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
In the diagram, the straight lines $PR$ and $SQ$ cross at $M$ .

$PS = QR$ and angle $SPM$ = angle $RQM$ .Diagram NOT accurately drawn

Prove that triangle $PSM$ is congruent to triangle $QRM$ .
Level 4 · 3 marksTry it
2
$ABCD$ is a rectangle. The diagonal $BD$ is drawn.Prove that triangle $ABD$ is congruent to triangle $CDB$ .
Level 4 · 3 marksTry it
3
$KLMN$ is a kite, with $KL = KN$ and $ML = MN$ . The diagonal $KM$ is drawn.(a) Prove that triangle $KLM$ is congruent to triangle $KNM$ .

(b) Hence explain why the diagonal $KM$ bisects angle $LKN$ .
Level 4 · 4 marksTry it