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Secondary 2 Mathematics · Congruence and quadrilaterals

Name: ______________________

Date: ____________

1. Which of these is NOT a test for congruent triangles?
- ☐ (a) SSS
- ☐ (b) SAS
- ☐ (c) AAA
- ☐ (d) RHS
2. Two triangles have all three pairs of matching sides equal. Which test shows they are congruent?
- ☐ (a) SSS
- ☐ (b) SAS
- ☐ (c) AAS
- ☐ (d) RHS
3. Two right-angled triangles have equal hypotenuses and one other pair of equal sides. Which test applies?
- ☐ (a) SAS
- ☐ (b) AAS
- ☐ (c) RHS
- ☐ (d) SSS
4. Which of these quadrilaterals always has diagonals of equal length?
- ☐ (a) Parallelogram
- ☐ (b) Rhombus
- ☐ (c) Rectangle
- ☐ (d) Kite
5. In which quadrilateral do the diagonals always bisect each other at right angles?
- ☐ (a) Rectangle
- ☐ (b) Rhombus
- ☐ (c) Trapezium
- ☐ (d) Parallelogram
6. One angle of a parallelogram is 70°. What is the size of the angle opposite it, in degrees?
7. One angle of a parallelogram is 70°. What is the size of an angle next to it (an adjacent angle), in degrees?
8. △ABC ≡ △XYZ. AB = 6 cm, BC = 8 cm and AC = 9 cm. How long is YZ?

Answer sheet

1. AAA — AAA only shows the triangles are the same shape. They could be different sizes.
2. SSS — Three pairs of equal sides is the side–side–side (SSS) test.
3. RHS — Right angle, hypotenuse and one side is the RHS test.
4. Rectangle — A rectangle's diagonals are always equal. A parallelogram, rhombus or kite usually has unequal diagonals.
5. Rhombus — A rhombus's diagonals bisect each other at 90°. A rectangle's diagonals only do this if it is a square.
6. 70° — Opposite angles of a parallelogram are equal.
7. 110° — Adjacent angles in a parallelogram are co-interior angles between parallel sides, so they add to 180°: 180 − 70 = 110°.
8. 8 cm — The letter order shows B matches Y and C matches Z, so YZ matches BC = 8 cm.