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NCERT solutions for class 7 maths chapter 14 Symmetry

Delving into the Art of Symmetry Chapter 14 of NCERT Class 7 Maths, "Symmetry," is your key to unlocking the world of geometric balance and harmony. This chapter's detailed solutions provide comprehensive answers to all questions from the NCERT textbook, helping students solidify their grasp on the subject. Expert educators have meticulously unraveled each problem, presenting a step-by-step approach with lucid explanations. With three distinct exercises within "Symmetry," our NCERT Solutions for Class 7 Math comprehensively tackle each exercise, offering a systematic path to problem resolution and exam preparedness. Exercise 14.1 is dedicated to the exploration of "Lines of Symmetry for a Regular Polygon." These solutions have been meticulously curated by subject matter experts to empower students in their exam readiness, ultimately supporting their quest to secure commendable marks in the realm of mathematics.

Exercise 14.1

Question 1 :

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 35

(b)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 37

(c)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 39

(d)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 41

(e)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 43

(f)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 45

 

Answer :

(a) The concept of line of symmetry is closely related to mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 36

The name of the figure is square.

(b) The concept of line of symmetry is closely related to mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 38

The name of the figure is triangle.

(c) The concept of line of symmetry is closely related to mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 40

The name of the figure is rhombus.

(d) The concept of line of symmetry is closely related to mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 42

The name of the figure is circle.

(e) The concept of line of symmetry is closely related to mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 44

The name of the figure is pentagon.

(f) The concept of line of symmetry is closely related to mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 46

The name of the figure is octagon.

 


Question 2 :
undefined
Answer :


Question 3 :

The following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 47

Identify multiple lines of symmetry, if any, in each of the following figures:

(a)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 48

(b)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 50

(c)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 52

(d)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 54

(e)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 56

(f)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 58

(g)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 60

(h)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 62

 

Answer :

(a)

The figure given has 3 lines of symmetry.

So, it has multiple lines of symmetry.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 49

(b)

The figure given has 2 lines of symmetry.

So, it has multiple lines of symmetry.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 51

(c)

The figure given has 3 lines of symmetry.

So, it has multiple lines of symmetry.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 53

(d)

The figure given has 2 lines of symmetry.

So, it has multiple lines of symmetry.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 55

(e)

The figure given has 4 lines of symmetry.

So, it has multiple lines of symmetry.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 57

(f)

The figure given has only 1 line of symmetry.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 59

(g)

The figure given has 4 lines of symmetry.

So, it has multiple lines of symmetry.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 61

(h)

The figure given has 6 lines of symmetry.

So, it has multiple lines of symmetry.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 63

 


Question 4 :

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?

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 64

 

Answer :

 

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 65

By observing the above figure,

Yes, the figure will be symmetrical about both diagonals.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 66

By observing the above figure,

Yes, the figure can be made symmetrical in more than one way.

 


Question 5 :

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

(a)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 67

(b)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 69

(c)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 71

 

Answer :

(a)

The concept of line of symmetry is closely related to mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 68

(b)

The concept of line of symmetry is closely related to mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 70

(c)

The concept of line of symmetry is closely related to mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 72

 


Question 6 :

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)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

An equilateral triangle which has 3 lines of symmetry is shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 73

(b)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

An isosceles triangle which has 1 line of symmetry is shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 74

(c)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A scalene triangle which has no line of symmetry is shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 75

(d)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A square which has 4 lines of symmetry is shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 76

(e)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A rectangle which has 2 lines of symmetry is shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 77

(f)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A rhombus which has 2 lines of symmetry is shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 78

(g)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A parallelogram which has no line of symmetry is shown in the figure below,

 

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 79

(h)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A quadrilateral which has no line of symmetry is shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 80

(i)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A regular hexagon which has 6 lines of symmetry is shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 81

(j)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A circle which has infinite lines of symmetry,

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 82

 


Question 7 :

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

 

Answer :

(a) a vertical mirror

The English letters which have reflection symmetry about a vertical mirror are A, H, I, M, O, T, U, V, W, X, Y

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 83

(b) a horizontal mirror

The English letters having reflection symmetry about a horizontal mirror are B, C, D, E, H, I, K, O, X

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 84

(c) both horizontal and vertical mirrors

The English alphabet have reflection symmetry about both horizontal and vertical mirrors are, H, I, O, X

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 85

 

 


Question 8 :

Give three examples of shapes with no line of symmetry.

Answer :

A shape has no line of symmetry if there is no line about which the figure may be folded, and parts of the figure will not coincide.

A scalene triangle, a quadrilateral and a parallelogram

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 86

 

 


Question 9 :

What other name can you give to the line of symmetry of

(a) an isosceles triangle?

(b) a circle?

Answer :

(a)

The other name for the line of symmetry of an isosceles triangle is median or altitude.

(b)

The other name for the line of symmetry of a circle is diameter.


Question 10 :

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

(a)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 25

(b)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 27

(c)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 29

(d)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 31

(e)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 33

 

Answer :

(a) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

So, the other hole is shown in the figure below.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 26

(b) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

So, the other hole is shown in the figure below.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 28

(c) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

So, the other hole is shown in the figure below.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 30

(d) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

So, the other hole is shown in the figure below.

 

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 32

(e) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

So, the other hole is shown in the figure below.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 34

 


Question 11 :

Copy the figures with punched holes and find the axes of symmetry for the following:

(a)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 1

(b)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 3

(c)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 5

(d)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 7

(e)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 9

(f)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 11

(g)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 13

(h)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 15

(i)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 17

(j)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 19

(k)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 21

(l)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 23

 

Answer :

(a) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 2

(b) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

 

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 4

(c) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 6

(d) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 8

(e) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 10

(f) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 12

(g) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 14

(h) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 16

(i) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 18

(j) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 20

(k) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 22

(l) A figure has a line of symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 24

 


Exercise 14.2

Question 1 :

Give the order of rotational symmetry for each figure:

(a)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 93

(b)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 95

(c)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 97

(d)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 99

(e)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 101

(f)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 103

(g)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 105

(h)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 107

 

Answer :

(a)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 94

The above figure has rotational symmetry of order 2.

(b)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 96

The above figure has rotational symmetry of order 2.

(c)

NCERT Solutions for Class 7 Maths Chap 14 Image 2

The above figure has rotational symmetry of order 3.

(d)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 100

The above figure has rotational symmetry of order 4.

(e)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 102

The above figure has rotational symmetry of order 4.

(f)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 104

The above figure has rotational symmetry of order 5.

(g)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 106

The above figure has rotational symmetry of order 6.

(h)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 108

The above figure has rotational symmetry of order 3.

 


Question 2 :

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

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 87

 

 

Answer :

(a)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 88

So, the above figure has rotational symmetry of order 4.

(b)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 89

So, the above figure has rotational symmetry of order 3.

(c) So, the given figure has rotational symmetry of order 1.
NCERT Solutions for Class 7 Maths Chap 14 Image 1

(d)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 90

So, the above figure has rotational symmetry of order 2.

(e)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 91

So, the above figure has rotational symmetry of order 3.

(f)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 92

So, the above figure has rotational symmetry of order 4.

By observing all the figures (a), (b), (c), (d), (e) and (f) have rotational symmetry of order more than 1.

 


Exercise 14.3

Question 1 :

After rotating by 60° about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

 

Answer :

The other angles are, 120°, 180°, 240°, 300°, 360°

So, the figure is said to have rotational symmetry about the same angle as the first one. Hence, the figure will look exactly the same when rotated by 60° from the last position.

 


Question 2 :

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

 

Answer :

Equilateral triangle and Circle.


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, then it will 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 :

 

Shape

Centre of Rotation

Order of Rotation

Angle of Rotation

Square

Intersecting point of diagonals

4

90o

Rectangle

Intersecting point of diagonals

2

180o

Rhombus

Intersecting point of diagonals

2

180o

Equilateral Triangle

Intersecting point of medians

3

120o

Regular Hexagon

Intersecting point of diagonals

6

60o

Circle

Centre

Infinite

Every angle

Semi-circle

Mid-point of diameter

1

360o

 


Question 5 :

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

 

Answer :

The quadrilateral, which has both line and rotational symmetry of order more than 1, is a square.

Line symmetry:

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 113

Rotational symmetry:

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 114

 

 


Question 6 :

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.

 

Answer :

(i) A triangle with both line and rotational symmetries of order more than 1 is an equilateral triangle.

Line symmetry

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 109

Rotational symmetry

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 110

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

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 111

(iii) A quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry is not possible to draw. Because a quadrilateral with a line symmetry may have rotational symmetry of order one but not more than one.

(iv) A quadrilateral with line symmetry but not a rotational symmetry of order more than 1 is a rhombus.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 112

 

 


Question 7 :

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

(i) 45°?

(ii) 17°?

Answer :

(i) Yes. We can have a rotational symmetry of order more than 1 whose angle of rotation is 45o.

(ii) No. We cannot have a rotational symmetry of order more than 1 whose angle of rotation is 17o.

 


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