Discussion
PQRS is a quadrilateral in which PQ = PS and RQ = RS. Which of the following statements is true about this quadrilateral ?
Answer: B
The true statement is that its diagonals are perpendicular to each other.
A quadrilateral with two pairs of equal adjacent sides (PQ = PS and RQ = RS) is a kite. P and R are each equidistant from Q and S, so both lie on the perpendicular bisector of QS. The diagonal PR is therefore that perpendicular bisector, and the diagonals cross at right angles.
The other properties do not hold for a kite in general. Equal diagonals belong to rectangles, diagonals bisecting each other to parallelograms, and both diagonals bisecting the vertex angles to a rhombus; in a kite only PR bisects the angles at P and R.
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