Mark says he can prove the Pythagorean Theorem using the following diagram. He explains that he can fill the squares on the two shorter sides with equal- sized circles. He can then rearrange the circles to fill the square on the hypotenuse, which proves that the sum of the squares on the two shorter sides equals
the square on the hypotenuse. Explain.
Is this a valid geometrical proof that a2 + b2 = c for all right triangles?