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Grade 12 · Euclidean Geometry
Proportionality & Similarity Theorems (Grade 12)
WORKSHEET
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  / 20

Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    In △ABC below, DE ∥ BC. Write down the proportion that follows, with a reason.
    (2)
    ABCDEADDBAEECDE ∥ BC
  2. 2
    DE ∥ BC with AD = 4, DB = 6 and AE = 5. Calculate EC.
    (3)
    ABCDEADDBAEECDE ∥ BC
  3. 3
    In △ABC below with DE ∥ BC, prove that △ADE ||| △ABC.
    (4)
    ABCDEADDBAEECDE ∥ BC
  4. 4
    If AD = 4 and DB = 6, write down the length of AB.
    (1)
  5. 5
    How many pairs of equal angles must you prove for AAA?
    (1)
  6. 6
    △ABC ||| △DEF with AB = 8, DE = 12 and BC = 10. Calculate EF.
    (3)
  7. 7
    State the reason you must quote when using the proportion theorem.
    (1)
  8. 8
    Two triangles are equiangular. What can you conclude?
    (2)
  9. 9
    The sides of △ABC are 4 cm, 6 cm and 8 cm. The sides of △KLM are 6 cm, 9 cm and 12 cm. Are the triangles similar? Give a reason.
    (3)
TOTAL: 20 marks
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