What is Symmetry ? Definition with examples

Symmetry Definition

When two or more parts of an object or shape are identical after a flip, slide or turn (rotation), then the shape has symmetry.
Symmetry is a quality of being made up of exactly similar parts facing each other or around an axis.

What is Line of Symmetry

The imaginary line or axis along which you fold the figure to obtain the symmetrical halves is called the line of symmetry. It basically divides an object into mirror-image halves

what is the axis of symmetry

Note – The line of symmetry can be vertical, horizontal or diagonal

what is the line of symmetry
examples of line of symmetry

One line of symmetry. – Figure is symmetrical only about one line. This line of symmetry can be horizontal, vertical or diagonal.

one line of symmetry example

Two line of symmetry. – Figure is symmetrical only about 2 line. These lines of symmetry can be horizontal or vertical.

Two line of symmetry example

Note – Some figures have more than two lines of symmetry
In the following figures, you can see there are multiple lines of symmetry which can cut the figure to form mirror image

what is line of symmetry

Symmetry of a circle

In a circle (all the lines passing through the center are lines of symmetry)

symmetry of circle. 
In circle there are multiple lines of symmetry

Asymmetry or Asymmetrical objects/shapes – objects or shapes which have no any line of symmetry are asymmetrical objects or shapes. Asymmetry is lack of symmetry

what are asymmetrical objects

Types of Symmetry

Types of symmetry with example

a. Reflection symmetryWhen one side of the object is the mirror image of the part on the other side, when the line of symmetry is drawn, then called reflection symmetry.

what is reflection symmetry

b. Rotational SymmetryRotational symmetry (or radial symmetry) is when an object is rotated in a certain direction around a point.

what is rotational symmetry

In above example the figure is rotated by 90o, hence, they are also called 90o rotational symmetry.

examples of rotational symmetry
examples of  symmetry

c. Point SymmetryA figure has point symmetry if there is a central point so that the part of the figure on one side of the central point is the reflection of the part on the other side

what is point symmetry

Note – 180o rotational symmetry is also a point symmetry

point symmetry definition

d. Translational Symmetry If the object is moved from one position to another, the same orientation in the forward and backward motion is called translational symmetry.

In other words, it is defined as the sliding of an object about an axis. 

what is translational symmetry
what are examples of translational symmetry

Real life examples of symmetry

some real life examples of symmetry
are wings of butterfly symmetrical
examples of symmetry

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