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.

**What are Quadrilaterals?**

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

Examples of Quadrilateral are:

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

**Types of Quadrilateral**

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

**Summary of Quadrilateral**

**Questions on Quadrilaterals**

**(01) Identify the below quadrilateral**

**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

**(03) Identify the below quadrilateral **

**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

Side AD = BC

And all angles are 90 degree

**Hence, the above figure is of rectangle**