IGCSE Maths / Pythagoras theorem
Introducing Pythagoras theorem revision notes
Edexcel International GCSE Maths (4MA1), chapter 15: Pythagoras theorem, specification point 4.8a-f. Free lesson.
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Pythagoras’ theorem links the three sides of a right-angled triangle. It lets you find a missing side, but only when the triangle has a right angle.
Find the hypotenuse
The hypotenuse is the side opposite the right angle. It is always the longest side and is the side called c in the theorem. To find it, locate the small square marking the right angle, then look at the side directly opposite. The hypotenuse is the side on its own in the theorem.
What Pythagoras’ theorem says
For a right-angled triangle, the squares of the two shorter sides add to the square of the hypotenuse. The rule is a² + b² = c², where c is the hypotenuse. Pythagoras’ theorem is not printed on the Edexcel formula sheet, so you need to know it. Use the theorem only when the triangle has a right angle.
Find a missing hypotenuse
When you know both shorter sides, square each length, add the squares, then take one square root at the end. For example, sides of 3 cm and 4 cm give a hypotenuse of 5 cm.
Avoid adding the side lengths
The theorem adds the squares of the side lengths, not the lengths themselves. Adding 3 + 4 gives 7, which is not the hypotenuse. The direct route between two corners is shorter than travelling along the other two sides, so the hypotenuse cannot be 3 + 4. For sides of 3 cm and 4 cm: 3² + 4² = 9 + 16 = 25.
Check that the triangle is right-angled
Pythagoras’ theorem does not work in every triangle. Check for a right angle before using it. Without a right angle, the squares of the two shorter sides do not add to the square of the longest side. The cosine rule is needed instead. Look for the small square marking the right angle before writing any numbers.