Class 9 Maths — Congruent triangles
Decide when two triangles are congruent using SSS, SAS, ASA and RHS.
Name: ________________________
1.Triangle ABC is congruent to triangle PQR. The area of ABC is 24 square centimetres. What is the area of PQR, in square centimetres?
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 right-angled triangles
- c) Only for isosceles triangles
- d) Yes, always
3.Two right-angled triangles have equal hypotenuses and one pair of equal shorter sides. Which rule proves they are congruent?
- a) ASA
- b) RHS
- c) SAS
- d) SSS
4.Two triangles have two pairs of sides equal, and the angle between those sides is equal too. Which rule proves they are congruent?
- a) SAS
- b) ASA
- c) RHS
- d) SSS
5.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) SAS
- d) SSS
6.Triangle ABC is congruent to triangle PQR. AB is 7 cm long. How long is PQ, in centimetres?
7.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
- RHS
- SAS
- ASA
- SSS
8.In an isosceles triangle, the line from the apex to the midpoint of the base splits it into two triangles that are...
- a) the same shape but different sizes
- b) not related to each other
- c) congruent, by AAA
- d) congruent, by SSS
Answer key — Class 9 Maths — Congruent triangles
- 1. 24
- 2. a) No — that only makes them the same shape, not the same size
- 3. b) RHS
- 4. a) SAS
- 5. a) ASA
- 6. 7
- 7. 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
- 8. d) congruent, by SSS