## Using Similarity to Prove the Pythagorean Theorem

The Pythagorean Theorem is one of the most interesting theorems for two reasons: First, it’s very elementary; even high school students know it by heart. Second, it has hundreds of proofs. The proof below uses triangle similarity.

Pythagorean Theorem

In a right triangle with side lengths $a$ and $b$ and hypotenuse $c$,  the following equation always holds:

$c^2 = a^2 + b^2$. » Read more