Grade 10 Math — Congruent triangles

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

Name: ________________________

1.Two right-angled triangles have equal hypotenuses and one pair of equal shorter sides. Which rule proves they are congruent?
- a) RHS
- b) ASA
- c) SAS
- d) SSS
2.Triangle ABC is congruent to triangle PQR. Angle A is 55°. How big is angle P, in degrees?
3.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) SAS
- c) SSS
- d) RHS
4.Match each set of matching parts to the congruence rule it gives you.
- Three pairs of sides
- Two sides and the angle between them
- Two angles and the side between them
- Hypotenuse and one side, in right-angled triangles
- ASA
- RHS
- SAS
- SSS
5.Triangle ABC is congruent to triangle PQR. AB is 7 inches long. How long is PQ, in inches?
6.Two triangles have all three pairs of sides equal. Which rule proves they are congruent?
- a) SAS
- b) RHS
- c) ASA
- d) SSS
7.Two triangles have two pairs of angles equal, and the side between those angles is equal too. Which rule proves they are congruent?
- a) ASA
- b) RHS
- c) SSS
- d) SAS
8.Sort each set of matching parts by whether it is enough to prove congruence.
Groups: Proves congruence · Does not prove congruence
- AAA
- SSA
- SSS
- ASA
- SAS
- RHS

Answer key — Grade 10 Math — Congruent triangles

1. a) RHS
2. 55
3. b) SAS
4. Three pairs of sides → SSS; Two sides and the angle between them → SAS; Two angles and the side between them → ASA; Hypotenuse and one side, in right-angled triangles → RHS
5. 7
6. d) SSS
7. a) ASA
8. SSS → Proves congruence; SAS → Proves congruence; ASA → Proves congruence; RHS → Proves congruence; AAA → Does not prove congruence; SSA → Does not prove congruence