Symmetry Class 6 Maths Notes - Chapter 13

Symmetry And Line Of Symmetry Definition

The symmetry of an object is defined as one half of the object is a mirror image of the other half. When an object is split into half, both the sides are exactly the same. The line which divides them is called the line of symmetry. One simple example is reflection symmetry. The object can be divided into one or more than one lines of symmetry.

Below are some types of line of symmetry along with examples-

S.NO Type Example
1 No line of symmetry Scalene triangle
2 1  line of symmetry Isosceles triangle
3 2  lines of symmetry Rectangle
4 3  lines of symmetry Equilateral triangle

Introduction to Symmetry

When figures have equally balanced proportions, they are said to be symmetrical.

Symmetry-1

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Bilateral symmetry

If a figure is divided into two halves by only one line and these halves overlap each other completely, then the figure is said to have bilateral symmetry.
Example: A butterfly shows bilateral symmetry.

Symmetry-2

 

Line symmetry

A figure has line symmetry if a line can be drawn dividing the figure into two symmetrical parts. The line is called a line of symmetry.
Example: The dotted lines in the following figures show line symmetry.

Symmetry-3

 

Lines of symmetry

A figure can have any number of lines of symmetry passing through it. Some can have one, two or even multiple lines of symmetry.
Example of a single line of symmetry: A door lock.

Symmetry-4
Example of two lines of symmetry: A rectangle.
Symmetry-5
Example of multiple lines of symmetry (two or more): an equilateral triangle.

Symmetry-6

Point Symmetry and Reflection Symmetry

Reflection Symmetry

Reflection symmetry is very similar to line symmetry except for the change in orientation.

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For example, when you view yourself in the mirror, your right hand becomes the left hand in the mirror.

Symmetry-8

 

Point Symmetry

Point symmetry exists when a figure is drawn around a single central point.
It is for figures having a point through which the symmetry can be established. This point is called the centre of symmetry.

For example, the hourglass shows point symmetry.

symmetry-9

 

Kaleidoscope

A kaleidoscope uses mirrors to produce images that have several lines of symmetry.
Symmetry-10
Usually, two mirror strips forming a V-shape are used.
The angle between the mirrors determines the number of lines of symmetry.
The figure below shows the pattern formed by a kaleidoscope.

Symmetry-11

 

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