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Converse of Opposite Sides of a Parallelogram Are Equal

Question 25Wh...

Question

Question 25
Which one has all the properties of a kite and a parallelogram?
a) Trapezium
b) Rhombus
c) Rectangle
d) Parallelogram

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Solution

Properties of a kite:
Two pairs of equal sides.
Diagonals bisect at $90^{\circ}$ .
One pair of opposite angles are equal.

Properties of a parallelogram:
Opposite sides are equal.
Opposite angles are equal.
Diagonals bisect each other.

So, from the given options, all these properties are satisfied by the rhombus.

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Q. Question 25
Which one has all the properties of a kite and a parallelogram?
a) Trapezium
b) Rhombus
c) Rectangle
d) Parallelogram

Q. State whether True or False.
(a) All rectangles are squares.
(b) All rhombuses are parallelograms.
(c) All squares are rhombuses and also rectangles.
(d) All squares are not parallelograms.
(e) All kites are rhombuses.
(f) All rhombuses are kites.
(g) All parallelograms are trapeziums.
(h) All squares are trapeziums.

Q. 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)

A = {P a r a l l e l o g r a m s}

B = {S q u a r e, R e c t a n g l e, R h o m b u s, T r a p e z i u m}

B - A

.

A rhombus has the properties of a parallelogram and that of a kite.

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