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Question

Which of the quadrilaterals mentioned in brackets have the following properties?

(1) Diagonals are congruent. (square, rectangle, rhombus)
(2) The longer diagonal is the perpendicular bisector of the shorter and the shorter of the longer. (trapezium, kite, rhombus)
(3) All sides and angles are congruent. (rhombus, square, rectangle)
(4) Opposite angles are congruent. (kite, parallelogram, rectangle)
(5) Opposite sides are congruent. (trapezium, rectangle, parallelogram)
(6) Diagonals bisect each other at right angles. (square, rectangle, rhombus)
(7) Diagonals bisect each another. (rectangle, parallelogram, kite)
(8) One pair of opposite sides is parallel. (kite rhombus trapezium)

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Solution

(1) In a square and in a rectangle, diagonals are congruent.
(2) In a kite and in a rhombus, the longer diagonal is the perpendicular bisector of the shorter and the shorter of the longer.
(3) In a square, all the sides and all the angles are congruent.
(4) In a parallelogram and in a rectangle, opposite angles are congruent.
(5) In a rectangle and in a parallelogram, opposite sides are congruent.
(6) In a square and in a rhombus, diagonals bisect each other at right angles.
(7) In a rectangle and in a parallelogram, diagonals bisect one another.
(8) In a trapezium, one pair of opposite sides is parallel.

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