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WAEC Mathematics 2000 Question 46

Question 46

Triangles and Quadrilaterals

In the diagram, |PQ| = |PS|. Which of the following statements is true?

Diagram for this question
  1. A.∠QPS = ∠QRS
  2. B.|PO| = |RO|
  3. C.QR||PS
  4. D.∠PQR = ∠PSR
Show the answer and explanation

Answer: D (∠PQR = ∠PSR)

Explanation

PQRS is a kite (PQ = PS and RQ = RS), symmetric about PR, so the angles at Q and S are equal: ∠PQR = ∠PSR.