Skip to content
← Back to lesson

Success Homeschool

Year 11 Mathematics · Geometric reasoning and proof

Name: ______________________

Date: ____________

  1. 1. Which of these is NOT a valid test for congruent triangles?

    • ☐ (a) SSS
    • ☐ (b) SAS
    • ☐ (c) AAA
    • ☐ (d) RHS

  2. 2. Two angles of a triangle are 48° and 67°. What is the size of the third angle, in degrees?

  3. 3. When a transversal crosses two parallel lines, co-interior angles are…

    • ☐ (a) Equal
    • ☐ (b) Supplementary (they add to 180°)
    • ☐ (c) Complementary (they add to 90°)
    • ☐ (d) Always 45°

  4. 4. In a circle, an arc subtends an angle of 110° at the centre. What angle does the same arc subtend at the circumference, in degrees?

  5. 5. AB is a diameter of a circle and C is any other point on the circumference. What is the size of ∠ACB?

    • ☐ (a) 45°
    • ☐ (b) 60°
    • ☐ (c) 90°
    • ☐ (d) 180°

  6. 6. An isosceles triangle has an apex angle (between its two equal sides) of 40°. What is the size of each base angle, in degrees?

  7. 7. Two straight lines cross at Q, forming ∠PQR and ∠SQT opposite each other. What is the correct reason for ∠PQR = ∠SQT?

    • ☐ (a) Alternate angles are equal
    • ☐ (b) Vertically opposite angles are equal
    • ☐ (c) Angles in a triangle add to 180°
    • ☐ (d) Corresponding angles are equal

  8. 8. Two triangles have all three pairs of corresponding angles equal. What can you conclude?

    • ☐ (a) They are congruent
    • ☐ (b) They are similar
    • ☐ (c) They are both right-angled
    • ☐ (d) Nothing at all

Answer sheet

  1. 1. AAA — Triangles with three equal angles have the same shape but can be different sizes, so AAA only proves similarity.
  2. 2. 65° — Angles in a triangle add to 180°: 180 − 48 − 67 = 65.
  3. 3. Supplementary (they add to 180°) — Co-interior angles between parallel lines add to 180°.
  4. 4. 55° — The angle at the centre is twice the angle at the circumference, so the angle at the circumference is 110 ÷ 2 = 55°.
  5. 5. 90° — The angle in a semicircle is a right angle.
  6. 6. 70° — The base angles are equal and the angles add to 180°: (180 − 40) ÷ 2 = 70.
  7. 7. Vertically opposite angles are equal — Angles directly opposite each other where two lines cross are vertically opposite and equal.
  8. 8. They are similar — Equal angles guarantee the same shape (similar), but not necessarily the same size.

© Success Tutoring · homeschool.successtutoring.com · Free for home and personal use. Awaiting educator review.