Year 9 Interactive Maths - Second Edition

## Pythagoras' Theorem

Pythagoras' Theorem states that:

In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. That is:

Pythagoras' Theorem was discovered by Pythagoras, a Greek mathematician and philosopher who lived between approximately 569 B.C. and 500 B.C.

### Proof of Pythagoras' Theorem

Cut out four congruent right-angled triangles.  Place them as shown in the following diagram.

The figure ABCD is a square with side length a + b, and it consists of the four congruent right-angled triangles and a square, EFGH, with side length c.

This proof was devised by the Indian mathematician, Bhaskara, in 1150 A.D.

## Applications of Pythagoras' Theorem

Pythagoras' Theorem is used to find the length of the third side of a right-angled triangle when the lengths of two other sides are known.

### Finding a Hypotenuse

#### Example 12

Find the length of the hypotenuse of the right-angled triangle shown in the diagram.

##### Solution:

Let the length of the hypotenuse be x cm.
By Pythagoras' Theorem,

So, the length of the hypotenuse is 7.45 cm.