## Proof Without Words: Pythagorean Theorem

Why is** c^{2} = a^{2} + b^{2}?** Watch a dynamic, geometric "proof without words" of the Pythagorean Theorem. Can you explain the proof?

The sliders at the top of the screen indicate the lengths (*a* and *b*) of the legs of the right triangle. Adjust these sliders to change the size of the triangle.

Press the **Arrange Four Copies** button to begin the "proof without words." More buttons will appear to lead you through the proof.

The **Start Over** button will return you to the beginning.

This proof is attributed to Bhaskara (12^{th} century) in the book *Proofs Without Words: Exercises In Visual Thinking*, by Roger B. Nelsen, Mathematical Association of America,1993.

Adjust the size of the triangle by using the sliders at the top of the screen.

- Call the length of the longer leg
*a*, the length of the shorter leg*b*, and the length of the hypotenuse*c*.

Press the **Arrange Four Copies** button. This will show you an outline of how four copies of the triangle and a small square can be arranged to make a larger square. Press the **Color the Copies** button to color-code the pieces.

- What is the area of this square, in terms of
*c*?

Press the **Rearrange the Shapes** button to show how these five pieces can be arranged in a different configuration. Press the **Behold!** button to color-code the pieces.

- Can you explain how this configuration is equal to
*a*^{2}+*b*^{2}?

If you need help answering the last question, press the **Why It Works** button. The thick blue segment divides the arrangement into two squares. Do you see that the area of one of the squares is *a*^{2} and the area of the other is *b*^{2}?