Fiducia TogetherSimilar shapes and congruence
Shapes the same shape but different size, and shapes that are identical.
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
Congruent shapes are identical in shape and size. Similar shapes have the same angles and proportional sides, related by a scale factor.
Where it applies
Both tiers. Area and volume scale factors are higher tier.
How it works
For similar shapes, lengths scale by k, AREAS scale by k², and VOLUMES by k³. That is the single most tested and most missed idea in the topic.
Congruence is proved by one of four conditions: SSS, SAS, ASA and RHS.
How to use it in your work
Square the scale factor for area and cube it for volume. Doubling the lengths gives four times the area and eight times the volume.
For congruence proofs, name the condition — SSS, SAS, ASA, RHS — and state the three matching facts.
Where to get help
Your teacher and your board's specification. Bitesize for worked examples, and the subject song for the topic list.
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.