Knowledge Organiser: Congruence
Part of Congruence · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Congruence within Congruence for GCSE Mathematics. Revise Congruence in Geometry & Measures for GCSE Mathematics with 15 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 11 of 11 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 11 of 11
Practice
15 questions
Recall
12 flashcards
Knowledge Organiser: Congruence
Key Terms
- Congruent: Identical in both shape AND size (≅)
- Similar: Same shape but different size (scale factor ≠ 1)
- Corresponding vertices: Matching vertices in the same order (e.g. A↔D, B↔E)
- Included angle: The angle directly between two known sides
- Hypotenuse: Longest side of a right-angled triangle, opposite the right angle
Must-Know Facts
- Four valid congruence conditions: SSS, SAS, ASA (or AAS), RHS
- AAA proves SIMILAR triangles only — NOT congruent
- SSA (two sides + non-included angle) is NOT valid — ambiguous case
- SAS: the angle MUST be between the two sides
- RHS: only for right-angled triangles
- In proofs, state three pieces of evidence, the condition, and a conclusion
Key Methods
- SSS: all three sides equal
- SAS: two sides + included angle equal
- ASA: two angles + included side equal
- RHS: right angle + hypotenuse + one side equal
- Common side/angle: often the key third piece of evidence in proofs
Key Formulas
- SSS: all 3 sides equal
- SAS: 2 sides and the INCLUDED angle equal
- ASA: 2 angles and the INCLUDED side equal
- RHS: right angle + hypotenuse + one other side equal
Common Mistakes
- AAA is NOT congruence: Equal angles only means similar (same shape), not necessarily same size
- SAS — angle must be included: The angle must be between the two given sides — SSA (angle not included) is not a valid test
- Corresponding vertices: When stating congruence, match vertices in the correct order: △ABC ≅ △DEF means A↔D, B↔E, C↔F
- Similar vs congruent: Congruent = same shape AND same size; similar = same shape, different size
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Read this section alongside the surrounding pages in Congruence. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Congruence
Which of the following is NOT a valid congruence condition for triangles?
When writing a congruence statement, such as triangle ABC ≅ triangle PQR, explain what it tells you about the sides and angles of the two triangles.
Quick Recall Flashcards
15 questions on Congruence — practise free
Instant marking, adaptive difficulty, and 12 spaced repetition flashcards. Free until your GCSEs.
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