NCERT Solutions for Class 7 Maths Chapter 12 Symmetry
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Book Name: Maths
Subject: Maths
Chapter Number: 14
Chapter Name: Symmetry
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Book Name: Maths
Subject: Maths
Chapter Number: 14
Chapter Name: Symmetry
You can also bookmark this page by clicking + Save to Library icon and refer to these NCERT Solutions anytime from your account. More Detail
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NCERT Solutions for Class 7 Maths Chapter 12 Symmetry – Text
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Page 1
NCERT
SOLUTIONS
CLASS - 7TH
aglase .co
SOLUTIONS
CLASS - 7TH
aglase .co
Page 2
Book : Mathematics Ncert Solutions | Chapter-14 Maths
Class : 7th
Subject : Maths
Chapter : 14
Chapter Name : Symmetry
Exercise 14.1
Q1 Copy the �gures with punched holes and �nd the axes of symmetry for the following:
Answer. The axes of symmetry in the given �gures are as follows.
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Class : 7th
Subject : Maths
Chapter : 14
Chapter Name : Symmetry
Exercise 14.1
Q1 Copy the �gures with punched holes and �nd the axes of symmetry for the following:
Answer. The axes of symmetry in the given �gures are as follows.
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Page 3
Book : Mathematics Ncert Solutions | Chapter-14 Maths
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Book : Mathematics Ncert Solutions | Chapter-14 Maths
Page : 268 ; Block Name : Exercise 14.1
Q2 Given the line(s) of symmetry, �nd the other hole(s):
Answer.
Page : 269 ; Block Name : Exercise 14.1
Q3 In the following �gures, the mirror line (i.e., the line of symmetry) is given as a dotted line.
Complete each �gure performing re�ection 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 �gure you complete?
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Page : 268 ; Block Name : Exercise 14.1
Q2 Given the line(s) of symmetry, �nd the other hole(s):
Answer.
Page : 269 ; Block Name : Exercise 14.1
Q3 In the following �gures, the mirror line (i.e., the line of symmetry) is given as a dotted line.
Complete each �gure performing re�ection 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 �gure you complete?
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Page 5
Book : Mathematics Ncert Solutions | Chapter-14 Maths
Answer. The given �gures can be completed as follows.
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Answer. The given �gures can be completed as follows.
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Page 6
Book : Mathematics Ncert Solutions | Chapter-14 Maths
Page : 269 ; Block Name : Exercise 14.1
Q4 The following �gures have more than one line of symmetry. Such �gures are said to have
multiple lines of symmetry.
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Page : 269 ; Block Name : Exercise 14.1
Q4 The following �gures have more than one line of symmetry. Such �gures are said to have
multiple lines of symmetry.
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Page 7
Book : Mathematics Ncert Solutions | Chapter-14 Maths
Identify multiple lines of symmetry, if any, in each of the following �gures:
Answer. (a) The given �gure has 3 lines of symmetry. Hence, it has multiple lines of symmetry.
(b) The given �gure has 2 lines of symmetry. Hence, it has multiple lines of symmetry.
(c) The given �gure has 3 lines of symmetry. Hence, it has multiple lines
of symmetry.
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Identify multiple lines of symmetry, if any, in each of the following �gures:
Answer. (a) The given �gure has 3 lines of symmetry. Hence, it has multiple lines of symmetry.
(b) The given �gure has 2 lines of symmetry. Hence, it has multiple lines of symmetry.
(c) The given �gure has 3 lines of symmetry. Hence, it has multiple lines
of symmetry.
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Page 8
Book : Mathematics Ncert Solutions | Chapter-14 Maths
Page : 269 ; Block Name : Exercise 14.1
Q5 Copy the �gure given here.
Take any one diagonal as a line of symmetry and shade a few more squares to make the �gure
symmetric about a diagonal. Is there more than one way to do that? Will the �gure be symmetric
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Page : 269 ; Block Name : Exercise 14.1
Q5 Copy the �gure given here.
Take any one diagonal as a line of symmetry and shade a few more squares to make the �gure
symmetric about a diagonal. Is there more than one way to do that? Will the �gure be symmetric
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Page 9
Book : Mathematics Ncert Solutions | Chapter-14 Maths
about both the diagonals?
Answer.
Page : 270 ; Block Name : Exercise 14.1
Q6 Copy the diagram and complete each shape to be symmetric about the mirror line(s):
Answer. The given �gures can be completed about the given mirror lines as follows.
Page : 270 ; Block Name : Exercise 14.1
Q7 State the number of lines of symmetry for the following �gures:
(a) An equilateral triangle
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about both the diagonals?
Answer.
Page : 270 ; Block Name : Exercise 14.1
Q6 Copy the diagram and complete each shape to be symmetric about the mirror line(s):
Answer. The given �gures can be completed about the given mirror lines as follows.
Page : 270 ; Block Name : Exercise 14.1
Q7 State the number of lines of symmetry for the following �gures:
(a) An equilateral triangle
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Book : Mathematics Ncert Solutions | Chapter-14 Maths
(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) There are 3 lines of symmetry in an equilateral triangle.
(b)There is only 1 line of symmetry in an isosceles triangle.
(c) There is no line of symmetry in a scalene triangle.
(d)There are 4 lines of symmetry in a square.
(e) There are 2 lines Of symmetry in a rectangle.
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(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) There are 3 lines of symmetry in an equilateral triangle.
(b)There is only 1 line of symmetry in an isosceles triangle.
(c) There is no line of symmetry in a scalene triangle.
(d)There are 4 lines of symmetry in a square.
(e) There are 2 lines Of symmetry in a rectangle.
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Page 11
Book : Mathematics Ncert Solutions | Chapter-14 Maths
(f)There are 2 lines of symmetry in a rhombus.
(g) There is no line Of symmetry in a parallelogram.
(h) There is no line Of symmetry in a quadrilateral.
(i) There are 6 lines of symmetry in a regular hexagon.
(j)There are in�nite lines of symmetry in a circle. Some of these are represented as
follows.
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(f)There are 2 lines of symmetry in a rhombus.
(g) There is no line Of symmetry in a parallelogram.
(h) There is no line Of symmetry in a quadrilateral.
(i) There are 6 lines of symmetry in a regular hexagon.
(j)There are in�nite lines of symmetry in a circle. Some of these are represented as
follows.
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Page 12
Book : Mathematics Ncert Solutions | Chapter-14 Maths
Page : 270 ; Block Name : Exercise 14.1
Q8 What letters of the English alphabet have re�ectional symmetry (i.e., symmetry related to
mirror re�ection) about.
(a) a vertical mirror
(b) a horizontal mirror
(c) both horizontal and vertical mirrors
Answer. (a) A, H, I, M, O, T, U, V, W, X, Y are the letters having a re�ectional symmetry about a
vertical mirror.
(b) B, C, D, E, H, I, K, O, X are the letters having a re�ectional symmetry about a horizontal mirror.
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Page : 270 ; Block Name : Exercise 14.1
Q8 What letters of the English alphabet have re�ectional symmetry (i.e., symmetry related to
mirror re�ection) about.
(a) a vertical mirror
(b) a horizontal mirror
(c) both horizontal and vertical mirrors
Answer. (a) A, H, I, M, O, T, U, V, W, X, Y are the letters having a re�ectional symmetry about a
vertical mirror.
(b) B, C, D, E, H, I, K, O, X are the letters having a re�ectional symmetry about a horizontal mirror.
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Book : Mathematics Ncert Solutions | Chapter-14 Maths
(c) H, I, O, X are the letters having a re�ectional symmetry about both the vettical mirror and the
horizontal mirror.
Page : 270 ; Block Name : Exercise 14.1
Q9 Give three examples of shapes with no line of symmetry.
Answer. A scalene triangle, a parallelogram, and a trapezium do not have any line of symmetry.
Page : 270 ; Block Name : Exercise 14.1
Q10 What other name can you give to the line of symmetry of
(a) an isosceles triangle? (b) a circle?
Answer. (a) An isosceles triangle has only 1 line Of symmetry.
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(c) H, I, O, X are the letters having a re�ectional symmetry about both the vettical mirror and the
horizontal mirror.
Page : 270 ; Block Name : Exercise 14.1
Q9 Give three examples of shapes with no line of symmetry.
Answer. A scalene triangle, a parallelogram, and a trapezium do not have any line of symmetry.
Page : 270 ; Block Name : Exercise 14.1
Q10 What other name can you give to the line of symmetry of
(a) an isosceles triangle? (b) a circle?
Answer. (a) An isosceles triangle has only 1 line Of symmetry.
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Page 14
Book : Mathematics Ncert Solutions | Chapter-14 Maths
Therefore, this line of symmetry is the median and also the altitude of this isosceles triangle.
(b) There are in�nite lines of symmetry in a circle. Some of these are represented as follows.
It can be concluded that each line Of symmetry is the diameter for this circle.
Page : 270 ; Block Name : Exercise 14.1
Exercise 14.2
Q1 Which of the following �gures have rotational symmetry of order more than 1:
Answer.
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Therefore, this line of symmetry is the median and also the altitude of this isosceles triangle.
(b) There are in�nite lines of symmetry in a circle. Some of these are represented as follows.
It can be concluded that each line Of symmetry is the diameter for this circle.
Page : 270 ; Block Name : Exercise 14.1
Exercise 14.2
Q1 Which of the following �gures have rotational symmetry of order more than 1:
Answer.
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Book : Mathematics Ncert Solutions | Chapter-14 Maths
(c) The given �gure has its rotational symmetry as 1.
(d) The given �gure has its rotational symmetry as 2.
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(c) The given �gure has its rotational symmetry as 1.
(d) The given �gure has its rotational symmetry as 2.
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Book : Mathematics Ncert Solutions | Chapter-14 Maths
Hence, �gures (a), (b), (d), (e), and (f) have rotational symmetry of order more than 1.
Page : 274 ; Block Name : Exercise 14.2
Q2 Give the order of rotational symmetry for each �gure:
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Hence, �gures (a), (b), (d), (e), and (f) have rotational symmetry of order more than 1.
Page : 274 ; Block Name : Exercise 14.2
Q2 Give the order of rotational symmetry for each �gure:
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Book : Mathematics Ncert Solutions | Chapter-14 Maths
Answer.
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Answer.
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Book : Mathematics Ncert Solutions | Chapter-14 Maths
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Book : Mathematics Ncert Solutions | Chapter-14 Maths
Page : 274 ; Block Name : Exercise 14.2
Exercise 14.3
Q1 Name any two �gures that have both line symmetry and rotational symmetry.
Answer. Equilateral triangle and regular hexagon have both line of symmetry and rotational
symmetry.
Page : 275 ; Block Name : Exercise 14.3
Q2 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) Equilateral triangle has 3 lines of symmetry and rotational symmetry of order 3.
(ii) Isosceles triangle has only 1 line of symmetry and no rotational symmetry of order more than 1.
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Page : 274 ; Block Name : Exercise 14.2
Exercise 14.3
Q1 Name any two �gures that have both line symmetry and rotational symmetry.
Answer. Equilateral triangle and regular hexagon have both line of symmetry and rotational
symmetry.
Page : 275 ; Block Name : Exercise 14.3
Q2 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) Equilateral triangle has 3 lines of symmetry and rotational symmetry of order 3.
(ii) Isosceles triangle has only 1 line of symmetry and no rotational symmetry of order more than 1.
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Book : Mathematics Ncert Solutions | Chapter-14 Maths
(iii) A parallelogram is a quadrilateral which has no line of symmetry but a rotational symmetry Of
order 2.
(iv) A kite is a quadrilateral which has only 1 line of symmetry and no rotational symmetry of order
more than 1.
Page : 275 ; Block Name : Exercise 14.3
Q3 If a �gure has two or more lines of symmetry, should it have rotational symmetry of order more
than 1?
Answer. Yes. If a �gure has two or more lines of symmetry, then it will de�nitely have its rotational
symmetry' Of order more than 1.
Page : 275 ; Block Name : Exercise 14.3
Q4 Fill in the blanks:
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(iii) A parallelogram is a quadrilateral which has no line of symmetry but a rotational symmetry Of
order 2.
(iv) A kite is a quadrilateral which has only 1 line of symmetry and no rotational symmetry of order
more than 1.
Page : 275 ; Block Name : Exercise 14.3
Q3 If a �gure has two or more lines of symmetry, should it have rotational symmetry of order more
than 1?
Answer. Yes. If a �gure has two or more lines of symmetry, then it will de�nitely have its rotational
symmetry' Of order more than 1.
Page : 275 ; Block Name : Exercise 14.3
Q4 Fill in the blanks:
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Page 21
Book : Mathematics Ncert Solutions | Chapter-14 Maths
Answer. The given table can be completed as follows.
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Answer. The given table can be completed as follows.
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Book : Mathematics Ncert Solutions | Chapter-14 Maths
Page : 275 ; Block Name : Exercise 14.3
Q5 Name the quadrilaterals which have both line and rotational symmetry of order more than 1.
Answer. Square, rectangle, and rhombus are the quadrilaterals which have both line and rotational
symmetry of order more than 1. A square has 4 lines of symmetry and rotational symmetry of order
4. A rectangle has 2 lines of symmetry and rotational symmetry Of order 2. A rhombus has 2 lines
Of symmetry and rotational symmetry Of order 2.
Page : 276 ; Block Name : Exercise 14.3
Q6 After rotating by 60° about a centre, a �gure looks exactly the same as its original position. At
what other angles will this happen for the �gure?
Answer. It can be observed that if a �gure looks symmetrical on rotating by 60∘ , then it will also
look symmetrical on rotating by 120∘ , 180∘ , 240∘ , 300∘ and 360∘ i.e., further multiples Of 60∘ .
Page : 276 ; Block Name : Exercise 14.3
Q7 Can we have a rotational symmetry of order more than 1 whose angle of rotation is
(i) 45°?
(ii) 17°?
Answer. It can be observed that if the angle of rotation of a �gure is a factor of 3600, then it will
have a rotational symmetry of order more than 1. It can be checked that 450 is a factor of 3600 but
170 is not. Therefore, the �gure having its angle Of rotation as 450 will have its rotational
symmetry Of order more than 1. However, the �gure having its angle of rotation as 170 will not be
having its rotational symmetry of order more than 1.
Page : 276 ; Block Name : Exercise 14.3
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Page : 275 ; Block Name : Exercise 14.3
Q5 Name the quadrilaterals which have both line and rotational symmetry of order more than 1.
Answer. Square, rectangle, and rhombus are the quadrilaterals which have both line and rotational
symmetry of order more than 1. A square has 4 lines of symmetry and rotational symmetry of order
4. A rectangle has 2 lines of symmetry and rotational symmetry Of order 2. A rhombus has 2 lines
Of symmetry and rotational symmetry Of order 2.
Page : 276 ; Block Name : Exercise 14.3
Q6 After rotating by 60° about a centre, a �gure looks exactly the same as its original position. At
what other angles will this happen for the �gure?
Answer. It can be observed that if a �gure looks symmetrical on rotating by 60∘ , then it will also
look symmetrical on rotating by 120∘ , 180∘ , 240∘ , 300∘ and 360∘ i.e., further multiples Of 60∘ .
Page : 276 ; Block Name : Exercise 14.3
Q7 Can we have a rotational symmetry of order more than 1 whose angle of rotation is
(i) 45°?
(ii) 17°?
Answer. It can be observed that if the angle of rotation of a �gure is a factor of 3600, then it will
have a rotational symmetry of order more than 1. It can be checked that 450 is a factor of 3600 but
170 is not. Therefore, the �gure having its angle Of rotation as 450 will have its rotational
symmetry Of order more than 1. However, the �gure having its angle of rotation as 170 will not be
having its rotational symmetry of order more than 1.
Page : 276 ; Block Name : Exercise 14.3
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Document Details
| Board / Org | NCERT |
| Exam | Class 7 |
| Type | Solution |
| Pages | 22 |
| Updated | 30 Apr 2026 |