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Year 7 Maths — Congruent triangles

Decide when two triangles are congruent using SSS, SAS, ASA and RHS.

Name: ________________________

  1. 1.Two right-angled triangles have equal hypotenuses and one pair of equal shorter sides. Which rule proves they are congruent?

    • a) ASA
    • b) SAS
    • c) SSS
    • d) RHS

  2. 2.Triangle ABC is congruent to triangle PQR. AB is 7 cm long. How long is PQ, in centimetres?

  3. 3.Two triangles have two pairs of angles equal, and the side between those angles is equal too. Which rule proves they are congruent?

    • a) SAS
    • b) SSS
    • c) ASA
    • d) RHS

  4. 4.Triangle ABC is congruent to triangle PQR. The area of ABC is 24 square centimetres. What is the area of PQR, in square centimetres?

  5. 5.Two triangles have two pairs of sides equal, and the angle between those sides is equal too. Which rule proves they are congruent?

    • a) ASA
    • b) RHS
    • c) SAS
    • d) SSS

  6. 6.Triangle ABC is congruent to triangle PQR. Angle A is 55°. How big is angle P, in degrees?

  7. 7.Sort each set of matching parts by whether it is enough to prove congruence.

    Groups: Proves congruence · Does not prove congruence

    • AAA
    • ASA
    • SSA
    • SAS
    • SSS
    • RHS

  8. 8.Is knowing that all three pairs of angles are equal enough to prove two triangles congruent?

    • a) Yes, always
    • b) Only for right-angled triangles
    • c) Only for isosceles triangles
    • d) No — that only makes them the same shape, not the same size

Answer key — Year 7 Maths — Congruent triangles

  1. 1. d) RHS
  2. 2. 7
  3. 3. c) ASA
  4. 4. 24
  5. 5. c) SAS
  6. 6. 55
  7. 7. SSS → Proves congruence; SAS → Proves congruence; ASA → Proves congruence; RHS → Proves congruence; AAA → Does not prove congruence; SSA → Does not prove congruence
  8. 8. d) No — that only makes them the same shape, not the same size