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Let us take another trapezium whose non-parallel sides are equal.

A trapezium in which the non-parallel sides are equal, is called an D C
isosceles trapezium.
In the adjoining figure, ABCD is an isosceles trapezium, where AB || DC
and non-parallel sides AD = BC.
We have ∠A + ∠D = 180° and ∠B + ∠C = 180°. A B

Also, ∠A = ∠B and ∠C = ∠D.
Kite

Kite is a special type of quadrilateral. The sides with the same markings A
in the figure are equal.
So, we can say that if two pairs of adjacent sides are equal in a B O D
quadrilateral, then it is called a kite.

In the adjoining figure, ABCD is a kite, where AB = BC and AD = CD. C
Properties of a Kite

• The two diagonals are perpendicular to each other.

• One of the diagonals bisects the other one.
• ∠A = ∠C but ∠B ≠ ∠D

activity
l Take a white sheet of paper and fold it once. Cut out a shape as shown in
the figure.
l You will get a shape as of a kite. Now, fold both the diagonals of the kite.
Use a set-square to check whether the diagonals cut at right angles. By
folding an angle of the kite on its opposite, check whether the angles are
of equal measure, and also check for the diagonals as the angle bisectors.

Parallelogram

A quadrilateral in which both pairs of opposite sides are parallel is called a parallelogram.

In the adjoining figure, quadrilateral ABCD is a parallelogram where AB || CD and AD || BC.
In the parallelogram ABCD, A B
• Pairs of opposite sides are AB and DC, AD and BC.

• Pairs of opposite angles are ∠A and ∠C, ∠B and ∠D. D C
• Pairs of adjacent sides are AB and BC, BC and CD, CD and DA, and DA and AB.

• Pairs of adjacent angles are ∠A and ∠B, ∠B and ∠C, ∠C and ∠D, and ∠D and ∠A.
Properties of Parallelogram

1. The opposite sides and the opposite angles of a parallelogram are equal.
Let us take a parallelogram ABCD in which AB||CD and BC||AD.

Draw a diagonal AC in it. By doing so, the parallelogram ABCD is divided into two triangles
ABC and CDA.

67 Quadrilaterals