relationship meant. They do the obvious thing: squares protruding from the triangle’s sides, and explain that the surface areas of the smaller ones taken together match the surface area of the big one.
Sadly, it did not help me understand why the theorem is true.
Even if you animate it with changing sides of the triangle, you never get any kind of congruence that would be convincing visually. The proportions might seem about right, but exact equality still seems like a leap of faith.
