Page 80 - Maths Class 06

Quad ri lat eral
C
You know that a quadrilateral is a polygon having four sides. It can also be defined as D
a simple closed figure bounded by four line segments. Fig. 5.10 shows quadrilateral
ABCD. Some special types of quadrilaterals are trapezium, parallelogram, rhombus,
rectangle, square, etc. A B
Quadrilateral
Properties of Special Types of Quadrilaterals
Fig. 5.10
Let us learn about the properties of some special types of quadrilaterals.
1. Trapezium : A quadrilateral whose one pair of opposite D C
sides is parallel is called a trapezium. Fig. 5.11 shows
trapezium ABCD in which sides ABand CD are parallel.
Parallel sides are written as AB DC|| . A Trapezium B

Fig. 5.11 S R
If non-parallel sides of a trapezium are equal, then it is called isosceles
trapezium. In trapezium PQRS, shown in Fig. 5.12, the non-parallel sides
P Q
PS and QR are equal, i e. . PS = QR. Isosceles Trapezium
Fig. 5.12
D C
2. Parallelogram : A quadrilateral whose both pairs of opposite
sides are parallel is called a parallelogram. In Fig. 5.13,
quadrilateral ABCD is a parallelogram in which opposite sides
A B D C
are parallel, i e. . AB DC AD BC|| , || . Parallelogram
Fig. 5.13
3. Rhombus : A parallelogram in which all sides are equal is called a rhombus. In Fig. 5.14
all sides of rhombus ABCD are of equal length, i e. . AB = BC = CD = DA. A B
Rhombus
Fig. 5.14
S R
4. Rectangle : A parallelogram in which opposite sides are equal and
each angle is a right angle is called a rectangle. In Fig. 5.15, opposite
sides of rectangle PQRS are equal and all the angles are right angles, i e. .
PQ = SR PS =, QR and Ð = ÐP Q = ÐR = Ð =S 90 °. P Rectangle Q
Fig. 5.15 D C

5. Square : A parallelogram in which all sides are equal and each angle is a right angle is
called a square. Fig. 5.16 shows square ABCD whose all sides are equal and all angles are
right angles, i e. ., AB = BC = CD = DA and Ð A = Ð = Ð = ÐB C D = 90 °. A Square B
Fig. 5.16
NOTE
D
A square is also called a regular quadrilateral as all its sides are equal and all its angles are equal.

A C
6. Kite : A quadrilateral whose two pairs of adjacent sides are equal is called a kite.
Fig. 5.17 shows kite ABCD which has two pairs of equal sides,
i e. . AD = CD and AB = BC.
B
Fig. 5.17
80