If the triangle had a right angle (90°), and you made a square on each of the three sides, then the biggest square had the **exact same area** as the other two squares put together.

It is called “Pythagoras Theorem” and can be written in one short equation:** \(a^2 + b^2 = c^2\)**

## Definition:

In a right angled triangle, the **square of the hypotenuse is equal to the sum of the squares of the other two sides.**

Let’s see if it really works using an example.

### Pythagoras Theorem Example:

A “3,4,5” (pythagorean triple) triangle has a right angle in it.

**Let’s check if the areas are the same:**

\(3^2\) + \(4^2\) = \(5^2\)

Calculating this becomes:

9 + 16 = 25.

If we know the lengths of two sides of a right angled triangle, we can find the length of the third side. (But remember it only works on right angled triangles!)