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.