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,

Key Terms

Pythagoras' Theorem, hypotenuse