TYPES OF QUADRILATERALS

TYPES OF QUADRILATERALS

TRAPEZIUM:

A quadrilateral which has one pair of opposite sides parallel, is called a trapezium. In figure, PQ || RS and therefore, the quadrilateral PQRS is a trapezium.

PARALLELOGRAM:

It is a quadrilateral in which both the pairs of opposite sides are parallel. The adjoining figure shows a quadrilateral ABCD in which AB is parallel to DC and AD is parallel to BC, therefore ABCD is a parallelogram.

RECTANGLE:

In a parallelogram, if one angle is right angle, then the quadrilateral is called a rectangle. Each angle of a rectangle is a right angle.

In figure, PQ || SR, PS || RQ and ∠P = ∠Q = ∠R = ∠S = 90°

Therefore, quadrilateral PQRS is a rectangle.

RHOMBUS:

It is a quadrilateral whose all the sides are equal. The adjoining figure shows a quadrilateral ABCD in which AB = BC = CD = DA ; therefore it is a rhombus.

SQUARE:

In a quadrilateral if all the four sides are equal and one angle is right angle, then all the other three angles are also right angles. Such a quadrilateral is called a square.

In figure PQ = SR = PS = RQ and ∠P = ∠Q = ∠R = ∠S = 90° Therefore, quadrilateral PQRS is a square.

KITE:

It is a quadrilateral in which two pairs of adjacent sides are equal. The adjoining figure shows a quadrilateral ABCD in which adjacent sides AB and AD are equal i.e., AB = AD and also the other pair of adjacent sides are equal i.e., BC = CD; therefore it is a kite or kite shaped figure.

Remark:

1. Square, rectangle and rhombus are all parallelograms.
2. Kite and trapezium are not parallelograms.
3. A square is a rectangle.
4. A square is a rhombus.
5. A parallelogram is a trapezium.