a
b
c
a2
b2
c2

This is an animated proof of the Pythagorean Theorem. The diagram shows a green square and four right triangles with edges of length a, b, and c. Moving the triangles does not change the area of the green region. That area is a2 + b2 in one configuration and c2 in another. Therefore, a2 + b2 = c2, as asserted by the Pythagorean Theorem.