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Edited By Ravindra Pindel | Updated on Feb 07, 2024 06:18 PM IST

**NCERT Solutions for Maths Chapter 14 Symmetry Class 7: **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 class 7th maths chapter 14 solution . It is an important concept of the geometrical part used in artists, designing of jewellery or clothes, architects, car manufacturers, etc. 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.

This Story also Contains

- NCERT Solutions for Class 7 Maths Chapter 14 Symmetry - Important Formulae
- NCERT Solutions for Maths Chapter 14 Symmetry Class 7- Important Points
- NCERT Solutions for Maths Chapter 14 Symmetry Class 7
- NCERT Solutions for Maths Chapter 14 Symmetry Class 7 Exercise 14.1 Question:1 (a) Copy the figures with punched holes and find the axes of symmetry for the following:
- NCERT Solutions for Class 7th Math Chapter 14 Symmetry Topic 14.3
- NCERT Solutions for Class 7th Math Chapter 14 Symmetry Exercise 14.2
- NCERT Solutions for Chapter 14 Maths Class 7 Symmetry Exercise 14.3
- Symmetry Class 7 Maths Chapter 14-Topics

In this chapter of NCERT, 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. You can get NCERT Solutions from Classes 6 to 12 by clicking on the above link. Here you will get NCERT Solutions for Class 7. It is advisable that you must complete the NCERT Class 7 Maths Syllabus as soon as possible and then refer to the given solutions.

Angle of Rotation in regular polygon = 360°/Number of sides

A half-turn = Rotation by 180°

A quarter-turn = Rotation by 90°

Reflection in the x-axis , ( X , Y ) → ( X , -Y )

Reflection in the y-axis , ( X , Y ) → ( -X , Y )

**Line Symmetry: **

If it can be divided into two identical parts by a line, there will be a line of symmetry.

Regular polygons have equal angles and equal sides so they have multiple lines of symmetry. The table given below shows the number of lines of symmetry in regular polygons.

Regular Polygons | Regular Hexagon | Regular Pentagon | Square | Equilateral Triangle |

Number of the line of Symmetry | 6 | 5 | 4 | 3 |

Angle of Rotation in regular polygon = 360°/Number of sides

**Rotational Symmetry:** When we rotate an object if it looks exactly the same , we say that it has rotational symmetry.

**Centre of rotation:** That fixed point about which object rotates.

**Angles of rotation:** The angle by which the object rotates.

**Order of Rotational Symmetry:**

The number of times an object looks exactly the same, in a complete turn

(360°) is called the order of rotational symmetry.

Some objects have only line of symmetry ( like letter E), some objects have only rotational symmetry ( like the letter S), and some have both symmetries ( like the letter H).

Formulas for Reflection:

Reflection in the x-axis , ( X , Y ) → ( X , -Y )

Reflection in the y-axis , ( X , Y ) → ( -X , Y )

Free download **NCERT Solutions for Class 7 Maths Chapter 14 Symmetry PDF **for CBSE Exam.

Question:1

** Answer:**

The axes of symmetry is as shown :

** Question:1.(b) ** Copy the figures with punched holes and find the axes of symmetry for the following:

** Answer: **

The axes of symmetry is as shown :

** Question: 1.(c) ** Copy the figures with punched holes and find the axes of symmetry for the following:

** Answer: **

The axes of symmetry is as shown :

** Question: ** ** 1.(d) ** Copy the figures with punched holes and find the axes of symmetry for the following:

** Answer:**

The axes of symmetry is as shown :

** Question: ** ** 1 .(e) ** Copy the figures with punched holes and find the axes of symmetry for the following:

** Answer: **

The axes of symmetry is as shown :

** Question: ** ** 1 (f) ** Copy the figures with punched holes and find the axes of symmetry for the following:

** Answer: **

The axes of symmetry is as shown :

** Question: ** ** 1 (g) ** Copy the figures with punched holes and find the axes of symmetry for the following:

** Answer:**

The axes of symmetry is as shown :

** Question: ** ** 1( h) ** Copy the figures with punched holes and find the axes of symmetry for the following:

** Answer:**

The axes of symmetry are as shown :

** Question: 1(i) ** Copy the figures with punched holes and find the axes of symmetry for the following:

** Answer:**

The axes of symmetry is as shown :

** Question: ** ** 1(j) ** Copy the figures with punched holes and find the axes of symmetry for the following:

** Answer:**

The axes of symmetry is as shown :

** Question: ** ** 1.(k) ** Copy the figures with punched holes and find the axes of symmetry for the following:

** Answer:**

The axes of symmetry is as shown :

** Question:1.(l) ** 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 :

** Answer:**

The complete figures are as shown :

(a) square (b)triangle (c)rhombus

(c) circle (d) pentagon (e) Octagon

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: 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?

** Answer: **The figure with symmetry may be as shown :

The figure with symmetry may be as shown :

Yes,there more than one way .

Yes,the figure be symmetric about both the diagonals

Yes, there more than one way.

Yes,the figure be symmetric about both the diagonals

** 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: ****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

** 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

(a) a vertical mirror

(b) a horizontal mirror

(c) both horizontal and vertical mirrors

** Answer: **(a) a vertical mirror : A,H,I,M,O,T,U,V,W,X and Y

(b) horizontal mirror : B,C,D,E,H,I,O and X

(c) both horizontal and vertical mirrors : H,I,O and X.

** 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:1****0.(a) ** What another 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.

** 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 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 . 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.

**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 so it has ordered as 2.

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

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

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

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

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

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

(h) The given figure has rotational symmetry about so it has ordered as 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 a 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.

** 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 | |

Rectangle | Intersection point of digonals. | 2 | |

Rhombus | Intersection point of digonals. | 2 | |

Equilateral Triangle | Intersection point of medians. | 3 | |

Regular Hexagon | Intersection point of digonals. | 6 | |

Circle | centre of circle | infinite | any angle |

Semi-circle | centre of circle | 1 |

** 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

** Answer: **After rotating by about a centre, a figure looks exactly the same as its original position, then it will look symmetrical on rotating by All angles are multiples of .

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

** Answer: **We can observe that the angle of rotation is the factor of ,then it will have rotational symmetry of order more than 1.

(i) is a factor of so the figure having its angle of rotation as will have rotational symmetry of order more than 1.

(ii) is not a factor of so the figure having its angle of rotation as will not have rotational symmetry of order more than 1.

- Lines of Symmetry For Regular Polygons
- Rotational Symmetry
- Line Symmetry And Rotational Symmetry

Chapter No. | Chapter Name |

Chapter 1 | |

Chapter 2 | |

Chapter 3 | |

Chapter 4 | |

Chapter 5 | |

Chapter 6 | |

Chapter 7 | |

Chapter 8 | |

Chapter 9 | |

Chapter 10 | |

Chapter 11 | |

Chapter 12 | |

Chapter 13 | |

Chapter 14 | Symmetry |

Chapter 15 |

- 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 practise questions also.

** Happy learning!!! **

**Also Check NCERT Books and NCERT Syllabus here:**

1. What is the order of rotational symmetry for each figure?

- The order of rotational symmetry of a figure refers to the number of times it can be rotated by a certain angle and still appear the same.
- For a figure with n-fold rotational symmetry, you can rotate it by 360°/n to achieve this symmetry.
- A figure with no rotational symmetry has an order of 1, as it looks the same only after a full 360-degree rotation.
- Regular polygons like squares and equilateral triangles often have rotational symmetries of higher orders, such as 4-fold and 3-fold symmetry.
- Irregular shapes might have lower-order rotational symmetries or none at all.

Students also practice questions based on 'give the order of rotational symmetry for each figure' which are very helpful to get deeper understanding of concepts.

2. What are the topics covered in NCERT Class 7 Chapter 14?

Here are the topics covered in NCERT Class 7 chapter 14 maths

- Lines of Symmetry For Regular Polygons
- Rotational Symmetry
- Line Symmetry And Rotational Symmetry

You should practice class 7 chapter 14 maths solutions to get command on the concepts.

3. How many exercises in NCERT Class 7 chapter 14?

There are 3 exercises in NCERT Class 7 chapter 14

NCERT symmetry class 7 Exercise 14.1 - 10 Questions

NCERT symmetry class 7 Exercise 14.2 - 2 Questions

NCERT symmetry class 7 Exercise 14.3 - 7 Questions

Practice these exercise from NCERT solution for class 7 maths chapter 14 pdf which can be downloaded from the link given above.

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