Pythagorean Theorem Proof by Transformation
There are three stages:
1- For 0<n<1, a² and b² are sheared parallel to their sides to become parallelograms.
2- For 1<n<2, these parallelograms are translated downward.
3- For 2<n<3, the parallelograms are sheared to become rectangles whose areas sum to c².
Point C can be moved to create different values of a and b.
- credits to: https://www.youtube.com/watch?v=cLW6ZiZvAnM

Why do the two squares maintain their area when sheared into parallelograms?
Why do the two parallelograms maintain their area when sheared into rectangles?