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4024/21 May/Jun 2024, Question 3: Similar Triangles

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 5 marks

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The question, in short

Use an isosceles triangle PQR with exterior angle 142° at R to find angle PQR, then prove triangles ABE and CDE are similar in trapezium ABCD with diagonals meeting at E.

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Part (a) · 2 marks

Triangle PQR has PQ = QR and exterior angle at R is 142°. Calculate angle PQR.

  1. 1Angle QRP = 180 − 142 = 38° (angles on a straight line)
  2. 2Angle QPR = 38° (isosceles triangle)
  3. 3Angle PQR = 180 − 2 × 38 = 104°

Answer104

Part (b) · 3 marks

In trapezium ABCD with AB parallel to DC, diagonals AC and BD meet at E. Show triangle ABE is similar to triangle CDE, giving a reason for each statement.

  1. 1Angle AEB = angle CED (vertically opposite angles)
  2. 2Angle EAB = angle ECD (alternate angles, AB parallel to DC)
  3. 3Angle EBA = angle EDC (alternate angles)
  4. 4All three angles are equal, so triangle ABE is similar to triangle CDE

Answerangle AEB = angle CED (vertically opposite angles) angle EAB = angle ECD (alternate angles) angle EBA = angle EDC (alternate angles, or angles in a triangle add to 180°) Hence similar

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Also searched as: 4024/21/M/J/24 · 4024_s24_qp_21 · 4024 s24 21 · question 3.
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