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0580/23 May/Jun 2021, Question 15: Finding Missing Sides

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 6 marks

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The question, in short

In a diagram with AB parallel to CD and diagonals AD and BC crossing at X, use the given lengths to identify similar triangles and find lengths and areas.

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

Part (a) · 1 mark

Complete the similarity statement naming the triangle that ABX is similar to.

  1. 1AB ∥ CD gives equal alternate angles, and vertically opposite angles at X are equal
  2. 2So the triangles are similar

AnswerSimilar

Part (b) · 2 marks

Calculate the length of BX using the given side lengths and similarity.

  1. 1Scale factor = 6/12 = 1/2
  2. 2BX corresponds to CX = 8
  3. 3BX = 8 × 1/2 = 4

Answer4

Part (ci) · 2 marks

Given the area of triangle DCX is 26.906 cm², find the area of triangle ABX.

  1. 1Length scale factor = 1/2, so area factor = 1/4
  2. 2Area ABX = 26.906 ÷ 4
  3. 3= 6.7265

Answer6.7265 or 6.73 or 6.726 to 6.727

Part (cii) · 1 mark

Using the same area value, find the area of triangle ACX.

  1. 1Triangles ACX and ABX share the same height from A to line BC
  2. 2CX = 8 and BX = 4, so area ACX = 2 × area ABX
  3. 3Area ACX = 6.7265 × 2 = 13.453

Answer13.453 or 13.5 or 13.45 to 13.46

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