NCERT Solutions Class 7 Maths Chapter 12 Symmetry

Symmetry is an essential concept in mathematics, art, and nature. It helps us understand balanced and proportionate designs in different contexts. For students, learning symmetry is crucial as it lays the foundation for recognising patterns and structures in various objects and shapes. 

If you wish to understand symmetry in-depth, NCERT Solutions for Class 7 Maths Chapter 12 will guide you with step-by-step explanations. NCERT Solutions Class 7 Maths Chapter 12 explains symmetry in everyday life and its mathematical significance. These solutions help students grasp the concepts and prepare well for their exams.

In this blog, we have provided the details about the NCERT solutions, why they are important, and the number of questions you will get to practice to strengthen your understanding of each concept of symmetry. 

1.0Download Class 7 Maths Chapter 12 NCERT Solutions PDF Online

NCERT solutions for class 7 Maths chapter 12 provide clear explanations of all the important concepts, making it easy for students to understand all the concepts and then apply them in real life situations. Every exercise has detailed instructions to ensure awareness and improved topic retention. Here we have provided the NCERT class 12 symmetry downloadable PDF so you can practice and improve your knowledge at your convenience. 

2.0Brief about the NCERT Solutions of Class 7 Maths Chapter 12

Chapter 12 explores concepts like line symmetry and rotational symmetry, providing students with tools to analyse and create symmetric shapes.

This chapter helps students develop spatial reasoning skills and apply these concepts to solve mathematical problems efficiently. Mastering symmetry is a critical skill in academics and practical applications. This chapter allows students to explore how symmetry is used to organise shapes, patterns, and objects systematically.

3.0Why are NCERT Solutions of Class 7 Maths Chapter Symmtery Important?

Understanding symmetry is not just a mathematical skill; it has practical applications in various fields. Here are five reasons why symmetry is important:

1. Enhances Visual Understanding: Symmetry helps recognise patterns and organise shapes, making visual learning more effective.
2. Practical Applications: Symmetry is used in design, architecture, and art to create balanced and aesthetically pleasing structures.
3. Foundation for Geometry: It forms the basis for understanding geometric concepts, such as shapes, transformations, and angles.
4. Improves Problem-Solving Skills: Learning symmetry sharpens logical thinking and spatial reasoning, which is essential for solving complex problems.
5. Connection to Nature: Symmetry is observed in natural objects, such as flowers and animals, helping students relate mathematical concepts to the real world.

4.0NCERT Solutions Class 7 Maths Chapter 12 Subtopics

The subtopics of Chapter 12 give a detailed understanding of symmetry, preparing students to identify and apply these principles effectively. Below are the key subtopics covered in Chapter 12:

1. Introduction to Symmetry
2. Line of Symmetry For Regular Polygons
3. Rotational Symmetry
4. Line Symmetry and Rotational Symmetry

5.0NCERT Solutions for Class 7 Maths Chapter 12 Symmetry: All Exercises

Below are the exercises from Chapter 12, Symmetry, along with the number of questions and a brief description of what each exercise covers:

• Class 7 Maths Chapter 12 Exercise 14.1: 8 Questions
• Class 7 Maths Chapter 12 Exercise 14.2: 6 Questions
• Class 7 Maths Chapter 12 Exercise 14.3: 4 Questions

6.0NCERT Questions with Solutions for Class 7 Maths Chapter 12 - Detailed Solutions

Exercise : 14.1

• Copy the figures with punched holes and find the axes of symmetry for the following :
  
  Sol.
  
  
• Given the line(s) of symmetry, find the other hole(s) : (a)
  
  (b)
  
  (c)
  
  (d)
  
  (e)
  
  Sol. (a)
  
  (b)
  
  (c)
  
  (d)
  
  (e)
  
• In the following figures, the mirror line (i.e., the line of symmetry) is given as a dotted line. Complete each figure performing reflection in the dotted (mirror) line. (You might perhaps place a mirror along the dotted line and look into the mirror for the image). Are you able to recall the name of the figure you complete? (a)
  
  (b)
  
  (c)
  
  (d)
  
  (e)
  
  (f)
  
  Sol.
  
  (b)
  
• The following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry.
  
  Identify multiple lines of symmetry, if any, in each of the following figures :
  

(e)

Sol. (a)

• Copy the figure given here.
  
  Take any one diagonal as a line of symmetry and shade a few more squares to make the figure symmetric about a diagonal. Is there more than one way to do that? Will the figure be symmetric about both the diagonals? Sol.
  
  Yes, there is more than one way. Yes, this figure will be symmetric about both the diagonals.
• Copy the diagram and complete each shape to be symmetric about the mirror line(s) : (a)
  
  (b)
  
  (c)
  
  Sol. (a)
  
  (b)
  
• State the number of lines of symmetry for the following figures : (a) An equilateral triangle (b) An isosceles triangle (c) A scalene triangle (d) A square (e) A rectangle (f) A rhombus (g) A parallelogram (h) A quadrilateral (i) A regular hexagon (j) A circle Sol. (a) Number of lines of symmetry is 3 .
  
  (b) Number of line of symmetry is 1 .
  
  (c) No line of symmetry.
  
  (d) Number of lines of symmetry is 4 .
  
  (e) Number of lines of symmetry is 2 .
  
  (f) 2 lines of symmetry.
  
  (g) Number of lines of symmetry is 0 .
  
  (h) No line of symmetry.
  
  (i) Number of lines of symmetry is 6 .
  
  (j) Infinite number of lines of symmetry.
  
• What letters of the English alphabet have reflectional symmetry (i.e., symmetry related to mirror reflection) about. (a) a vertical mirror (b) a horizontal mirror (c) both horizontal and vertical mirrors Sol. (a) vertical mirror - A, H, I, M, O, T, U, V, $\mathrm{W},\mathrm{X}$ and Y
  
  (b) horizontal mirror - B, C, D, E, H, I, O and H
  
  (c) both horizontal and vertical mirror H, I, O and X
• Give three examples of shapes with no line of symmetry. Sol. The three examples are (i) Quadrilateral (ii) Scalene triangle (iii) Parallelogram
• What other name can you give to the line of symmetry (a) an isosceles triangle ? (b) a circle ? Sol. (a) The line of symmetry of an isosceles triangle is median or altitude. (b) The line of symmetry of a circle is diameter.

Exercise : 14.2

• Which of the following figures have rotational symmetry of order more than 1. (a)
  
  (b)
  
  (c)
  
  (d)
  
  
  Sol. Rotational symmetry of order more than 1 are (a), (b), (d), (e) and (f) because in these figures, a complete turn, more than 1 number of times, an object looks exactly the same.
• Give the order of rotational symmetry for each figure :
  
  Sol. (a)
  
  Order of rotational symmetry is 2 . (b)
  
  Order of rotational symmetry is 2 . (c)
  
  Order of rotational symmetry is 3 . (d)
  
  Order of rotational symmetry is 4 . (e)
  
  Order of rotational symmetry is 4 . (f) Order of rotational symmetry is 5 . (g)
  
  
  
  Order of rotational symmetry is 6 .
  
  (h)
  
  Order of rotational symmetry is 3 .

Exercise: 14.3

• Name any two figures that have both line symmetry and rotational symmetry. Sol. Circle and square.
• Draw, wherever possible, a rough sketch of (i) a triangle with both line and rotational symmetries of order more than 1. (ii) a triangle with only line symmetry and no rotational symmetry of order more than 1. (iii)a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry. (iv)a quadrilateral with line symmetry but not a rotational symmetry of order more than 1. Sol. (i) An equilateral triangle has both line and rotational symmetries of order more than 1. Line symmetry:
  
  Rotational symmetry:
  
  (ii) An isosceles triangle has only one line of symmetry and no rotational symmetry of order more than 1. Line symmetry:
  
  Rotational symmetry:
  
  (iii) Parallelogram
  
  (iv) A trapezium which has equal nonparallel sides, a quadrilateral with line symmetry but not a rotational symmetry of order more than 1. Line symmetry:
  
  Rotational symmetry:
  
• If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1 ? Sol. Yes, because every line through the centre forms a line of symmetry and it has rotational symmetry around the centre for every angle.
• Fill in the blanks:

Sol.

• Name the quadrilaterals which have both line and rotational symmetry of order more than 1. Sol. Square has both line and rotational symmetry of order more than 1. Line symmetry:
  
  Rotational symmetry :
  
• After rotation by $60^{\circ }$ about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure? Sol. Other angles will be $120^{\circ },180^{\circ },240^{\circ }$, $300^{\circ },360^{\circ }$. For $60^{\circ }$ rotation: It will rotate six times.
  
  (i)
  
  (iii)
  
  (ii)
  
  (iv)
  
  (v) (vi) For $120^{\circ }$ rotation: It will rotate three times.
  
  (i) (ii)
  
  (iii) For $180^{\circ }$ rotation: It will rotate two times.
  
  (i)
  
  (ii) For $360^{\circ }$ rotation: It will rotate one time.
  
• Can we have a rotational symmetry of order more than 1 whose angle of rotation is (i) $45^{\circ }$ (ii) $17^{\circ }$ Sol. If the angle of rotation is $45^{\circ }$, then symmetry of order more than one is possible and would be 8 rotations. If the angle of rotation is $17^{\circ }$, then symmetry of order more than one is not possible because $360^{\circ }$ is not completely divisible by $17^{\circ }$.