# Types of Symmetry – Line, Translation, Rotational, Reflection, Glide | Different Types of Symmetry with Examples

Symmetry is one of the important concepts of geometry. If one part of the object looks like the same as another part of the object when we turn, flip, or slide, then it is called symmetry. If an object is not looking like another part of the object then it is called asymmetric.

To find out a given object is symmetric, we need to follow some steps. Firstly, draw a line on the middle of the image or object, and observe the image or object whether the left side of the object is the same as the right side or not. If the image is symmetrical, then the left side of the image is looking like a mirror image of the right side of the image or not. We can define different types of symmetries as below.

## Example Images of Symmetry

### Line of Symmetry

An object is divided into two parts with the help of a line and the two parts are mirror images of an object, then it is called a line of symmetry. The line of symmetry is also called as ‘axis of symmetry’. The line may be either vertical or horizontal or diagonal.

#### Vertical Line of Symmetry

The above figure shows the hexagonal image divided into two parts with the help of a vertical line. Here, the vertical line divides the above image into two parts and these two parts are mirror images for each other. That means, both the parts of an image are the same. This type of symmetry is called as Vertical line of Symmetry.

#### Horizontal Line of Symmetry

The above diagram shows that the image is split into two parts with the help of a horizontal line. Here, the horizontal line dividing the above image into two parts, and these two parts are equal halves of the image. This type of symmetry is called a horizontal line of symmetry.

#### Diagonal Line of Symmetry

From the above diagram, an image is divided into two equal halves by the diagonal line. These two equal halves are mirror images of each other. This type of line of symmetry is called as Diagonal Line of Symmetry.

Again we have a number of types in line of symmetry. Yes, we can divide the image into a number of parts with the help of one line, two-line,s or more lines. Every part must be the mirror image of another.

#### One Line of Symmetry

By using the vertical or horizontal or diagonal line, we need to divide the image into equal halves and it is called one line of symmetry. Above mentioned, vertical, horizontal, and diagonal lines of symmetry are examples of one line of symmetry.

#### Two Lines of Symmetry

Same like one line of symmetry, in two lines of symmetry also we can use the vertical or horizontal or diagonal lines but we need to use only two lines to divide the image equally. This type of line of symmetry is called Two lines of Symmetry.

#### Infinite Lines of Symmetry

An image or object is divided into a number of parts with the help of a number of lines and these equal halves of the image. It is called Infinite Lines of Symmetry. These lines are either vertical or horizontal or diagonal lines.

### Some Other Types of Symmetry

We have different types of symmetries considered depending on the various cases. They are

1. Translational Symmetry
2. Rotational Symmetry
3. Reflexive Symmetry
4. Glide Symmetry

#### 1.Translational Symmetry

An object or image is moving forward or backward or changing the position from one place to another, but there is no change in the image or object. This type of Symmetry is called Translational Symmetry.

#### 2.Rotational Symmetry

An object or image is rotated in a particular direction but the position of an object or image is identical to the origin of an image or object, then it is called rotational symmetry. It is also called radial symmetry.

From the above figure, we can observe the rotational symmetry. If you rotate the hexagonal object or image in a 60° clockwise direction with respect to the origin, there is no change in the shape of an image. More Examples for Rotational Symmetry are Circle, Hexagonal, Square, Rectangle, and etc…

#### 3.Reflexive Symmetry

Reflexive Symmetry is the same as a line of symmetry. Yes, in this type of symmetry one part of the image or object represents the mirror image of another part of the image. Reflexive Symmetry is also called a line of symmetry or mirror symmetry. The below figure is a better example of Reflexive symmetry.

The above object is divide into two parts and the left side part is the mirror image of the right side of the image.

#### 4.Glide Symmetry

It is the combination of both translation symmetry and reflection symmetry.

### Point Symmetry

When an object is in opposite direction, every part of the object must be matched with the original object. It is called Point Symmetry. It is the same as Rotational Symmetry, so we can call it Rotational Symmetry order 2.

### Solved Examples on Types of Symmetry

1. Name and draw the shape which possesses linear symmetry, point symmetry, and rotational symmetry?

Solution:
(i) Line Segment

• Linear symmetry is a line of symmetry. here, it indicates ‘AB’.
• Point symmetry, the mid-point of the line of origin of the image that is ‘O’.
• Rotational Symmetry, If we move the above image in any direction with respect to the origin, there is no change in the image. Here, the origin of the image is ‘O’

(ii) Square

• Linear symmetry, two lines of symmetry.
• Point symmetry, the intersection of two lines that is ‘O’.
• Rotational Symmetry order of 2.

2. If the following figure shows a line of symmetry, then complete the figure?

Solution:
The line of symmetry, vertical or horizontal line divides the image into two equal halves and two parts are look as same. So, the remaining part of the image also the same as the above figure. That is,

3. Identify which of the following figure is the example for symmetry?

Solution:
In the symmetry method, an image or object is divided into equal halves either it may be vertical lines or horizontal lines. Each part must be a mirror image of the other part of the image. That particular image, we can consider as the example for symmetry. In the above diagrams, figure ‘c’ is showing as an example of symmetry. In that one only, the image is divided into two equal halves and the remaining A and B are not divided into equal halves.

4. How many lines of symmetry does a rectangle have?

Solution:
Four lines of symmetry. One horizontal line, one vertical line, and two diagonal lines.

5. Identify which of the following image indicates the rotational symmetry?

Solution:
By moving in a forward or backward direction, an object or image will be in the same as the original image, which is called rotational symmetry. From the above, Figure (A) is the best example for Rotational symmetry.

### FAQs on Types of Symmetry

1. What is Symmetry?

In symmetry, an object is divided into equal parts and each part of an object is a mirror image of another part of the object.

2. What are the Types of Symmetry?

There are four types of symmetry. They are

1. Translational Symmetry
2. Rotational Symmetry
3. Reflexive Symmetry
4. Glide Symmetry

3. What is a Line of Symmetry?

An object or image is divided into equal halves with horizontal or vertical or diagonal lines. But the left side of the image is the same as the right side of the image that is called a line of symmetry.

4. What is Point Symmetry?

If we place the image or object in the opposite direction, then every part of the image must be matched with the equal distance that is called point symmetry.

5. What is Asymmetric?

An object is divided into equal parts but the left side of the image is not the same as the right side of the image and it is called an asymmetric method.