## 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

## Properties of Similar Triangles Part 2

This is the third and the conclusion of the Triangle Similarity Series. The two prequels  are 1. Introduction to Similarity and 2. Properties of Similar Triangles (Part 1).

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In the previous post, we have investigated the properties of similar triangles. We have learned that corresponding angles of similar triangles are congruent. In this post, we are going to discuss more about the properties of similar triangles.  If you have not performed the investigation in the previous post, you can use the applet below.