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NCERT Solutions for Class 7 Maths Chapter 14 Symmetry - Download PDF

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry - Download PDF

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.

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.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry - Important Formulae

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 )

NCERT Solutions for Maths Chapter 14 Symmetry Class 7- Important Points

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.

NCERT Solutions for Maths Chapter 14 Symmetry Class 7

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NCERT Solutions for Class 7 Maths Chapter 14 Questions and Exercise

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:

4656556

Answer: 4656556

The axes of symmetry is as shown :

46564441

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

454454

Answer: 454454

The axes of symmetry is as shown :

1444655

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

445465454

Answer: 445465454

The axes of symmetry is as shown :

4544113215641

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

4444145

Answer: 4444145

The axes of symmetry is as shown :

445456444

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

4654511654

Answer: 4654511654

The axes of symmetry is as shown :

4444454

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

454544546

Answer: 454544546

The axes of symmetry is as shown :

445411466

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

154454544

Answer: 154454544

The axes of symmetry is as shown :

154545454545

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

114444466

Answer: 114444466

The axes of symmetry are as shown :

154544444

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

15444545441

Answer: 15444545441

The axes of symmetry is as shown :

132323232

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

123154545

Answer:123154545

The axes of symmetry is as shown :

112121215

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

11545422

Answer: 11545422

The axes of symmetry is as shown :

1215454544

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

4548487

Answer: 4548487

The axes of symmetry is as shown :

154544

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

15454326

Answer: The other holes from the symmetry are as shown :

1643868353545

Question: 4 The following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry

1643868544642 Identify multiple lines of symmetry, if any, in each of the following figures:

15444545454

Answer:

The lines of symmetry of figures are:

(a)There are 3 lines of symmetry. Thus, it has multiple lines of symmetry.

1643868595122

(b) There are 2 lines of symmetry. Thus, it has multiple lines of symmetry.

1643868593196

(c)There are 3 lines of symmetry. Thus, it has multiple lines of symmetry.

1643868594468

(d)There are 2 lines of symmetry. Thus, it has multiple lines of symmetry.

1643868593461

(e)There are 4 lines of symmetry. Thus, it has multiple lines of symmetry.

1643868594836

(f)There is 1 line of symmetry.

1643868592764

(g)There are 4 lines of symmetry. Thus, it has multiple lines of symmetry.

1643868593747

(h)There are 6 lines of symmetry. Thus, it has multiple lines of symmetry.

1643868594168


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?

1115545

Answer: The figure with symmetry may be as shown :

The figure with symmetry may be as shown :

1643868628657

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):

154874874

Answer: The complete shape symmetric about the mirror line(s) are :

15787779

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

1643868681893

(b) An isosceles triangle

The number of lines of symmetry = 1

1643868679726

(c) A scalene triangle

The number of lines of symmetry = 0

1643868680739

(d) A square

The number of lines of symmetry = 4

1643868682798

(e) A rectangle

The number of lines of symmetry = 2

1643868680328

(f) A rhombus

The number of lines of symmetry = 2

1643868681626

(g) A parallelogram

The number of lines of symmetry = 0

1643868681034

(h) A quadrilateral

The number of lines of symmetry = 0

1643868681333

(i) A regular hexagon

The number of lines of symmetry = 6

1643868682331

(j) A circle

The number of lines of symmetry = infinite

1643868682570

Question: 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

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:10.(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.

NCERT Solutions for Class 7th Math Chapter 14 Symmetry Topic 14.3

Question: 1.(a) Can you now tell the order of the rotational symmetry for an equilateral triangle?

154487795

Answer: An equilateral triangle has rotational symmetry at 120 \degree 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°?

154487795

Answer: All the triangles look same when rotated by 120 \degree . 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.

654411544

Answer: Among the above-given shapes, (i),(ii) and (iv) have rotational symmetry about the marked point.

NCERT Solutions for Class 7th Math Chapter 14 Symmetry Exercise 14.2

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

14444546565

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:

1444446544

Answer: (a) The given figure has rotational symmetry about 180 \degree so it has ordered as 2.

(b) The given figure has rotational symmetry about 180 \degree so it has ordered as 2.

(c) The given figure has rotational symmetry about 120 \degree so it has ordered as 3.

(d) The given figure has rotational symmetry about 90 \degree so it has ordered as 4.

(e) The given figure has rotational symmetry about 90 \degree so it has ordered as 4.

(f) The given figure has rotational symmetry about 72 \degree so it has ordered as 5.

(g) The given figure has rotational symmetry about 60 \degree so it has ordered as 6.

(h) The given figure has rotational symmetry about 120 \degree so it has ordered as 3.

NCERT Solutions for Chapter 14 Maths Class 7 Symmetry Exercise 14.3

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 :

1643868736523

The rotational symmetry as shown below :

1643868736942

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.

1643868755614

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.

1643868803476

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,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
90 \degree
Rectangle
Intersection point of digonals.
2
180 \degree
Rhombus
Intersection point of digonals.
2
180 \degree
Equilateral Triangle
Intersection point of medians.
3
120 \degree
Regular Hexagon
Intersection point of digonals.
6
60 \degree
Circle
centre of circle
infinite
any angle
Semi-circle
centre of circle
1
360 \degree










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

Question: 6 After rotating by 60^{0} about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

Answer: After rotating by 60^{0} about a centre, a figure looks exactly the same as its original position, then it will look symmetrical on rotating by 120 \degree,180 \degree,240 \degree,300 \degree,360 \degree. All angles are multiples of 60^{0} .

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

(i)\: 45^{o}?(ii)\: 17^{o}?

Answer: We can observe that the angle of rotation is the factor of 360 \degree ,then it will have rotational symmetry of order more than 1.

(i) 45^{o} is a factor of 360 \degree so the figure having its angle of rotation as 45^{o} will have rotational symmetry of order more than 1.

(ii) 17^{o} is not a factor of 360 \degree so the figure having its angle of rotation as 17^{o} will not have rotational symmetry of order more than 1.

Symmetry Class 7 Maths Chapter 14-Topics

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

NCERT Solutions for Class 7 Maths Chapter Wise

NCERT Solutions for Class 7 Subject Wise

Benefits of NCERT Solutions for Class 7th Chapter 14 Maths Symmetry

  • 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:

Frequently Asked Question (FAQs)

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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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

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Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

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increase two fold

Option 3)

remain unchanged

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be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

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Fraction of solute present in water

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Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

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A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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