Fiducia TogetherPythagoras' theorem
In a right-angled triangle, the square on the hypotenuse equals the sum of the squares on the other two sides.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
a² + b² = c², where c is the hypotenuse — the side opposite the right angle and always the longest.
Where it applies
Both tiers, and it extends to 3D shapes and to coordinates at Higher.
How it works
It finds a missing side when two are known, and it works in reverse to test whether a triangle is right-angled.
In coordinate geometry, the distance between two points is Pythagoras applied to the differences in x and y.
How to use it in your work
Identify the hypotenuse first. Most errors come from treating a shorter side as the hypotenuse.
If you are finding a shorter side, subtract rather than add.
Leave the answer in surd form when asked for an exact value.
Where to get help
Your teacher, your board's specification for what is on your paper, and Bitesize for worked examples. The maths song runs the topics in order.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.