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Pythagorean Puzzle

Click on the "show me how" button to see how to do this puzzle. When you're ready to try it yourself, click the "my turn" button. You can try variations on this puzzle by clicking the "next" button.

Can you use this puzzle to prove that the blue and yellow squares in the top figure take up the same amount of space as the red square? How?

This puzzle is named after Pythagoras, a Greek mathematician who gave us the earliest known proof of this special relationship.