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0580/42 May/Jun 2022, Question 9: Similar Triangles

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 7 marks

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The question, in short

Use the given triangle diagrams to justify a pair of similar triangles, then use similarity to find a missing length and an area.

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

Part (a) · 3 marks

Using the right angles and shared angle shown, give reasons why triangles PMR and MSR are similar.

  1. 1Angle PMR = angle MSR = 90° (both right angles)
  2. 2Angle PRM = angle MRS (same angle, common to both triangles)
  3. 3So the third angles are equal too (angle MPR = angle SMR): all three angles match, so the triangles are similar

AnswerPMR = MSR = 90° (right angles), PRM = MRS (same angle), so AAA (or MPR = SMR, third angle of triangle)

Part (bi) · 2 marks

Given similar triangles ABC and PQR with AC = 4.5 cm, BC = 8.1 cm, QR = 9.9 cm, find x, the length PR.

  1. 1Scale factor = 9.9 ÷ 8.1
  2. 2x = 4.5 × 9.9 ÷ 8.1 = 5.5

Answer5.5

Part (bii) · 2 marks

Triangle PQR has area 25 cm²; using the similarity, work out the area of triangle ABC.

  1. 1Area scale factor = (8.1/9.9)²
  2. 2Area of ABC = 25 × (8.1/9.9)² = 16.73… ≈ 16.7 cm²

Answer16.7 or 16.73 to 16.74

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