Let's take both drawings together. If you look at both drawings, you'll be able to easily demonstrate to yourself that they both cover the same overall area. Once you realize that both drawings cover the same area, take a closer look. Both drawings have areas that are covered by triangles and areas that are not covered by triangles. For the drawing on the left, the area left uncovered by triangles has the area of c^2. And for the drawing on the right, the uncovered area is a^2 + b^2. Since the area covered by the triangles hasn't changed between the two drawings, that indicates that the uncovered area for both drawings is the same. Therefore c^2 = a^2 + b^2 which is the Pythagorean identity.
