NCERT Solutions for Class 6 Maths Chapter 13 - Symmetry

Exercise – 13.1

1. List any four symmetrical from your home or school.

Ans: The four symmetrical objects are a pencil box, blackboard, computer disc and eraser.

2. For the given figure, which one is the mirror line, ${l_1}$ or ${l_2}$ ?

Ans: In the above figure ${l_2}$ is the mirror part of the image. When a given figure is folded then the line ${l_2}$ the left part exactly covers the right part and vice versa .

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

Ans:  A line of symmetry cuts the image in equal half. It means that if we fold the shape in the cut line then  then both halves of the shape will match exactly like the mirror image. Now,  lets draw the lines of symmetry on each of the given figures:

From the above figure, it can be concluded that :

(a) Yes. It is symmetric.

(b) Yes. It is symmetric

(c) No, it is not symmetric

(d) Yes. It is symmetric

(e) Yes. It is symmetric

(f) Yes. It is symmetric

4. Copy the following on a square paper. A square paper is what you would have used in your arithmetic notebook in earlier classes. Then complete them such that the dotted line is the line of symmetry.

Ans: To make the dotted line as the line of symmetry, the above figure can be drawn as: 

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

Ans: The vertical line of symmetry is the line which divides the shape in equal half.  Now, let us draw the lines of symmetry on each of the given figures:

6. In the figure, l is the line of symmetry. Draw the image of the triangle and complete the diagram, so that it becomes symmetric.

Ans: To make the figure symmetric, required figure is to be drawn; the horizontal line of symmetry i.e. “l”

Exercise – 13.2

1. Find the number of lines of symmetry for each of the following shapes:

Ans:

(a) In the first figure, there are $4$ lines of symmetry.

(b) In the second figure, there are $4$ lines of symmetry.

(c) In the third figure, there are $4$ lines of symmetry.

(d) In the fourth figure, there is only $1$ line of symmetry 

(e) In the fifth figure, there are $6$ lines of symmetry.

(f) In the sixth figure, there are $6$ lines of symmetry.

(g) In the seventh figure, there is no line of symmetry.

(h) In the eight-figure, there is no line of symmetry.

(i) In the ninth figure, there are $3$ lines of symmetry.

This can be seen from the diagram below: 

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

Ans: The line of symmetry is shown by dotted line as in the figure below: 

The fourth figure is a scalene triangle, So there will be no lines of symmetry. 

3. Complete the following table:

Ans:

Shape	Rough figure	No. of lines of Symmetry
Equilateral triangle		3
Square		4
Rectangle		2
Isosceles triangle		1
Rhombus		2
Circle		Infinite

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.

Ans: 

(a) Yes, we can draw triangle with one line of symmetry: 

(b) There is no any triangle possible with two lines of symmetry.

(c) There is an equilateral triangle with three lines of symmetry:

(d) There is an scalene triangle with no lines of symmetry:

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 with 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) .

Ans:

(a) Yes, the diagram is of an isosceles triangle:

(b) Rectangle (quadrilateral) shows both the horizontal and vertical lines of symmetry.

(c) Trapezium (quadrilateral) shows the horizontal but no vertical line of symmetry.

(d)  The hexagon drawn below shows only two lines of symmetry.

(e) The regular hexagon shows the six lines of symmetry.

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

Ans: A line of symmetry cuts the image in equal half. It means that if we fold the shape in the cut line then  then both halves of the shape will match exactly like the mirror image. 

(a) In the first figure, it has no line of symmetry as it is not symmetrical.

(b) In this figure, it has two lines of symmetry.

(c) The given figure has four lines of symmetry.

(d) In the given figure has two lines of symmetry.

(e) This figure has only one horizontal line of symmetry.

(f) The given figure has two lines of symmetry.

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) 

Ans: 

(a) The  letters that have vertical lines of symmetry are :
A, H, I, M, O, T, U, V, W, X, and Y

(b) The following letters have horizontal lines of symmetry:
B, C, D, E, H, I, K, O and X.

(c)  The  letters that have no lines of symmetry are as follows:
F, G, J, L, N, P, Q, R, S and Z.

8. Given here are figures of a few folded sheets and designs drawn about the fold. In each case, draw a rough diagram of the complete figure that would be seen when the design is cut off.

Ans: When the figures will be fully completed, they will look like this:

Exercise – 13.3

1. Find the number of lines of symmetry in each of the following shapes. How will you check your answer?

Ans: 

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?

Ans: 

These figures can be completed by drawing similar parts as shown in the above figures. First draw the vertical line of symmetry and then draw the horizontal line of symmetry or first draw the horizontal line of symmetry and then the vertical line of symmetry.

3. In each figure below, 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 O E M N P H L T S V X

Ans: 

The mirror images of the above figures are as follows:

The letters having vertical lines of symmetry will have the same mirror images. And the letters such as  O, M, H, T, V, X and thus these letters will look the same.

NCERT Solution for Class 6 Maths Chapter 13 – Free PDF Download

This concept of symmetry is relatively new to the students, and with accurately solved questions offered by NCERT solutions for Class 6 Maths Chapter 13, they can get the basics of this topic right.

NCERT solutions like these are readily available on this page for free in PDF format. Students can easily access this vital study material by clicking on the pdf link given below to secure better marks.

NCERT Solutions for Class 6 Maths Chapter 13 Symmetry - Topic-Wise Discussion

There are a total of five sections in this chapter. Here is a topic-wise brief discussion:

1. Introduction

The chapter begins with a standard overview of Symmetry Class 6. It explains how symmetry exists in the real world, and how various architectural marvels have this characteristic. It also includes how one can fold a picture and then place a mirror beside to see the exact symmetrical reflection.

2. Making Symmetric Figures: Ink - Blot Devils

Class 6 Maths NCERT solutions Chapter 13 continues this discussion about symmetry with various activities that students can try at their home to know more about this concept.

One of the prominent ones here is to take a piece of paper and fold it in two halves. Then spill a few drops of ink on one side and then press them together. Learners can then study the figures it forms and review whether it has symmetry or not. In case it does not, they can try folding the paper differently and repeat the same.

Another easy experiment mentioned in Class 6 Maths Chapter 13 is to dip a string in paint or ink and then press it along the fold of a paper. Students can then review it to check if it is symmetrical or not, and try different paper folds to create different patterns.

This section further encourages students to study the object around them to learn about symmetry, and the line of symmetry it has.

3. Figures with Two Lines of Symmetry

In this section of NCERT Class 6 Maths Chapter 13, students explore another concept of symmetry further. Here they learn how different figures can have more than one line of symmetry. To simplify this concept, candidates can place squares available in their instrument box side by side. Doing so will create a shape of kite, and now they can review how many symmetric lines this particular figure has.

Similarly, Class 6 Symmetry includes the study of a rectangle as well. One can take a piece of rectangular paper and fold it along the length first and observe the lines, and then open it up and repeat the same process along its width. Once finished, they can check how many symmetric lines this process creates.

Class 6 Math Symmetry includes another DIY experiment where students can fold a piece of paper like mentioned before. However, this time they can draw a design along the folds, and then cut it out. Once they open the folded paper, this design unfolds as well. They can now check if there is any symmetry in the design or not.

NCERT solutions for Class 6 Maths Chapter 13 include accurate answers for the exercise problems.

4. Figures with Multiple (More Than Two) Lines of Symmetry

This section of Symmetry for Class 6 includes discussion and DIY exercise to learn about objects that have multiple symmetrical lines. There are several experiments with papers and drawing that individuals can perform to understand this topic clearly.

Chapter 13 Symmetry Class 6 further includes a discussion regarding how road signs have different symmetrical shapes. Also, the playing cards and the surroundings have various objects and living beings that have multiple symmetrical lines.

5. Reflection and Symmetry

Symmetry Class 6 NCERT solutions discuss how reflection and symmetry are linked to each other. A single line known as a mirror line or line of symmetry divides an object and its reflection.

When an object portrays a reflection, it has no alterations to its shape or size or angles, it creates a perfect symmetry. To learn more about this concept, students can see their reflections on the mirror, or hold any object in front of the mirror. They will comprehend the topic better. Additionally, they also learn about the applications of reflection symmetry in this NCERT solutions Class 6 Maths Chapter Symmetry.

We Cover all Exercises in the Chapter Given Below: 

• Exercise 13.1 - 6 Questions with Solutions.

• Exercise 13.2 - 8 Questions with Solutions.

• Exercise 13.3 - 3 Questions with Solutions.

Know The Reasons Why NCERT Solutions is a Must - Read

NCERT solutions for Class 6 Maths Chapter 13 is a perfect study material to improve exam preparations for the following reasons:

1. CBSE Class 6 Maths Chapter 13 solutions follow the curriculum drafted by CBSE, helping students to prepare their syllabus better.

2. Subject experts are in-charge of preparing these study materials; thus, they are accurate and precise.

3. Also, the use of simple language helps students to comprehend the topics easily.

4. The answers are comprehensive and to the point and aid students to prepare quickly.

5. Additionally, the detailed explanation of every topic eliminates the need for referring to other books.

NCERT solutions for Class 6 Maths Chapter 13 are available online in PDF format. Students can easily download it for free from the website and mobile application of Vedantu - one of India’s leading e-learning platforms.

Conclusion

The NCERT Solutions for Class 6 Maths Chapter 13 - "Symmetry" offer a comprehensive and insightful guide for students navigating the intricacies of symmetry in mathematics. The solutions not only provide clarity on the theoretical aspects of symmetry but also offer step-by-step explanations for practical problem-solving. By addressing a spectrum of exercises and problems, these solutions empower students to develop a strong foundation in understanding and applying symmetry concepts. This resource is an invaluable companion for Class 6 students, facilitating a deeper comprehension of symmetry and fostering confidence in tackling related mathematical challenges.