**EMAT
6700**

**by
Brad Simmons**

**Creating Pythagorean Puzzles**

Use geometer's sketchpad to create a Pythagorean puzzle.

By drawing two squares and cutting them in a certain way, a puzzle that demonstrates the Pythagorean Theorem can be made. This page creates a Pythagorean puzzle.

1. Carefully construct a square and label the length of
a side as **a**. Then construct a smaller square to the right of it and
label the length of a side as **b**, as shown in the figure below. The
bases should be adjacent and collinear.

2.
Mark a point X that is **b** units from the left edge of the larger
square. Then draw the segments from the upper left corner of the larger
square to point X, and from point X to the upper right corner of the smaller
square.

3. Cut out and rearrange your five pieces to form a larger square. The diagram below shows the answer.

4. Verify that the length of each side of the square
shown above is equal to the square root of **a** squared plus **b**
squared.

Please click here for a geometer's sketchpad sketch that can be manipulated.

**Try to create a different puzzle.**