# Quadrilaterals : Definition and its Types

In this chapter we will discuss basics of quadrilateral and its types.

Important properties of quadrilateral are also discussed in the chapter so make sure you remember it.

Any two dimensional closed shape with 4 sides are known as Quadrilaterals.

From the above examples we can note that:
(a) All the figure have four sides
(b) The figures can be of different shapes and sizes

Some of the common form of quadrilateral used in geometry are;
(a) Square
(b) Rectangle
(c) Parallelogram
(d) Rhombus
(e) Trapezium

Let us study their property one by one.

## Square

Its a 2D figure of four sides in which all sides are equal and each angle measures 90 degree

Important Points for Square
(a) It has 4 sides
(b) Opposite sides are parallel
(c) Each angle is 90 degree

Given above are two examples of square.

(a) Side Length: All sides are equal

(b) Side Orientation : Opposite sides are parallel

(c) Angles: All angles are 90 degree
∠ A = ∠ B = ∠ C = ∠ D = 90 degree

## Rectangle

Its a quadrilateral in which Opposite sides are equal and parallel and all angles measure 90 degree

Given above is the rectangle ABCD in which:
(a) Side Length: Opposite sides are equal
AB = CD and AD = BC

(b) Side Orientation : Opposite sides are parallel

(c) Angles: All angles are 90 degree
∠ A = ∠ B = ∠ C = ∠ D = 90 degree

## Parallelogram

Parallelogram is a quadrilateral in which Opposite sides are equal and parallel. Also in parallelogram opposite angles are equal.

The above parallelogram has following features;

(a) Side Length: Opposite sides are equal
AB = CD and AD = BC

(b) Side Orientation : Opposite sides are parallel

(c) Angles: Opposite angles are equal
∠ D = ∠B
∠ A = ∠ C

## Rhombus

Rhombus is a quadrilateral with following properties;
(a) All sides are equal
(b) Opposite sides are parallel
(c) Opposite angles are equal

Rhombus can also be imagined as tilted square in which sides has been tilted at certain angle.
The quadrilateral looks like a star.

The above rhombus ABCD has following features;

(a) Side Length: All sides are equal

(b) Side Orientation: Opposite sides are parallel
AB parallel to CD
CB parallel to DA

(c) Angles : Opposite angles are equal
∠ D = ∠B
∠ A = ∠ C

## Trapezium

Trapezium is a quadrilateral with following properties;

(a) one pair of opposite sides are parallel
(b) the other pairs are non parallel

Given above is figure of trapezium ABCD with following features;
Sides AB & CD are parallel pairs
Sides AD and BC are non parallel pairs

Solution
The Quadrilateral is a square as:
⟹ Its opposite sides are equal and parallel
⟹ All angles are 90 degree

(02) Identify the below image

Solution
The Quadrilateral is a square as:
⟹ all sides are equal
⟹ all angles are 90 degrees

Solution
The given quadrilateral is a trapezium because:
(a) One pair of opposite sides are parallel ( AD II BC)
(b) Other pairs of sides are not parallel

(04) Given below is the diagram of Rhombus.
The side AB = 6 cm, find the length of side CD

In Rhombus all sides are equal.
Hence, AB = BC = CD = DA = 6 cm

(05) Given below is the figure of parallelogram.
Here ∠B = 75 degree. Find value of ∠D

Solution
We know that in parallelogram opposite angles are equal to each other.
So ∠B = ∠D = 75 degree

(06) Identify the below figure

The above quadrilateral is Rhombus because:
(a) All sides are equal
(b) Opposite sides are parallel
(c) Opposite angles are equal

(07) Below is the image of rectangle
Find the value of all angles

In rectangle all the angles are 90 degree
Hence, ∠A = ∠B = ∠C = ∠D = 90 degree

(08) Two squares ABCD & EFGH are joined to form rectangle PQRS
Its given that AD = 2 cm, find the length of side PQ of the rectangle

Its given that ABCD is a square.
We know that in square, all sides are equal.
Hence, AD = CD = 2 cm

Similarly EFGH is a square with side 2 cm

From the image we can observe that:
⟹ DC + HG = SR
⟹ 2 + 2 = SR
⟹ SR = 4 cm

Since PQSR is a rectangle, the opposite sides are equal
PQ = SR
PQ = 4 cm

Hence, length of side PQ is 4 cm

(09) Identify the below shape

Solution
From the above image you can observe that:
Side AB = CD