GCSE · Congruence & similarity

Congruent triangles & proofExam-style questions

The four congruence conditions SSS, SAS, ASA/AAS and RHS, why SSA is not one of them, and how to write a congruence proof that earns every mark.

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15 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
$ABCD$ is a parallelogram. The diagonal $AC$ is drawn.Diagram NOT accurately drawn

Prove that triangle $ABC$ is congruent to triangle $CDA$ .
Level 3 · 4 marksTry it
2
Here are four statements about two triangles.

A Two sides and the angle between them are equal.

B Two sides and an angle that is not between them are equal.

C All three angles are equal.

D A right angle, the hypotenuse and one other side are equal.

(a) Write down the letters of the two statements that prove the triangles are congruent.

(b) Explain why statement C does not prove the triangles are congruent.
Level 3 · 3 marksTry it
3
For each pair of triangles, write down the congruence condition (SSS, SAS, ASA or RHS) that proves they are congruent.

(a) All three pairs of corresponding sides are equal.

(b) Both triangles are right-angled, with equal hypotenuses and one other pair of equal sides.

(c) Two pairs of corresponding angles are equal, and the sides between those angles are equal.
Level 3 · 3 marksTry it
4
$ABCD$ is a parallelogram.Diagram NOT accurately drawn

Prove that triangle $ABC$ is congruent to triangle $CDA$ . (3 marks)
Level 3 · 3 marksTry it
5
In triangle $ABC$ , $AB = AC$ . $M$ is the midpoint of $BC$ .

(a) Prove that triangles $ABM$ and $ACM$ are congruent. [3]

(b) Hence explain why angle $AMB = 90°$ . [1]
Level 3 · 4 marksTry it