Pythagoras' Theorem
Pythagoras’ Theorem

Pythagoras’ theorem states that “In any rightangled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides”. This can be written as a² = b² + c²

The theorem can be used to calculate the length of any side in a rightangle triangle, provided the lengths of the other two sides are known.

Remember that Pythagoras’ Theorem applies only to rightangled triangles. A common mistake is to try and apply it to triangles that are not rightangled.
Applying Pythagoras’ Theorem

First identify the hypotenuse (the longest side, which is opposite the right angle).

Then, use the Pythagorean theorem to find the lengths of the other two sides.

Always check that your answer makes sense; it should never be longer than the length of the hypotenuse, or shorter than the shortest side.

Remember to use the correct units, they could be centimetres, metres, kilometres etc.
Proving Pythagoras’ Theorem

You can also use Pythagorean theorem to prove that a triangle is rightangled. If the square of the length of the longest side is equal to the sum of the squares of the other two sides, the triangle is rightangled.

This can be a powerful tool in problems where you need to verify if a triangle is a right triangle or not.
Remember, practice is key to understanding and applying Pythagoras’ theorem. Work through as many different types of problems as you can. This will also help you get familiar with how the theorem might be applied in different ways in different problems.