Proof of the Pythagorean Theorem

Move the mouse over the figure to start the animation. Double click the picture to stop/restart the animation.

Outline of the Proof

  • The goal is to prove that a2+b2=c2. In terms of areas, we need to show that the area of the green square plus the area of the yellow square equals the area of the brown square.
  • As the blue triangles move around, they cover up part of the brown area, but they uncover an equal amount of area behind them. So the total amount of brown area stays the same.
  • Once the triangles have moved, the yellow and green squares will move to show that they exactly cover up the brown area.

When the animation is stopped, you can use the following controls:

  • Click and drag the black dots to adjust the values of a and b.
  • Click and drag horizontally with the right mouse button to step through the animation frame-by-frame.

(Be careful: if you drag vertically while holding down the right mouse button, you might make some of the pieces disappear. Press the Home key on your keyboard to reset the picture.

You may also be interested in another interactive proof, using shearing, on the NCTM website.