Appendix 4

A Simple Visual Proof of the Pythagorean Theorem

The area of a square of side a + b is (a + b)² or a² + b² + 2ab (I).

On the other hand, if the interior of the square is divided up into a square of side c and four right-angled triangles of sides a, b as shown below, its area equals the sum of the areas of these five figures, that is c2 + 4(ab/2) or c² + 2ab (II).

Since the expressions (I) and (II) represent the same area, we have

a² + b² + 2ab = c² + 2ab, which implies

a² + b² = c²