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
Triangle $ABC$ has sides $5$ cm, $7$ cm and $9$ cm. Triangle $PQR$ also has sides $5$ cm, $7$ cm and $9$ cm. Which condition shows the two triangles are congruent? (SSS, SAS, ASA or RHS)
Level 1 · 1 markTry it
2
In two triangles, two sides and the angle between them are equal. Which congruence condition is this? (SSS, SAS, ASA or RHS)
Level 1 · 1 markTry it
3
Two triangles each have angles of $40°$ , $60°$ and $80°$ . Must the triangles be congruent? Explain your answer.
Level 2 · 1 markTry it
4
$ABCD$ 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
5
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

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