Symmetry And Line Of Symmetry: An Introduction

Symmetry is defined as a balanced and a proportionate similarity which is found in two halves of an object, that is, one-half is the mirror image of the other half. The imaginary line or axis along which you can fold a figure to obtain the symmetrical halves is called the line of symmetry.  In this article, let us discuss the meaning of symmetry in Maths, line of symmetry, types of symmetry with more examples and video tutorial.

Symmetry in Mathematics

In Mathematics, a meaning of symmetry defines that one shape is exactly like the other shape when it is moved, rotated, or flipped. Consider an example, when you are told to cut out a ‘heart’ from a piece of paper, don’t you simply fold the paper, draw one-half of the heart at the fold and cut it out to find that the other half exactly matches the first half? The heart carved out is an example of symmetry.


Symmetry Math definition states that “symmetry is a mirror image”. When an image looks identical to the original image after the shape is being turned or flipped, then it is called symmetry. It exists in patterns. You may have often heard of the term ‘symmetry’ in day to day life. It is a balanced and proportionate similarity found in two halves of an object, that is, one-half is the mirror image of the other half. And a shape that is not symmetrical is referred to as asymmetrical. Symmetric objects are found all around us, in nature, architecture, and art.

Line of Symmetry

The imaginary line or axis along which you fold a figure to obtain the symmetrical halves is called the line of symmetry. It basically divides an object into two mirror-image halves. The line of symmetry can be vertical, horizontal or diagonal. There may be one or more lines of symmetry.

  • 1 line: Figure is symmetrical only about one axis. It may be horizontal or vertical. The word ATOYOTA has one axis of symmetry along the axis passing through Y.


  • 2 lines: Figure is symmetrical only about two lines. The lines may vertical and horizontal lines as viewed in the letters H and X.


  • Infinite lines: Some figures have not one or two, but infinite lines passing through the centre, and the figure is still symmetrical. Example: a circle.



Types of Symmetry

Symmetry may be viewed when you flip, slide or turn an object. There are types of Symmetry which are:

  • Reflexive
  • Rotational Symmetry

Reflective or Line: A figure is symmetrical about a dotted line which divides it into two equal halves. This is often referred to as the basic type.

Read: Reflection Symmetry

Rotational Symmetry: You rotate a shape about an axis and it appears exactly the same as it did before rotation. Example: a square, a rectangle, etc.

Read: Rotational Symmetry

A number of other kinds of symmetric types exist such as the point, translational, glide reflectional, helical, etc. which are beyond the scope of learning at this stage. Know much more about two lines of symmetry and reflection symmetry and also get the detailed solutions to the questions of the NCERT Books for the chapter Symmetry at BYJU’S.


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