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0580/43 May/Jun 2026, Question 8: Similar Triangles

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 5 marks

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The question, in short

Parallel lines AB and CD with transversals AD and BC meeting at X; angle ABX is y°. Complete a reason for angle DCX, then use similar triangles ABX and DCX with CX = 5 cm, XD = 8 cm, AD = 20 cm and angle CXD = 80.5°.

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

Part (a) · 1 mark

State the geometrical reason why angle DCX equals angle ABX, given the parallel lines and the straight lines crossing at X.

  1. 1AB is parallel to CD and BC is a transversal
  2. 2Angle DCX and angle ABX are alternate angles, so they are equal

AnswerAlternate angles are equal

Part (bi) · 2 marks

Using the similar triangles and the given lengths CX = 5 cm, XD = 8 cm and AD = 20 cm, find BX.

  1. 1AX = 20 − 8 = 12
  2. 2BX/CX = AX/DX
  3. 3BX/5 = 12/8
  4. 4BX = 5 × 1.5 = 7.5 cm

Answer7.5

Part (bii) · 2 marks

With angle CXD = 80.5° and the given side lengths, work out the area of triangle CXD.

  1. 1Area = 1/2 × CX × XD × sin 80.5°
  2. 2= 1/2 × 5 × 8 × sin 80.5°
  3. 3= 19.72… = 19.7 cm²

Answer19.7 or 19.72 to 19.73

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Also searched as: 0580/43/M/J/26 · 0580_s26_qp_43 · 0580 s26 43 · question 8.
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