In this chapter we will learn the concept of linear symmetry and line of symmetry with examples and properties.

## Linear Symmetry definition

It is a symmetry in which a** line drawn from the middle of given figure divides it into two equal halves**.

The two equal figures will be **mirror image of each other** such that when we fold the figure across the line of symmetry, the image will completely overlap each other.

**Note:**

Line of symmetry is sometimes also called **axis of symmetry**.

## What is Line of Symmetry?

The line which **completely divide the figure into two equal symmetrical shape** is called line of symmetry.

There are three types of Line of symmetry;

(a) Horizontal line of symmetry

(b) Vertical line of symmetry

(c) Diagonal line of symmetry

Let us learn each of the one by one.

Horizontal Line of Symmetry

The horizontal line which divide the given shape into two equal halves is called horizontal line of symmetry.

For example;

Given above is the square ABCD and Line MN is a horizontal line of symmetry.

Note that line MN divide the square into two equal halves such that they are mirror image of each other.

In the above example, letter ” H ” is divided into two equal halves by horizontal line of symmetry MN.

### Vertical Line of Symmetry

The vertical line which divide the given figure into two equal parts such that the divided part is mirror image of each other.

For Example;

Given above is the square ABCD with vertical line of symmetry PQ.

Note that the line PQ divides the square into two equal halves such that both the halves are mirror image of each other.

Similarly in the above image, the letter ” H ” is divided into two equal halves by vertical line PQ.

### Diagonal Line of symmetry

A tilted line which divides the given shape into two equal halves is called Diagonal line of symmetery.

The divided parts are equal and mirror image to each other.

For Example;

In the above image square ABCD get divided into two halves by line RS.

The divided parts ACD and ACB are equal and mirror image to each other.

Hence, line RS is a diagonal line of symmetry.

Similarly in the above image, line MN divides the square into two equal halves.

Hence, line MN is diagonal line of symmetry.

**Note: **

Any given shape can have one or more line of symmetry.

## Common Line of Symmetry Examples

**(a) Equilateral triangle**

It is a triangle in which all sides and angles are equal.

Given above is the equilateral triangle in which ED, FG and HI are the line of symmetry.

Hence, in equilateral triangle, there are **three lines of symmetry**.

**(b) Isosceles Triangle**

In Isosceles triangle, two sides and angle are equal.

Given above is the isosceles triangle such that AB = AC.

Line MN is the line of symmetry which divides the triangle in two equal halves.

Hence, isosceles triangle have only **one symmetry line**.

**(c) Square**

It is a polygon with 4 equal sides and angle measurement.

Note that the square have **4 line of symmetry**.

In the above image; MN, RS, YZ & PQ are the symmetry lines which divide the square into 4 equal halves.

**(d) Rectangle**

Rectangle is a polygon in which opposite sides are equal & parallel.

In rectangle, all the angle measure 90 degree.

In the above rectangle, line MN & OP are the axis of symmetry which divide the rectangle into two equal halves.

Hence in rectangle, there are **two axis of symmetry**.

**(e) Circle**

In circle there can be infinite numbers of line of symmetry.

In a circle, any straight line passing through the center will be the axis of symmetry.

Given above is the circle with **3 lines of symmetry **GH, CD & FE passing through the center.

Hence in a circle, there are infinite number of symmetry lines possible.

(f) **English Letter – I**

For letter I, there are **two line of symmetry MN and OP**.

(g)** English Letter – K**

For letter K, there is only **one line of symmetry**.