Pythagorean Therom Proof

This is a simple manipulative that shows how the Pythagorean Theorem can be proven using rearrangement.

We start with a tray that has a fixed internal area equal to (a+b)2 and four identical triangles with sides a, b and c.

If we arrange the triangles around the perimeter of the tray as shown in figure one the negative space (space not occupied by the triangles) is a square with sides of length c.

When we rearrange the triangles to form the rectangles as shown in figure two the negative