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.