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NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Ex 14.1

CBSE students can refer to NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Ex 14.1 Textbook Questions and Answers are provided by experts in order to help students secure good marks in exams.

Class 7 Maths NCERT Solutions Chapter 14 Symmetry Ex 14.1

Question 1.
Copy the figures with punched holes and find the axes symmetry for the following:

(a)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 61
Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 62

(b)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 63
Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 64

(c)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 65
Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 66

(d)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 67
Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 68

(e)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 69
Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 70

(f)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 71
Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 78

(g)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 72
Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 79

(h)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 73
Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 80

(i)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 74
Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 81

(j)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 75
Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 82

(k)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 76
Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 83

(l)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 77
Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 84

Question 2.
Given the lines of symmetry, find the order holes:

(a)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 85
Solution:
With the respect to the given lines of symmetry, the order holes are marked in the given figures as order:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 91

(b)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 86
Solution:
With the respect to the given lines of symmetry, the order holes are marked in the given figures as order:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 92

(c)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 87
Sol:
With the respect to the given lines of symmetry, the order holes are marked in the given figures as order:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 93

(d)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 89
Solution:
With the respect to the given lines of symmetry, the order holes are marked in the given figures as order:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 94

(e)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 90
Solution:
With the respect to the given lines of symmetry, the order holes are marked in the given figures as order:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 95

Question 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?
Solution:
(a)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 96
Solution:
Corresponding to the given line of symmetry, the completed figure is as under. Their respective names are also given the figures:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 102

(b)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 98
Solution:
Corresponding to the given line of symmetry, the completed figure is as under. Their respective names are also given the figures:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 103

(c)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 97
Solution:
Corresponding to the given line of symmetry, the completed figure is as under. Their respective names are also given the figures :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 104

(d)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 99
Solution:
Corresponding to the given line of symmetry, the completed figure is as under. Their respective names are also given the figures :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 105

(e)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 101
Solution:
Corresponding to the given line of symmetry, the completed figure is as under. Their respective names are also given the figures :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 106

(f)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 100
Solution:
Corresponding to the given line of symmetry, the completed figure is as under. Their respective names are also given the figures :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 107

Question 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 Algebraic Expreesions img 108
NCERT Solutions for Class 7 maths Algebraic Expreesions img 109
NCERT Solutions for Class 7 maths Algebraic Expreesions img 110
Identify, multiple lines of symmetry, if any, in each of the following figures :
Solution:

(a)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 111
solution:
The multiple lines of symmetry in respect of the given figures are shown by dotted lines as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 119

(b)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 112
solution:
The multiple lines of symmetry in respect of the given figures are shown by dotted lines as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 120

(c)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 113
solution:
The multiple lines of symmetry in respect of the given figures are shown by dotted lines as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 121

(d)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 114
solution:
The multiple lines of symmetry in respect of the given figures are shown by dotted lines as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 122

(e)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 115
solution:
The multiple lines of symmetry in respect of the given figures are shown by dotted lines as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 123

(f)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 116
solution:
The multiple lines of symmetry in respect of the given figures are shown by dotted lines as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 124

(g)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 117
solution:
The multiple lines of symmetry in respect of the given figures are shown by dotted lines as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 125

(h)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 118
solution:
The multiple lines of symmetry in respect of the given figures are shown by dotted lines as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 126

Question 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 Algebraic Expreesions img 127
Solution:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 128
Let us mark the vertices of the square as A, B, C and D. Take the diagonal BD as a line of symmetry and shade a few more squares as shown to make the figure symmetric about this diagonal. There is only one way to do it. Clearly, the figure is symmetric about the second diagonal AC. Hence, the figure is symmetric about both the diagonals.

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

(a)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 129
Solution:
Completed shape symmetric about the mirror lines are as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 133

(b)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 130
Solution:
Completed shape symmetric about the mirror lines are as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 134

(c)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 131
Solution:
Completed shape symmetric about the mirror lines are as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 135

(d)
NCERT Solutions for Class 7 maths Algebraic Expreesions img 132
Solution:
Completed shape symmetric about the mirror lines are as under :
NCERT Solutions for Class 7 maths Algebraic Expreesions img 136

Question 7.
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
Solution:

Figure Number of lines of symmetry
(a) An equilateral triangle 3
(b) An isosceles triangle 1
(c) A scalene triangle 0
(d) A square 4
(e) A rectangle 2
(f) A rhombus 2
(g) A parallelogram 0
(h) A quadrilateral 0
(i) A regular hexagon 6
(j) A circle Infinite

Question 8.
What letters of the English alphabet have reflectional symmetry (i.e., symmetry related to mirror reflection).

(a) a vertical mirror
Solution:
The English alphabet letters having reflectional symmetry about a vertical mirror are A, H, I, M, 0, T, U, V, W, X, Y

(b) a horizontal mirror
Solution:
The English alphabet having reflectional symmetry about a horizontal mirror are B, C, D, E, H, I, O, and X

(c) both horizontal and vertical mirrors.
Solution:
The English alphabet having reflectional symmetry about both horizontal and vertical mirrors are H, I, O, and X

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

  1. A scalene triangle
  2. A parallelogram
  3. An irregular quadrilateral

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

(a) an isosceles triangle?
Solution:
Another name for the line of symmetry of an isosceles triangle is median.

(b) a circle?
Solution:
Another name for the line of symmetry of a circle is the diameter.

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