## Pythagoras’ Theorem

Definition: The square of the hypotenuse is equal to the sum of the squares of the other two sides.

#### Proof

What this means is that if we draw three squares where the length of the sides of the squares are equal to the lengths of the sides of the triangle the area of the big square equals the area of the two smaller squares added together. (note: The hypotenuse is opposite the right angle and this side produces the largest square)

In the diagram above the largest square is the green square so this implies that

It follows that if we are finding a shorter side then we could use

Examples

Find the length of the hypotenuse.

Here

So using

We get

Find the length of the missing sideSince we are finding one of the shorter sides we will use

Here

We get

Find the value of This is a right-angled triangle so let’s use

Does 11cm, 59cm, 60cm produce a right-angled triangle?Use where since that is the longest length.But , therefore this is not a right-angled triangle.