## Pythagoras Theorem

When a triangle has a right angle (90°) and squares are made on each of the 3 sides, then the biggest square has the exact same area as the other 2 squares put together!

Pythagoras Theorem can be written in one short equation:

*a*^{2}* + b*^{2}* = c*^{2}

Where:

- c is the longest side of the triangle
- a and b are the other 2 sides

Table of Contents

## Definition

The longest side of the triangle is called the “hypotenuse”, so the formal definition is:

In a right angled triangle:

The square of the hypotenuse is equal to the sum of the squares of the other 2 sides.

## Is This Useful?

If we know the lengths of 2 sides of a right angled triangle, we can find the length of the third side.

It only works on right angled triangles!

## How Do I Use it?

Write it down as an equation

Find b!

*a*^{2} + *b*^{2} = *c*^{2}^{}

*b*^{2} = *c*^{2 }– *a*^{2}^{}

*b*^{2} = *13*^{2 }– *5*^{2}^{}

*b*^{2} = 169^{ }– 25

*b*^{2} = 144

*b* = 12