NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

 

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry- In mathematics, symmetry means that one shape becomes exactly like another when you move(turn, flip or slide) it in some way. In nature, tree-leaves,  beehives, flowers, and in the logo, symbols everywhere you can find various types of symmetrical designs. In this article, you will get CBSE NCERT solutions for class 7 maths chapter 14 symmetry. It is an important concept of the geometrical part used in artists, designing of jewelry or clothes, architects, car manufacturers, etc. In this chapter, you will learn some basic symmetry concepts like line symmetry, lines of symmetry for regular polygons, and rotational symmetry.

  • Line of Symmetry:- It is defined as the imaginary line or axis that passes through the center of the object or shape and divides it into two perfectly identical halves. Example-Regular polygons like square, regular pentagon, a regular hexagon, etc have equal sides and equal angles. They have more than one line of symmetry.

        Number of lines of symmetry of some regular polygon are given in the following table-    

Regular polygon Regular hexagon

Regular pentagon

  Square Equilateral triangle
No. of lines of symmetry 6 5 4 3

 

  • Rotational symmetry:- It is defined as the imaginary a center point (fixed point) around that an object or shape is rotated by a number of degrees and the object or shape looks exactly the same. In a complete turn of 360-degree, the number of times an object or shape looks exactly the same is called the order of rotational symmetry.

The order of symmetry for an equilateral triangle is 3 and the order of symmetry for a square is 4. In NCERT solutions for class 7 maths chapter 14 symmetry, you will get many questions related to the order of symmetry which will give you more clarity of the concept. In this chapter, there are  19 questions in three exercises. You will get detailed explanations of all these questions in CBSE NCERT solutions for class 7 maths chapter 14 symmetry. It will be very easy for you to understand the concept. You can get NCERT solutions from class 6 to 12 by clicking on the above link.

Topics of NCERT Grade 7 Maths Chapter 14  Symmetry

14.1 Introduction

14.2  Lines of Symmetry for Regular Polygons

14.3  Rotational Symmetry

14.4  Line Symmetry and Rotational Symmetry

The complete Solutions of NCERT for Class 7 Maths Chapter 14 symmetry is provided below:

CBSE NCERT solutions for class 7 maths chapter 14 symmetry-Exercise: 14.1
Question:1
.(a) Copy the figures with punched holes and find the axes of symmetry for the following:

              

Answer:

The axes of symmetry is as shown :

Question:2 Given the line(s) of symmetry, find the other hole(s):

           

Answer:

The other holes  from the  symmetry are as shown :

Question:4 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:

                 

                

Answer:

The  lines of symmetry of figures are:

(a)There are 3 lines of symmetry. Thus, it has multiple lines of symmetry.

(b) There are 2 lines of symmetry. Thus, it has multiple lines of symmetry.

 

(c)There are 3 lines of symmetry. Thus, it has multiple lines of symmetry.

(d)There are 2 lines of symmetry. Thus, it has multiple lines of symmetry.

(e)There are 4 lines of symmetry. Thus, it has multiple lines of symmetry.

(f)There is 1 line of symmetry.

(g)There are 4 lines of symmetry. Thus, it has multiple lines of symmetry.

(h)There are 6 lines of symmetry. Thus, it has multiple lines of symmetry.

 

 

Question:6 Copy the diagram and complete each shape to be symmetric about the mirror line(s):

             

Answer:

The  complete  shape  symmetric about the mirror line(s) are :

Question: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

Answer:

  (a) An equilateral triangle      

  The number of lines of symmetry  = 3

(b) An isosceles triangle  

  The number of lines of symmetry  = 1

        

(c) A scalene triangle

  The number of lines of symmetry  = 0

 (d) A square

     The number of lines of symmetry  = 4

                          

(e) A rectangle                          

  The number of lines of symmetry  = 2

(f) A rhombus

  The number of lines of symmetry  = 2

 (g) A parallelogram               

  The number of lines of symmetry  = 0

(h) A quadrilateral                     

  The number of lines of symmetry  = 0

(i) A regular hexagon

  The number of lines of symmetry  = 6

(j) A circle

  The number of lines of symmetry  = infinite

Question:9 Give three examples of shapes with no line of symmetry.

Answer:

The  three examples of shapes with no line of symmetry are :

1. Quadrilateral 

2. Scalene triangle 

3.Parallelogram

Question:10.(a)  What other name can you give to the line of symmetry of

an isosceles triangle?

Answer:

The line of symmetry of an isosceles triangle is median or altitude.

Question:10.(b) What other name can you give to the line of symmetry of

 a circle?

Answer:

The other name we can give to the line of symmetry of a circle is the diameter.

NCERT solutions for class 7 maths chapter 14 symmetry topic 14.3 rotational symmetry

Question:1.(a) Can you now tell the order of the rotational symmetry for an equilateral triangle?

              

Answer:

An equilateral triangle has rotational symmetry at 120 \degree angle. The order of the rotational symmetry for an equilateral triangle is 3.

Question:1.(b) How many positions are there at which the triangle looks exactly the same, when rotated about its centre              by 120°?

             

Answer:

All the triangles look same when rotated by 120 \degree. Thus, there are 4 positions at which the triangle looks exactly the same when rotated about its centre by 120°.

Question:2  Which of the following shapes (Fig 14.15) have rotational symmetry about the marked point.

             

Answer:

Among the above-given shapes, (i),(ii) and (iv) have rotational symmetry about the marked point.

Solutions of NCERT for class 7 maths chapter 14 symmetry-Exercise: 14.2

Question:1 Which of the following figures have rotational symmetry of order more than 1:

              

Answer:

Among the above-given shapes, (a),(b), (d),(e) and (f) have more than one rotational symmetry.

This is because, in these figures, a complete turn, more than 1 number of times, an object look exactly the same.

Question:2 Give the order of rotational symmetry for each figure:

             

Answer:

(a) The given figure has rotational symmetry about 180 \degree so it has ordered as 2.

 

(b) The given figure has rotational symmetry about 180 \degree so it has ordered as 2.

 

(c) The given figure has rotational symmetry about 120 \degree so it has ordered as 3.

 

(d) The given figure has rotational symmetry about 90 \degree so it has ordered as 4.

 

(e) The given figure has rotational symmetry about 90 \degree so it has ordered as 4.

 

(f) The given figure has rotational symmetry about 72 \degree so it has ordered as 5.

 

(g) The given figure has rotational symmetry about 60 \degree so it has ordered as 6.

 

(h) The given figure has rotational symmetry about 120 \degree so it has ordered as 3.

CBSE NCERT solutions for class 7 maths chapter 14 symmetry-Exercise: 14.3

Question:1 Name any two figures that have both line symmetry and rotational symmetry.

Answer:

The  two figures that have both line symmetry and rotational symmetry are :

(i) Equilateral triangle 

(ii) Regular hexagon

Question:2(i) Draw, wherever possible, a rough sketch of

 a triangle with both line and rotational symmetries of order more than 1.

Answer:

Line of symmetry as shown below :

  

The rotational symmetry as shown below :

Question:2(ii) Draw, wherever possible, a rough sketch of

 a triangle with only line symmetry and no rotational symmetry of order more than 1.

Answer:

A triangle with only line symmetry and no rotational symmetry of order more than 1 is isosceles triangle.

Question:2(iii) Draw, wherever possible, a rough sketch of

a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.

Answer:

A quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry is parallelogram.

Question:2(iv) Draw, wherever possible, a rough sketch of

 a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.

Answer:

A quadrilateral with line symmetry but not a rotational symmetry of order more than 1 is kite.

Question:3 If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?

Answer:

Yes. If a figure has two or more lines of symmetry,than it  should  have rotational symmetry of order more than 1.

Question:4 Fill in the blanks:

Shape    

Centre of Rotation    

Order of Rotation    

Angle of Rotation

Square

 

 

 

Rectangle

 

 

 

Rhombus

 

 

 

Equilateral Triangle

 

 

 

Regular Hexagon

 

 

 

Circle

 

 

 

Semi-circle

 

 

 

     

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer:

The given table is completed as shown:

Shape    

Centre of Rotation    

Order of Rotation    

Angle of Rotation

Square

intersection point of digonals.

        4

  90 \degree

Rectangle

Intersection point of digonals.

         2

  180 \degree

Rhombus

Intersection point of digonals.

         2

  180 \degree

Equilateral Triangle

Intersection point of medians.

         3

   120 \degree

Regular Hexagon

Intersection point of digonals.

         6

  60 \degree

Circle

centre of circle

         infinite

  any angle

Semi-circle

centre of circle

              1

   360 \degree

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Question:5 Name the quadrilaterals which have both line and rotational symmetry of order more than 1.

Answer:

The quadrilaterals which have both line and rotational symmetry of order more than 1 are :

1. Rectangle 

2. Square

3. Rhombus

Question:6 After rotating by  60^{0}  about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

Answer:

 After rotating by  60^{0}  about a centre, a figure looks exactly the same as its original position, then it will look symmetrical on rotating by 120 \degree,180 \degree,240 \degree,300 \degree,360 \degree. All angles are multiples of 60^{0}.

Question:7 Can we have a rotational symmetry of order more than 1 whose angle of rotation is:

            (i)\: 45^{o}?                 (ii)\: 17^{o}?

Answer:

We can observe that the angle of rotation is the factor of 360 \degree,then it will have rotational symmetry of order more than 1.

(i) 45^{o} is a factor of 360 \degree so the figure having its angle of rotation as 45^{o} will have rotational symmetry of order more than 1.

(ii)17^{o} is not a factor of 360 \degree so the figure having its angle of rotation as 17^{o} will not have rotational symmetry of order more than 1.

NCERT Solutions for Class 7 Maths- Chapter-wise 

Chapter No.

Chapter Name

Chapter 1

Solutions of NCERT for class 7 maths chapter 1 Integers

Chapter 2

CBSE NCERT solutions for class 7 maths chapter 2 Fractions and Decimals

Chapter 3

NCERT solutions for class 7 maths chapter 3 Data Handling

Chapter 4

Solutions of NCERT for class 7 maths chapter 4 Simple Equations

Chapter 5

CBSE NCERT solutions for class 7 maths chapter 5 Lines and Angles

Chapter 6

NCERT solutions for class 7 maths chapter 6 The Triangle and its Properties

Chapter 7

Solutions of NCERT for class 7 maths chapter 7 Congruence of Triangles

Chapter 8 NCERT solutions for class 7 maths chapter 8 comparing quantities

Chapter 9

CBSE NCERT solutions for class 7 maths chapter 9 Rational Numbers

Chapter 10

NCERT solutions for class 7 maths chapter 10 Practical Geometry

Chapter 11

Solutions of NCERT for class 7 maths chapter 11 Perimeter and Area

Chapter 12

CBSE NCERT solutions for class 7 maths chapter 12 Algebraic Expressions

Chapter 13

NCERT solutions for class 7 maths chapter 13 Exponents and Powers

Chapter 14

NCERT solutions for class 7 maths chapter 14 Symmetry

 NCERT Solutions for Class 7- Subject-wise 

Solutions of NCERT for class 7 maths

CBSE NCERT solutions for class 7 science

Benefits of NCERT solutions for class 7 maths chapter 14 symmetry-

  • You will learn to identify different types of symmetry and also the order of the symmetry.

  • It will make your homework easy as you will find the detailed explanations of all the NCERT questions including practice questions given below every topic in this article.

  • You should try to solve all the NCERT questions including examples. If you facing difficulties in solving them, you can take help from these solutions.

  • After every topic, there are some practice questions given in the textbook to give you conceptual clarity. In NCERT solutions for class 7 maths chapter 14 symmetry, you will find solutions to these practice questions also. 

Happy learning!!!

 

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