NCERT Class VI Mathematics Chapter 13 Symmetry

National Council of Educational Research and Training (NCERT) Book for Class VI
Subject: Mathematics
Chapter: Chapter 13 – Symmetry

Class VI NCERT Mathematics Text Book Chapter 13 Symmetry is given below.
13.1 Introduction

Symmetry is quite a common term used in day to day life. When we see certain figures with evenly balanced proportions, we say, “They are symmetrical”.


4. Can you draw a triangle which has

(a) exactly one line of symmetry?

(b) exactly two lines of symmetry?

(c) exactly three lines of symmetry?

(d) no lines of symmetry?

Sketch a rough figure in each case.

5. On a squared paper, sketch the following:

(a) A triangle with a horizontal line of symmetry but no vertical line of symmetry.

(b) A quadrilateral with both horizontal and vertical lines of symmetry.

(c) A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry.

(d) A hexagon with exactly two lines of symmetry.

(e) A hexagon with six lines of symmetry.

(Hint : It will be helpful if you first draw the lines of symmetry and then complete the figures.)

6. Trace each figure and draw the lines of symmetry, if any:


Rangoli patterns

Kolams and Rangoli are popular in our country. A few samples are given here. Note the use of symmetry in them. Collect as many patterns as possible of these and prepare an album.

Try and locate symmetric portions of these patterns alongwith the lines of symmetry.

What have we discussed?


1. A figure has line symmetry if a line can be drawn dividing the figure into two identical parts. The line is called a line of symmetry.

2. A figure may have no line of symmetry, only one line of symmetry, two lines of symmetry or multiple lines of symmetry. Here are some examples.

Number of lines of symmetry Example
No line of symmetry
Only one line of symmetryTwo lines of symmetry
Three lines of symmetry
A scalene triangle
An isosceles triangleA rectangle
An equilateral triangle

3. The line symmetry is closely related to mirror reflection. When dealing with mirror reflection, we have to take into account the left ↔ right changes in orientation.

Symmetry has plenty of applications in everyday life as in art, architecture, textile technology, design creations, geometrical reasoning, Kolams, Rangoli etc.

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