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4024/11 Oct/Nov 2021, Question 22: Similar Triangles

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

Using two straight lines crossing at C with AB parallel to ED, prove triangles ABC and DEC are similar, then use AB = 6 cm, ED = 2 cm and area of ABC = 45 cm² to find the area of DEC.

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Part (a) · 3 marks

Prove triangle ABC is similar to triangle DEC, giving a reason for every statement made.

  1. 1Angle ACB = angle DCE (vertically opposite angles)
  2. 2Angle CAB = angle CDE (alternate angles, AB parallel to ED)
  3. 3Angle ABC = angle CED (alternate angles, AB parallel to ED)
  4. 4All three angles equal, so triangles ABC and DEC are similar

Answerangle ACB = angle ECD, vertically opposite; angle CAB = angle CDE, alternate; angle ABC = angle CED, alternate; three angles equal therefore the triangles are similar

Part (b) · 2 marks

Given AB = 6 cm, ED = 2 cm and area of triangle ABC = 45 cm², calculate the area of triangle DEC.

  1. 1Length scale factor = 2/6 = 1/3, so area factor = (1/3)² = 1/9
  2. 2Area of DEC = 45 × 1/9 = 5 cm²

Answer5

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Also searched as: 4024/11/O/N/21 · 4024_w21_qp_11 · 4024 w21 11 · question 22.
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