# NCERT Solutions for Class 6 Maths Chapter 13

## NCERT Solutions for Class 6 Maths Chapter 13 – Symmetry

Symmetry provides accurate and comprehensive answers to every question present at the end of the chapter in the NCERT book.

NCERT Solutions are provided to make the study simple and interesting. Every student needs to have a good understanding of all concepts to be able to score high marks in exams. NCERT Solutions by Extramarks prepares them for the same. Prepared by subject matter experts as per the CBSE guidelines, the solutions help students understand the right manner to answer a question, which in turn helps them perform better in the exams.

## NCERT Solutions for Class 6 Maths Chapter 13

Symmetry is a relatively new concept for Class 6 students. The accurate and reliable solutions by Extramarks will make exam preparation and revision easy for students.

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

Symmetry in everyday language refers to a sense of harmonious, proportionate balance. In Maths, it has a more precise meaning and is usually used to refer to an object that remains invariant under some transformations, including rotation, translation, reflection or scaling.

### This chapter includes a total of five sections-

• Introduction
• Making Symmetric Figures: Ink – Blot Devils
• Figures with Two Lines of Symmetry
• Figures with Multiple (More Than Two) Lines of Symmetry
• Reflection and Symmetry

Here is a topic-wise discussion of the sections mentioned earlier:

1. ### Introduction

This section includes an introduction and an overview of Symmetry Class 6. It explains how symmetry exists in the real world and how many architectural marvels possess this characteristic. It also includes how when one folds a picture and places a mirror beside it, he/she can see the exact symmetrical reflection of the picture.

1. ### Making Symmetric Figures: Ink – Blot Devils

Class 6 Maths Chapter 13 has various activities that students can try at their home to know more about this concept.

For example, take a piece of paper and fold it into two halves. Then spill a few drops of ink on any folded side and press them together. After doing so, students can study the figure formed and review if it is symmetrical or not. If it is not, they can try folding the paper differently and repeat the same process again.

Another example is – Dipping a string in paint or ink and then pressing it along the fold of a paper. Then review it to check if it has symmetry or not. It might be fun to  try different paper folds to create different patterns for reviewing it over.

This section also includes studying the different objects around you to learn more about symmetry and the line of symmetry it has.

1. ### Figures with Two Lines of Symmetry

Chapter 13 Maths Class 6 tells students how different figures can have more than one line of symmetry.

To simplify this concept, students can place squares available in their compass box side by side. Doing so will create the shape of a kite, after which they can study how many symmetrical lines this particular figure has.

Class 6 Symmetry includes the study of a rectangle as well. One can take a piece of rectangular paper and fold it first along the length and observe the lines to see whether it has symmetry or not, and then open it up and repeat the same process along its width. Once finished, they can review how many symmetric lines are created by this process. Another example is a DIY experiment where students can fold a piece of paper in the previous DIY. However, this time they need to draw a design along the folds and cut it out. The paper design will unfold once they open the folded paper, and then they can check whether there is any symmetry in the design or not.

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

Symmetry for Class 6 discusses and includes DIY exercises to make students learn about objects having multiple symmetrical lines. Chapter 13 Symmetry Class 6 further discusses how road signs have varied symmetrical shapes. Additionally, the playing cards and our surroundings have many objects and living beings that have multiple symmetrical lines. Apart from this, this section includes other experiments with papers and drawings that students can perform to understand this topic clearly.

### 5. Reflection and Symmetry

Chapter 13 Class 6 Maths also discusses how symmetry and reflection are linked to each other.

A single line that divides an object and its reflection is known as a mirror line or line of symmetry. An object portraying a reflection has no alterations to its shape or size or angles, and has perfect symmetry. In this section, students will perform various DIY activities and observe their reflections in the mirror by holding the different objects in front of the mirror. They will also learn about the applications of reflection symmetry in this section of Class 6 Maths Chapter Symmetry.

### NCERT Solutions for Class 6 Maths Chapter 13 Exercises

 Chapter 13 – Symmetry Exercises Exercise 13.1 6 Questions & Solutions Exercise 13.2 8 Questions & Solutions Exercise 13.3 3 Questions & Solutions

### Know the Reasons Why NCERT Solutions is a Must-Read

NCERT Solutions Class 6 is an important study material that provides solutions to NCERT exercises from an exam perspective. Here are the reasons why students must refer to the solutions by Extramarks.

1.  These solutions answer all questions in this chapter
2.  NCERT Solutions is explained in simple language to help students comprehend the answers easily.
3. The solutions are prepared by subject experts and a team that have years of knowledge in the field. Thus, they are accurate and precise
4. The answers are comprehensive and to the point, so they aid students in the preparation for their exams.
5. Additionally, the detailed explanation of every answer eliminates the need for referring to multiple reference books.

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

Ans-

Four symmetrical objects are: Screen of LED, Top of table, a pair of scissors and black board.

Q.2 For the given figure, which one is the mirror line, l1 or l2? Ans-

Since, line l2 is dividing this figure into two equal parts. So, l2 is mirror line.

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

All figures are symmetrical except figure (c). These figures are shown below with line of symmetry. Q.4 Copy the following on a squared 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-

The completed figures around the dotted line as a line of symmetry are given below: Q.5 In the figure, l is the line of symmetry. Complete the diagram to make it symmetric. Ans-

Line l is the line of symmetry of the following figure. Q.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-

The triangle is symmetric about the line l which is the line of symmetry. Q.7 Find the number of lines of symmetry for each of the following shapes: Ans-

(a) Number of lines of symmetry in square are 4. (b) Number of lines of symmetry in given figure are 4. (c) Number of lines of symmetry in given figure are 4. (d) Number of lines of symmetry in given figure is 1. (e) Number of lines of symmetry in given figure are 6. (f) Number of lines of symmetry in given figure are 6. (g) There is no number of lines of symmetry in given figure. (h) There is no number of lines of symmetry in given figure. (i) Number of lines of symmetry in given figure are 5. Q.8 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!) Ans-

(a) This is an equilateral triangle and has three line of symmetry.

(b) This is an isosceles triangle and has one line of symmetry.

(c) This is an isosceles right angled triangle and has one line of symmetry.

(d) There is no lines of symmetry in a scalene triangle.

Q.9 Complete the following table. Ans-

The completed table is as given below: Q.10 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) An isosceles triangle has one line of symmetry. (b) There is no triangle which has two lines of symmetry.
(c) An equilateral triangle has three lines of symmetry. (d) A scalene triangle has no lines of symmetry. Q.11 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.

Ans-

(a) A triangle with a horizontal line of symmetry but no vertical line of symmetry is given below: (b) A quadrilateral with both horizontal and vertical lines of symmetry is given below: (c) A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry is given below: (d) A hexagon with exactly two lines of symmetry is given below: (e) A hexagon with six lines of symmetry is given below: Q.12 Trace each figure and draw the lines of symmetry, if any:   Ans-

(a) There are no lines of symmetry in given figure. (b) There are two lines of symmetry in given figure. (c) There are 4 lines of symmetry in given figure. (d) There are 2 lines of symmetry in given figure. (e) There is only one line of symmetry in given figure. (f) There are two lines of symmetry in given figure. Q.13 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) Letters of English alphabets having vertical lines of symmetry are:
A M U V W Y T

(b) Letters of English alphabets having horizontal lines of symmetry are:
B C D E K

(c) Letters of English alphabets having no lines of symmetry are:
F G J L N P Q R S Z

Q.14 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-

The designs that would be seen when the design is cut off are given below: Q.15 Find the number of lines of symmetry in each of the following shapes. How will you check your answers? Ans-

(a) There are two lines of symmetry in given figure. (b) There is only one line of symmetry in given figure. (c) There is only one line of symmetry in given figure. (d) There is only one line of symmetry in given figure. (e) There is only one line of symmetry in given figure. (f) There are two lines of symmetry in given figure. Q.16 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-

The figures are completed by using both lines of symmetry. First we use vertical line of symmetry and then horizontal line of symmetry to complete these figures. These figures are given below:
(a) (b) (c) (d) (e) (f) Q.17 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 O E M N P H L T S V X

Ans-

The mirror images of given letters are given below: Those letters which have vertical line of symmetry, they have same mirror images. These letters are O, M, H, T, V, X. These letters look the same after reflection.

## 1. What is symmetry?

Whenever an object or a diagram is divided, and the divided parts completely overlap each other, it is a case of symmetry. Both, the divided portions form a mirror image of each other and the line acting as an agent of division is known as the line of symmetry. Symmetry has various applications, especially in the field of Maths.

## 2. How many lines of symmetry can any figure have?

The maximum number of lines of symmetry that an object or figure can have depends on the number and types of symmetric axes and planes. Therefore, it is very important to learn about these first as it helps in solving questions related to symmetry.

## 3. What does lateral symmetry mean?

When pictures are reversed from left to right, an illusion created by a flat mirror is known as lateral symmetry. The reason behind this is that when an object is put in front of a plane mirror, its left side looks as if it is on the right side of the picture while its right side seems to be on the left side.

## 4. Explain the different types of symmetry according to the Class 6 Syllabus.

Symmetry can be divided into four types: Rotational, Translation, Glide and Reflection. Each one of these has its own sets of characteristics and rules, and hence it becomes important to study and understand each one of them. This will help in being well-versed with the basics before moving on to the advanced topics of the chapter.

## 5. Elaborate on effective ways to study the Chapter 13 Symmetry of Class 6 Maths?

The problems and solutions of Chapter 13 Symmetry play an essential role in building the foundational understanding of the chapter. The following are a few effective ways that will help you to study Chapter 13 Symmetry of Class 6 Maths more easily:

1. Developing a good understanding of the basic concepts of the chapter
2. Understanding what symmetry is
3. Learning the important formulas
4. Thoroughly practising the problems