Types of Symmetry

In this chapter, we will learn the types of symmetry with properties and example.

Let us first understand the basics of symmetry.

What is symmetry ?

An object is said to be symmetrical when it has similar parts / design around the imaginary axis.

For example, consider the English letter ” A “

The vertical red line is the axis O.

Note that the design on left part is same as the design on the right side.

So we can say that letter ” A ” is symmetrical around axis O.

There are 4 types of symmetry commonly used in geometry;

(a) Mirror symmetry or Reflexive symmetry
(b) Rotational symmetry
(c) Point Symmetry
(d) Translational Symmetry

We will discuss each type of symmetry in detail.

In reflexive symmetry, the object forms mirror image around the central axis.

In other words, one part of the image is the reflection of other.

For example;
Consider the image of butterfly with central axis O.

Note that the right part of butterfly is exact mirror image of the left part.

Hence, we can say that the above butterfly is Mirror symmetrical.

Other examples of this are given below;

An object is said to be in rotational symmetry when rotating the object around the central point will produce the same image.

For example, consider the below equilateral triangle ABC.

Observe that if we rotate the triangle by 120 degree clockwise, we will get the same image.

Hence, the above triangle is in rotational symmetry.

Given below are some other examples of Rotational symmetry.

When similar object is present equidistant from central point but in opposite direction then the image is in point symmetry.

For example, consider the below hourglass type object.

Draw the central point O and vertical & horizontal axis as shown below;

Now from the central point O, if you move same distance in opposite direction, you will get similar part of the image.

For example, if you travel in opposite direction OA & OB, you will reach similar parts of the image.

Example 02
Consider the below image.

Locate the central point and draw vertical & horizontal axis as shown below.

Now from point O, if you travel same distance in opposite direction you will get identical image.

If the same object is present with similar orientation and axis at a different position then the object is said to have translation symmetry.

In translation symmetry, it appears that the object is moved to another position keeping the orientation and axis same.

For example;

Note that all the three pentagons have same size and angle orientation.

It just appears that the same pentagon has been pushed in forward direction.