The Four Congruence Conditions for Triangles
Part of Congruence · GCSE GCSE Mathematics revision
This deep dive covers The Four Congruence Conditions for Triangles 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 3 of 11 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 3 of 11
Practice
15 questions
Recall
12 flashcards
The Four Congruence Conditions for Triangles
You only need to check a minimum set of measurements to guarantee two triangles are congruent. There are exactly four valid conditions:
1. SSS — Side-Side-Side
If all three sides of one triangle equal the three sides of another (in corresponding pairs), the triangles are congruent.
Triangle ABC ≅ Triangle DEF if: AB = DE, BC = EF, AC = DF
Why it works: Fixing three side lengths determines the triangle completely — there is only one triangle (up to reflection) with those three side lengths.
2. SAS — Side-Angle-Side
If two sides and the included angle (the angle between those two sides) are equal, the triangles are congruent.
Triangle ABC ≅ Triangle DEF if: AB = DE, angle B = angle E, BC = EF
Critical detail: The angle MUST be included (between) the two sides. Knowing two sides and a non-included angle is NOT sufficient (see SSA below).
3. ASA — Angle-Side-Angle
If two angles and the included side (the side between those two angles) are equal, the triangles are congruent.
Triangle ABC ≅ Triangle DEF if: angle A = angle D, AB = DE, angle B = angle E
Note: AAS (Angle-Angle-Side where the side is NOT included) is also valid because if two angles are known, the third is determined (angles sum to 180°), so AAS effectively gives you ASA.
4. RHS — Right angle-Hypotenuse-Side
For right-angled triangles only: if the hypotenuse and one other side are equal, the triangles are congruent.
Triangle ABC ≅ Triangle DEF if: angle C = angle F = 90°, AB = DE (hypotenuse), AC = DF (or BC = EF)
Why it works: The third side is determined by Pythagoras' theorem once two sides are fixed in a right-angled triangle.
Keep building this topic
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
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