NCERT Solutions for Class 7 Maths Exercise 14.1 Chapter 14 Symmetry

NCERT Solutions For Class 7 Maths Ex 14.1 PDF Free Download

NCERT Solutions for Class 7 Maths Exercise 14.1 Chapter 14 Symmetry in simple PDF are available here. Lines of symmetry for regular polygon is the only topic covered in this exercise of NCERT Solutions for Class 7 Chapter 14. Our expert professors formulate these exercises to assist you with your exam preparation to score good marks in Maths.

Download the PDF of NCERT Solutions For Class 7 Maths Chapter 14 Symmetry – Exercise 14.1

 

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Access other exercises of NCERT Solutions For Class 7 Chapter 14 – Symmetry

Exercise 14.2 Solutions

Exercise 14.3 Solutions

Access answers to Maths NCERT Solutions for Class 7 Chapter 14 – Symmetry Exercise 14.1

1. 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

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 3

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 5

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 7

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 9

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 11

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 13

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 15

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 17

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 19

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 21

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 23

Solution:-

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

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

(a)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 25

Solution:-

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, other hole is shown in the figure below.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 26

(b)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 27

Solution:-

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, other hole is shown in the figure below.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 28

(c)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 29

Solution:-

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, other hole is shown in the figure below.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 30

(d)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 31

Solution:-

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, other hole is shown in the figure below.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 32

(e)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 33

Solution:-

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, other hole is shown in the figure below.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 34

3. 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

Solution:-

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

Name of the figure is square.

(b)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 37

Solution:-

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

Name of the figure is triangle.

(c)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 39

Solution:-

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

Name of the figure is rhombus.

(d)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 41

Solution:-

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

Name of the figure is circle.

(e)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 43

Solution:-

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

Name of the figure is pentagon.

(f)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 45

Solution:-

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

Name of the figure is octagon.

4. 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

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 50

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 52

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 54

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 56

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 58

Solution:-

Figure given has only 1 line of symmetry.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 59

(g)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 60

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 62

Solution:-

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

5. 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

Solution:-

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 by more than one way.

6. 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

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 69

Solution:-

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)

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 71

Solution:-

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

7. State the number of lines of symmetry for the following figures:

(a) An equilateral triangle

Solution:-

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 has 3 lines of symmetry is shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 73

(b) An isosceles triangle

Solution:-

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 has 1 lines of symmetry is shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 74

(c) A scalene triangle

Solution:-

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

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 75

(d) A square

Solution:-

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

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 76

(e) A rectangle

Solution:-

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

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 77

(f) A rhombus

Solution:-

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

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 78

(g) A parallelogram

Solution:-

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

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 79

(h) A quadrilateral

Solution:-

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

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 80

(i) A regular hexagon

Solution:-

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 has 6 lines of symmetry is shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 81

(j) A circle

Solution:-

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 has infinite lines of symmetry,

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Image 82

8. 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

Solution:-

(a) a vertical mirror

The English alphabet 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 alphabet have 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

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

Solution:-

A shape has a no line of symmetry, if there is no line about which the figure may be folded and also 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

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

(a) an isosceles triangle?

Solution:-

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

(b) a circle?

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


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