instructions

=Pythagorean Puzzles =

A right triangle is chosen and its sides are labeled. To move a triangle or square at the bottom of the workspace, click and drag with the mouse. To rotate a piece, click on a corner, hold the mouse button down, and move the mouse in a circular motion.

**Puzzle #1:** Below each white region are four identical right triangles and a square of width //a// - //b//. If each white region can be filled, without overlapping, with these five pieces, then the two white regions must have the same area. The region on the left has area //c//2; the region on the right has area//a//2 + //b//2. So, //c//2 = //a//2 + //b//2.

**Puzzle #2:** In this demonstration, the two white regions are identical. If each white region can be filled with the pieces below it (no overlapping), then the sum of the areas of the pieces on the left must equal the sum of the areas of the pieces on the right. There are four identical triangles in each collection. If you remove them, then the remaining pieces must also have the same area. The green square remains on the left, and its area is //c//2. On the right, there are two squares remaining, one has area //a//2 and the other has area //b//2. So, //c//2 = //a//2 + //b//2.