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Year 9 Maths — Congruent triangles

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

Name: ________________________

  1. 1.In an isosceles triangle, the line from the apex to the midpoint of the base splits it into two triangles that are...

    • a) congruent, by SSS
    • b) congruent, by AAA
    • c) the same shape but different sizes
    • d) not related to each other

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

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

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

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

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

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

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

    Groups: Proves congruence · Does not prove congruence

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

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

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

  8. 8.Two triangles have all three pairs of sides equal. Which rule proves they are congruent?

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

Answer key — Year 9 Maths — Congruent triangles

  1. 1. a) congruent, by SSS
  2. 2. c) RHS
  3. 3. 55
  4. 4. b) ASA
  5. 5. 7
  6. 6. SSS → Proves congruence; SAS → Proves congruence; ASA → Proves congruence; RHS → Proves congruence; AAA → Does not prove congruence; SSA → Does not prove congruence
  7. 7. c) SAS
  8. 8. a) SSS