- AAA (Angle-Angle-Angle) is NOT sufficient for congruence. Three equal angles gives similar triangles, but they could be any size.
- SSA (or ASS) is NOT a valid congruence condition. Two sides and a non-included angle can produce two different triangles (the ambiguous case).
- In SAS, the angle must be between the two sides — it is not enough for any angle to be equal.
- RHS only works when you know there is a right angle — you cannot assume it.
This exam tips covers Invalid Conditions — Common Traps 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 4 of 11 in this topic. Treat this as a marking guide for what examiners are looking for, not just a fact list.
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
SAS Congruence Condition
Side-Angle-Side: Two sides and the INCLUDED angle (the angle between the two sides) are equal.
The angle MUST be between the two sides — if it is not included, SAS does not apply.
SSS Congruence Condition
Side-Side-Side: All three pairs of corresponding sides are equal.
If AB = DE, BC = EF, and AC = DF, then the triangles are congruent.
Fixing three side lengths determines the triangle completely.