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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Similar questions

In which of the following quadrilaterals, diagonals bisect each other?

i) Parallelogram

ii) Rhombus

iii) Rectangle

iv) Square

v) Kite

Complete each of the following statements by means of one of those given in brackets against each :

(i) If one pair of opposite sides is equal and parallel, then the figure is ........

(parallelogram, rectangle, trapezium)

(ii) If in a quadrilateral only one pair of opposite sides is parallel, the quadrilateral is .......

(square, rectangle, trapezium)

(iii) A line is drawn from the mid-point of one side of a triangle ......, another side intersects the third side at its mid-point.

(perpendicular to, parallel to, to meet)

(iv) If one angle of a parallelogram is a right angle, then it is necessarily a ......

(rectangle, square, rhombus)

(v) The consecutive angle of a parallelogram is......

(supplementary, complementary)

(vi) If both pairs of opposite sides of a quadrilateral are equal, then it is necessarily a ........

(rectangle, parallelogram, rhombus)

(vii) If opposite angles of a quadrilateral are equal, then it is necessarily a ...........

(parallelogram, rhombus, rectangle)

(viii) If consecutive sides of a parallelogram are equal, then it is necessarily a ..........

(kite, rhombus, square)

Say True of False:

(a) Each angle of a rectangle is a right angle.

(b) The opposite sides of a rectangle are equal in length.

(d) All the sides of a rhombus are of equal length.

(e) All the sides of a parallelogram are of equal length.

(f) The opposite sides of a trapezium are parallel.

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