Henry Boad Proof

Loomis 63

Part II, Proof 63, page 137 from E.S.Loomis, The Pythagorean Proposition (1940)

This three part "animation" begins with two squares.

As the squares open out, all the surrounding triangles expand. Note that there are an equal number of surrounding triangles for each color area.

Throughout the "growth" of this configuration, all parts, and their areas, (accept the blue base square) increase by equal amounts. Form this observation, we know the the blue shapes remains equal in area to the golden shapes throughout the animation. Hence the (blue) base and riser squares have equal area to the (golden) hypotenuse square.