Here is your task: Look at the two large squares. The squares, and triangles inside of them, are exactly the same size and shape. These squares are a nonverbal proof of the Pythagorean Theorem. Your task is to use the two squares and come up with two different conjectures which conceptually explain why a + b = c (a, b, and c have been labeled). Be aware that there are literally hundreds of conjectures which can explain the relationship between the squares in this problem.

a b a b 4 4 1 a a a 3 b 1 b b a 3 3 2 2 b a a b