Symmetry And Line Of Symmetry: An Introduction

What is Symmetry?

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

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, in architecture and in 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.

Symmetry

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

Symmetry

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

Symmetry

Types of Symmetry

Symmetry may be viewed when you flip, slide or turn an object. The different types are:

  • 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.
  • 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.

A number of other kinds of symmetric types exist such as the point, translational, glide reflectional, helical, etc. which are beyond of 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.


Symmetry

Two  shapes are  said to be symmetrical to each other, if they become exactly look like one another, upon turning, flipping or sliding one or more side of one of the shapes.  In simple words, two shapes are said to be symmetrical if they can completely overlap over each other without disturbing their geometry.

In fig. 1 given below, each image is symmetrical along the line drawn because when we fold each image along the line as shown, the left and right parts are exactly identical.

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Fig. 1

Whereas if you fold the images in fig. 2 along any line, the halves obtained would not be similar. Thus, these shapes are not symmetrical.

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Fig. 2

Types:

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Reflection Symmetry:

When a shape is symmetrical about a line then it is said to possess reflection or mirror or line symmetry.

The line along which the figure is symmetrical is known as line of symmetry. The following table explains symmetrical figures based on number of lines of symmetry.

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When you look at the mirror, you see your reflection. The mirror acts as the line of symmetry here. Do you know about Kaleidoscope? It is a cylindrical instrument having a peep hole at one end. When you look into the hole and rotate the kaleidoscope, beautiful symmetrical images are observed.

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Fig. 3 Symmetrical Patterns formed by Kaleidoscope

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Practise This Question

All human beings exhibit symmetry.