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WAEC Mathematics 2005 Question 27

Question 27

Angles and Polygons

The figure shows a quadrilateral PQRS having equal sides and opposite sides parallel. The diagonals PR and QS intersect perpendicularly at O, which of the following statements cannot be correct?

Diagram for this question
  1. A.|PO| = |RO|
  2. B.PQR is an equilateral triangle
  3. C.PQRS is a parallelogram
  4. D.There are two lines of symmetry.
Show the answer and explanation

Answer: B (PQR is an equilateral triangle)

Explanation

PQRS is a rhombus: its diagonals bisect each other, it is a parallelogram, and it has two lines of symmetry. Triangle PQR is isosceles but not, in general, equilateral.