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4024/11 Oct/Nov 2020, Question 25: Similar Triangles

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

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The question, in short

Using the diagram with straight lines ABP and ACQ and equal angles ACB and APQ, prove two triangles similar, then use given lengths AB = 4, AC = 3, AQ = 12 to find AP and express the quadrilateral BPQC area in terms of x.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Prove triangle ABC is similar to triangle AQP, justifying every statement with a reason.

  1. 1Angle ACB = angle APQ (given)
  2. 2Angle BAC = angle QAP (same angle, common to both triangles)
  3. 3Angle ABC = angle AQP (third angles in a triangle)
  4. 4All three angles are equal, so triangle ABC is similar to triangle AQP

AnswerAĈB = AP̂Q (given) BÂC = QÂP (same angle) AB̂C = AQ̂P (third angles in a triangle) Hence similar

Part (b) · 2 marks

Given AB = 4 cm, AC = 3 cm and AQ = 12 cm, work out the length AP.

  1. 1AP/AC = AQ/AB
  2. 2AP/3 = 12/4 = 3
  3. 3AP = 9 cm

Answer9

Part (c) · 1 mark

Given triangle ABC has area x cm², write the area of quadrilateral BPQC using x.

  1. 1Length scale factor = 3, so area scale factor = 3² = 9
  2. 2Area AQP = 9x
  3. 3Area BPQC = 9x − x = 8x

Answer8x

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Also searched as: 4024/11/O/N/20 · 4024_w20_qp_11 · 4024 w20 11 · question 25.
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