Year 8 Maths — Congruent triangles

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

Name: ________________________

1.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) RHS
- c) SSS
- d) ASA
2.Is knowing that all three pairs of angles are equal enough to prove two triangles congruent?
- a) No — that only makes them the same shape, not the same size
- b) Only for isosceles triangles
- c) Only for right-angled triangles
- d) Yes, always
3.Sort each set of matching parts by whether it is enough to prove congruence.
Groups: Proves congruence · Does not prove congruence
- AAA
- RHS
- SAS
- ASA
- SSA
- SSS
4.In an isosceles triangle, the line from the apex to the midpoint of the base splits it into two triangles that are...
- a) not related to each other
- b) congruent, by SSS
- c) the same shape but different sizes
- d) congruent, by AAA
5.Two right-angled triangles have equal hypotenuses and one pair of equal shorter sides. Which rule proves they are congruent?
- a) RHS
- b) SSS
- c) SAS
- d) ASA
6.Triangle ABC is congruent to triangle PQR. Angle A is 55°. How big is angle P, in degrees?
7.Triangle ABC is congruent to triangle PQR. AB is 7 cm long. How long is PQ, in centimetres?
8.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) SSS
- c) RHS
- d) SAS

Answer key — Year 8 Maths — Congruent triangles

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