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WAEC Mathematics 1996 Question 32

Question 32

Triangles and Quadrilaterals

In the diagram below, /PQ/ = /PS/ and /QR/ = /SR/. Which of the following is/are true? I. the line PR bisects < QRS II. The line PR is the perpendicular bisector of the line segment QS III. Every point on PR is equidistant from SP and QP.

Diagram for this question
  1. A.I only
  2. B.III only
  3. C.I and II only
  4. D.I and III only
  5. E.I, II and III
Show the answer and explanation

Answer: E (I, II and III)

Explanation

PQRS is a kite, symmetric about PR. So PR bisects angles R and P (I true), cuts QS at right angles through its midpoint (II true), and any point on the bisector of angle P is the same distance from the lines PS and PQ (III true).