# Angle of Rotational Symmetry

In this chapter we will look at the concept of Rotational symmetry with solved examples.

Let us first review the basics of Rotational Symmetry.

## What is Rotational Symmetry ?

An object which after rotation produce the same image and can coincide with each other is said to be in rotational symmetry.

For example, consider the below rectangle.

Let us rotate the rectangle by 90 degree clockwise.

Note that image (ii) and (iv) match the original object.

The above image shows that when we rotate the rectangle by 180 degree we get the same image.

Hence, rectangle has rotational symmery.

## What is Angle of Rotational symmetry ?

It’s the angle of rotation at which the identical image of the given object is produced.

Hence, it is the smallest angle of rotation in which the object can be rotated to coincide with itself.

For example, consider the rectangle used above.

We have seen that of we rotate the rectangle by 180 degree, we will get the same image.

Let us now look at some other example of angle of rotational symmetry.

Example 02
Rotational symmetry of equilateral triangle

Consider the below equilateral triangle.

If we rotate the equilateral triangle by 120 degree, we will get the same image.

Hence, the rotational symmetry for equilateral triangle is 120 degree.

You can consecutively rotate the above equilateral triangle and all the time you will get the same image.

Example 03
Rotational symmetry for Hexagon.

Consider the below regular hexagon with all equal sides.

If we rotate the hexagon by 60 degree we get the same image which can coincide each other.

Hence, the angle of rotational symmetry for hexagon is 60 degree.

Example 04
Consider the below triangle ABC

The given triangle does not have any angle of rotational symmetry as we can’t get the same image after the rotation.