# Pythagoras's Theorem/Proof 4

Jump to navigation
Jump to search

## Theorem

Let $\triangle ABC$ be a right triangle with $c$ as the hypotenuse.

Then:

- $a^2 + b^2 = c^2$

## Proof

Dissect the square on the left (which has area $c^2$) as shown.

Rearrange the pieces to make the two squares on the right, with areas $a^2$ and $b^2$.

$\blacksquare$

## Source of Name

This entry was named for Pythagoras of Samos.

## Historical Note

This proof was discovered by Bhaskara II Acharya.

As he is then reported as saying:

*Behold!*

## Sources

- For a video presentation of the contents of this page, visit the Khan Academy.

- 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {B}.1$: The Pythagorean Theorem