# NCERT Solutions for Class 6 Maths Chapter 13 Symmetry

NCERT Solutions for Class 6 Maths Chapter 13 Symmetry: In nature tree-leaves, humans, animals, beehives, flowers, and in the religious logo and symbols you can find various types of symmetrical designs. Symmetry means that one shape becomes exactly like another when you turn, flip or slide it in some way. In this chapter, you will learn some basic symmetry concepts like line symmetry, lines of symmetry for regular polygons, and rotational symmetry. In this article, you will get NCERT solutions for class 6 maths chapter 13 symmetry where you get questions related to finding basic symmetry of some mathematical geometry. It is an important concept of the geometrical part used by designers, artists, architects, and everybody who is working with some kind of design. In solutions of NCERT for class 6 maths chapter 13 symmetry, you will get questions related to different lines of symmetry such as a single line of symmetry, two lines of symmetry, three lines of symmetry or multiple lines of symmetry.

Line of symmetry:- If any object or figure can be divided into two identical parts by a virtual line it has a line of symmetry. For example, If you cut the image of a human vertically through the middle of the head then both half will be the same. So you can say that human has a single line of symmetry. In class 7 you will study the rotional symmetry and the order of symmetry. A scalene triangle (all three sides have different lengths) has no line of symmetry, an isosceles triangle has only one line of symmetry, a rectangle has two lines of symmetry and an equilateral triangle has three lines of symmetry. There are 17 questions in 3 exercises of this chapter that are related to line of symmetry. You will get detailed explanations of all these questions in the CBSE NCERT solutions for class 6 maths chapter 13 symmetry. You will get the conceptual clarity of line of symmetry once you go through these solutions. You can get NCERT solutions from class 6 to 12 to learn science and maths by clicking on the above link.

## The main topics of the NCERT Solutions for Class 6 Maths Chapter 13 Symmetry are listed below:

13.1 Introduction

13.2 Making Symmetric Figures: Ink-blot Devils

13.3 Figures with Two Lines of Symmetry

13.4 Figures with Multiple (more than two) Lines of Symmetry

13.5 Reflection and Symmetry

Solutions of NCERT for Class 6 Maths Chapter 13 Symmetry are given below-

## NCERT solutions for class 6 maths chapter 13 symmetry-Exercise: 13.1

Examples of symmetrical objects that we use in our home or school are as follows:

Book, DVD, spectacles, compass, etc.

From the figure we can say that line $\small l_2$ is the mirror line.

Because, when the figure is completely folded about the line $\small l_2$ then the left part is covered by the right part completely.

(a) Yes, it is symmetrical.

And the line of symmetry is shown in the figure.

(b) Yes, it is symmetrical.

And the line of symmetry is shown in the figure.

(c) No, it is not symmetrical hence there is no line of symmetry in it.

(d) Yes, it is symmetrical.

And the line of symmetry is shown in the figure.

(e) Yes, it is symmetrical.

And the line of symmetry is shown in the figure.

(f) Yes, it is symmetrical.

And the line of symmetry is shown in the figure.

After completion of the above-given figures, we obtain the following figures.

(a)

(b)

(c)

(d)

(e)

(f)

The given figure can be completed as follows:

The above diagram can be completed as follows:

## Solutions of NCERT for class 6 maths chapter 13 symmetry-Exercise: 13.2

The number of lines of symmetry for each of the following shapes is given:

(a)

The given figure has 4 lines of symmetry

(b) .

The given figure has 4 lines of symmetry.

(c)

The given figure has 4 lines of symmetry

(d)

The given figure has only 1 line of symmetry.

(e)

The given figure has 6 lines of symmetry.

(f)

The given figure has 6 lines of symmetry.

(g)

The given figure is asymmetrical and thus, there is no line of symmetry.

(h)

The given figure is asymmetrical and thus, there is no line of symmetry.

(i)

The given figure has 5 lines of symmetry.

(a) The line of symmetry of the given figure:

There is only one line of symmetry therefore, it is an isosceles triangle.

(b) The line of symmetry of the given figure:

There is only one line of symmetry therefore, it is an isosceles triangle.

(c) The line of symmetry of the given figure:

There is only one line of symmetry and an angle is right-angled therefore, it is a right-angled isosceles triangle.

(d) The line of symmetry of the given figure:

There is no line of symmetry therefore, it is a scalene triangle.

Question:3 Complete the following table.

 Shape Rough figure Number of lines of symmetry Equilateral triangle 3 Square Rectangle Isosceles triangle Rhombus Circle

The completed table is shown below:

 Shape Rough Figure No. of lines of symmetry Equilateral triangle 3 Square 4 Rectangle 2 Isosceles Triangle 1 Rhombus 2 Circle Infinite or countless

Question: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.

(a) Yes, with one line of symmetry we have the triangle:

This is an isosceles triangle.

(b) No, as there exists no triangle with only two symmetry lines.

Hence, no such triangle is possible.

(c) Yes, a triangle with three lines of symmetry is possible:

And it is an equilateral triangle, shown below in the figure.

(d) Yes, the triangle with no line of symmetry is possible and it is a scalene triangle:

Shown below,

(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.)

(a) Triangle with only one line of symmetry is the horizontal line of symmetry and no vertical line of symmetry.

Hence, for the given case,

The triangle can be drawn as:

(b) The quadrilateral which has both the horizontal line and the vertical line of symmetry.

Hence, for the given case:

The quadrilateral can be drawn as:

(c) The quadrilateral which has only one line of symmetry that is:

The horizontal line of symmetry and No, vertical line of symmetry.

Hence, for the given case we have:

The quadrilateral can be drawn as:

(d) The hexagon which has exactly two lines of symmetry that is:

The horizontal line of symmetry and the vertical line of symmetry.

Hence, for the given case, we have the hexagon can be drawn as:

(e) The hexagon has all six lines of symmetry.

First, draw the six lines of symmetry and then complete the hexagon.

Hence, for the given case,

The hexagon can be drawn as:

(a) The given figure is asymmetrical. Hence, there is no possibility of the line of symmetry.

(b) By observation, the given figure has two squares having a common vertex.

Hence, there are two lines of symmetry possible.

(c) By observation, the given figure has two squares with a common centre.

Hence, the given figure will have four lines of symmetry.

(d) By observation, the given is octagonal.

Hence, it will have two lines of symmetry.

(e) By observation, the given figure is not any specific.

Hence, It will have only one line of symmetry.

(f) Here, we can observe that the given figure is a four-cornered figure.

Hence, it will have four lines of symmetry.

(a) vertical lines of symmetry (like A)

(b) horizontal lines of symmetry (like B)

(c) no lines of symmetry (like Q)

(a) The letters having the vertical line of symmetry are as follows:

A, H, I, M, O, T, U, V, W, X, Y

(b) The letters having the horizontal line of symmetry are as follows:

B, C, D, E, H, I, K, O, X

(c) The letters that have no line of symmetry are as follows:

F, G, J, L, N, P, Q, R, S, Z

By observation we can complete the given figure as follows:

## CBE NCERT solutions for class 6 maths chapter 13 symmetry topic 13.5 reflection and symmetry

The image appears to be 200 cm away from us, i.e., 100 cm on the other of the mirror.

And if we move towards the mirror, the image moves closer to us and to the mirror, but the size remains the same.

NCERT solutions for class 6 maths chapter 13 symmetry-Exercise: 13.3

(a) From the given figure, we can observe that,

There are 4 lines of symmetry in the given figure and the lines of symmetry can be shown as:

(b) From the given figure, we can observe that,

There is only 1 line of symmetry in the given figure and it can be drawn as follows:

(c) From the given figure, we can observe that,

There are two lines of symmetry in the given figure and it can be drawn as follows:

(d) From the given figure, we can observe that,

There are two lines of symmetry and it can be drawn as follows:

(e) From the given figure, we can observe that,

There is only one line of symmetry possible and it can be drawn as follows:

(f) From the given figure, we can observe that,

There are 2 lines of symmetry possible in the given figure and it can be drawn as follows:

How did you go about completing the picture?

(a) The given figure can be completed with the help of two symmetric lines i.e., horizontal and vertical lines of symmetry.

Therefore, the completed figure is shown as follows:

(b) We can complete the figure with the help of horizontal and vertical lines of symmetry.

Therefore, the above-given figure can be completed as follows:

(c) The given figure can be completed with the help of horizontal and vertical lines of symmetry.

Therefore, the completed figure is shown below:

(d) The given figure can be completed with the help of horizontal and vertical lines of symmetry.

Therefore, the completed figure is shown below:

(e) The same parts can be drawn to complete the given figure with the help of horizontal and vertical lines of symmetry.

Therefore, the completed figure is shown below:

(f)  The same parts can be drawn to complete the given figure with the help of horizontal and vertical lines of symmetry.

Therefore, the completed figure is shown below:

Try for   $\fn_phv \LARGE O E M N P H L T S V X$

Mirror images for the given figures are shown as follows:

So, from the above-drawn figures, we can say that the figures having the vertical line of symmetry will have the same mirror images and the letters are:

O, M, H, T, V, X

Thus, the mirror images of these letters will look the same.

## NCERT Solutions for Class 6 Mathematics - Chapter-wise

 Chapters No. Chapters Name Chapter - 1 Solutions of NCERT for class 6 maths chapter 1 Knowing Our Numbers Chapter - 2 CBSE NCERT solutions for class 6 maths chapter 2 Whole Numbers Chapter - 3 NCERT solutions for class 6 maths chapter 3 Playing with Numbers Chapter - 4 Solutions of NCERT for class 6 maths chapter 4 Basic Geometrical Ideas Chapter - 5 CBSE NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes Chapter - 6 NCERT solutions for class 6 maths chapter 6 Integers Chapter - 7 Solutions of NCERT for class 6 maths chapter 7 Fractions Chapter - 8 NCERT solutions for class 6 maths chapter 8 Decimals Chapter - 9 CBSE NCERT solutions for class 6 maths chapter 9 Data Handling Chapter -10 NCERT solutions for class 6 maths chapter 10 Mensuration Chapter -11 Solutions of NCERT for class 6 maths chapter 11 Algebra Chapter -12 CBSE NCERT solutions for class 6 maths chapter 12 Ratio and Proportion Chapter -13 NCERT solutions for class 6 maths chapter 13 Symmetry Chapter -14 Solutions of NCERT for class 6 maths chapter 14 Practical Geometry

## Benefits of NCERT solutions for class 6 maths chapter 13 symmetry-

• You will learn solutions of NCERT for class 6 easily.

• You will get many questions related to line of symmetry which will give more clarity.

• In NCERT Solutions for Class 6 Maths Chapter 13 Symmetry, you will get all these questions related to line od symmetry explained with the help of figures. So it will help you to visualize the problem and understand it better.

• It is going to help you with your homework as all the practice questions given below every topic are also covered in this solution article.

Happy learning!!!