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.

Exercise 13.1

Exercise 13.2

Exercise 13.3

Topic 13.5

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

Question:1 List any four symmetrical objects from your home or school. 

Answer:

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

Book, DVD, spectacles, compass, etc.

Question:For the given figure, which one is the mirror line, \small l_1 or  \small l_2?

        

Answer:

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.

Question:3 Identify the shapes given below. Check whether they are symmetric or not. Draw the line of symmetry as well.

Answer:

(a) Yes, it is symmetrical.

And the line of symmetry is shown in the figure.

tala2

(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.

perntagon

 

Question:5 In the figure, l is the line of symmetry. Complete the diagram to make it symmetric.

        

Answer:

The given figure can be completed as follows:

q7

 

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

Question:1 Find the number of lines of symmety for each of the following shapes :

        

Answer:

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

(a) a figure 

The given figure has 4 lines of symmetry

(b) .b figure

The given figure has 4 lines of symmetry.

(c)   c fifure

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) swastik

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

(i) flower

The given figure has 5 lines of symmetry.

Question:Copy the triangle in each of the following figures on squared paper.  In each case, draw the line(s) of symmetry, if any and identify the type of triangle. (Some of you may like to trace the figures and try paper-folding first!)

    

Answer:

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

photo1

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

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

photo 2

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:

photo4

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

 

 

 

Answer:

The completed table is shown below:

Shape

Rough Figure

No. of lines of symmetry

Equilateral triangle

3

Square

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. 

Answer:

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

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.

equlaiteral

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

Shown below,

scalene trinagle

 

Question: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.) 

Answer:

(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:

horizontal

(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:

hexagon

(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:

hexagon2

 

Question:Trace each figure and draw the lines of symmetry if any:

        

         

Answer:

(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.

 octagonal

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

Hence, It will have only one line of symmetry.

not specific

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

Hence, it will have four lines of symmetry.

 

Question:7 Consider the letters of English alphabets, A to Z. List among them the letters which have

            (a) vertical lines of symmetry (like A)

            (b) horizontal lines of symmetry (like B)

            (c) no lines of symmetry (like Q) 

            

Answer:

(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

 

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

Question: If you are 100 cm in front of a mirror, where does your image appear to be? If you move towards the mirror, how does your image move?

Answer:

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

Question:Find the number of lines of symmetry in each of the following shapes. How will you check your answers?

        

           

Answer:

(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:

butterfly

(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:

Question:2  Copy the following drawing on squared paper. Complete each one of them such that the resulting figure has two dotted lines as two lines of symmetry.

How did you go about completing the picture?

Answer:

(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:

Question:3 In each figure alongside, a letter of the alphabet is shown along with a vertical line. Take the mirror image of the letter in the given line. Find which letters look the same after reflection (i.e. which letters look the same in the image) and which do not. Can you guess why?

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

Answer:

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

NCERT Solutions for Class 6 - Subject wise

NCERT Solutions for class 6 maths
Solutions of NCERT for class 6 science

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!!!

 

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