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NCERT Solutions for Class 6 Maths Chapter 9 - Symmetry

NCERT Solutions for Class 6 Maths Chapter 9 - Symmetry

Edited By Komal Miglani | Updated on Jul 07, 2025 09:51 AM IST

In mathematics, symmetry is the art of balance and beauty hidden in shapes. Symmetry teaches us that even in geometry, balance brings harmony. We find many objects around us in various forms. The sun, nature, stars, moon, birds, and humans are all a part of this beautiful universe. We as humans tend to analyse these objects with our eyes and find some similar patterns in them. We observe that certain patterns are repeated in some figures, such as flowers, bees, etc. This is known as symmetry. This article contains the step-by-step NCERT Solutions for class 6 Maths for all the exercise questions in this chapter on symmetry.

This Story also Contains
  1. NCERT Solutions for Class 6 Maths Chapter 9: Exercise Questions
  2. NCERT Solutions for Class 6 Maths Chapter 9 Symmetry - Notes
  3. Symmetry Class 6 Maths Chapter 9 - Topics
  4. NCERT Solutions for Class 6 Maths Chapter 9 Symmetry - Points to Remember
  5. NCERT Solutions for Class 6 Maths Chapter Wise
NCERT Solutions for Class 6 Maths Chapter 9 - Symmetry
NCERT Solutions for Class 6 Maths Chapter 9 - Symmetry

In the chapter of symmetry, math shows how a simple reflection creates beauty. These solutions help students understand the concept in a better and practical way. This article on the NCERT Solutions for this chapter is an important study resource that helps the students understand various topics like symmetry, lines of symmetry, rotational symmetry, reflection, etc. Students can refer to the NCERT Solutions for Class 6 to practice more problems during exam preparation.

Background wave

NCERT Solutions for Class 6 Maths Chapter 9: Exercise Questions

Page number: 219
Number of Questions: 2

Question 1: Do you see any line of symmetry in the figures at the start of the chapter? What about in the picture of the cloud?

17496220651211749622063678

Solution:

There is a line of symmetry in a flower, a butterfly, and a rangoli.

This flower has 6 lines of symmetry.
1749622064919

Butterfly has 1 line of symmetry.

1749622063960
This rangoli has 4 lines of symmetry.
1749622062192
But no line of symmetry can be found in the clouds or the pinwheel.

Question 2: For each of the following figures, identify the line(s) of symmetry if they exist.

1749622063408

Solution:

Shapes

Number of lines of symmetry

Graphical design

1749622061260

1 line of symmetry.

1749622062881

1749622060919

1 line of symmetry.

1749622065675

1749622061389

No lines of symmetry.

1749622060728

1 line of symmetry.

1749622060257

1749622060380

No lines of symmetry.

Page number: 223-230
Number of Questions: 13

Punching Game: The fold is a line of symmetry. Punch holes at different locations of a folded square sheet of paper using a punching machine and create different symmetric patterns.

1749622063493

Question 1: In each of the following figures, a hole was punched in a folded square sheet of paper, and then the paper was unfolded. Identify the line along which the paper was folded. Figure (d) was created by punching a single hole. How was the paper folded?

1749622064130

Solution:

a.

1749622069082

b.

1749622061996

c.

1749622063207

d.

1749622061889

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

1749622063547

Solution:

a.

1749622061148

b.

1749622063133

c.

1749622063357

d.

1749622062317

e.

1749622062239

Question 3: Here are some questions on paper cutting. Consider a vertical fold. We represent it this way:

1749622064598

Similarly, a horizontal fold is represented as follows:
1749622060844

Solution:

1749622069238

Question 4: After each of the following cuts, predict the shape of the hole when the paper is opened. After you have made your prediction, make the cutouts and verify your answer.

Solution:

a.

1749622062364

b.

1749622060485

c.

1749622061336

d.

1749622062713

Question 5: Suppose you have to get each of these shapes with some folds and a single straight cut. How will you do it?
a. The hole in the centre is a square.

1749622062051

b. The hole in the centre is a square.

1749622065268

Note: For the above two questions, check if the 4-sided figures in the centre satisfy both the properties of a square.

Solution:

a.

1749622064821

b.

1749622065840

Question 6: How many lines of symmetry do these shapes have?

a. 1749622065063

b. A triangle with equal sides and equal angles.
1749622060999

c. A hexagon with equal sides and equal angles.
1749622062623

Solution:

a. 1749622063617

b. 1749622062771

c. 1749622061771

Question 7: Trace each figure and draw the lines of symmetry, if any

Solution:

1749622065780

1749622066677

Question 8: Find the lines of symmetry for the kolam below.

1749622063268

Solution:

1749622068533

Question 9: Draw the following.

a. A triangle with exactly one line of symmetry.

b. A triangle with exactly three lines of symmetry.

c. A triangle with no line of symmetry. Is it possible to draw a triangle with exactly two lines of symmetry?

Solution:

Sr. No.

Types of triangles

Graphical representation

a.

An isosceles triangle has only 1 line of symmetry.

1749622067933

b.

An equilateral triangle has 3 lines of symmetry.

1749622061646

c.

A scalene triangle has no lines of symmetry.

1749622062572

Question 10: Draw the following. In each case, the figure should contain at least one curved boundary.

a. A figure with exactly one line of symmetry.

b. A figure with exactly two lines of symmetry.

c. A figure with exactly four lines of symmetry.

Solution:

Sr. No.DescriptionFigure
a.

A figure with exactly one line of symmetry.

1749622065933

b.

A figure with exactly two lines of symmetry.

1749622065558

c.

A figure with exactly four lines of symmetry.

1749622064383

Question 11: Copy the following on squared paper. Complete them so that the blue line is a line of symmetry. Problem (a) has been done for you.

1749622066097

Hint: For (c) and (f), see if rotating the book helps!

Solution:

B. 1749622061586

C. 1749622065391

D. 1749622060597

E. 1749622062487

F. 1749622063023

Question 12: Copy the following drawing on squared paper. Complete each one of them so that the resulting figure has the two blue lines as lines of symmetry.

1749622067354

Solution:

a.

1749622065482

b.

1749622064652

c.

1749622061094

d.

1749622061513

e.

1749622062830

f.

1749622062434

Question 13: Copy the following on a dot grid. For each figure, draw two more lines to make a shape that has a line of symmetry.

1749622066373

Solution:

1749622066003

Page number: 235-236
Number of Questions: 3

Question 1: Find the angles of symmetry for the given figures about the point marked •.

Solution:

a. The initial angle of symmetry in this figure is 90°.
Because after a 90° rotation, the figure remains the same.
∴ The angles of symmetry of the figure are: 90°, 180°, 270°, 360°
1749622066758

b. The angle of symmetry in this figure is 360°.
Because only after a whole 360° rotation, we will get the same figure.
1749622063802

c. The initial angle of symmetry in this figure is 180°.
Because after a 180° rotation, we will get the same figure.
∴ The angles of symmetry of the figure are: 180° and 360°
1749622067427

Question 2: Which of the following figures have more than one angle of symmetry?

Solution:

1749623495333

1749622064752

1749623610689

1749622063909

1749623647255

1749622064534

1749623673246

1749622066846

1749623718706

1749622066283

1749623753748

1749622068432

1749623780378

1749622064257

Question 3: Give the order of rotational symmetry for each figure:

Solution:


1749623930336

1749622067012

1749623948789

1749622067793

1749623964473

1749622066600

1749623980668

1749622068623

1749624030268

1749622064049

1749624079189

1749622066446

Page number: 238-239
Number of Questions: 11

Question 1: Colour the sectors of the circle below so that the figure has
i) 3 angles of symmetry, ii) 4 angles of symmetry, iii) What are the possible numbers of angles of symmetry you can obtain by colouring the sectors in different ways?

1749622061459

Solution:

(i) 3 angles of symmetry will appear after each 120-degree rotation.
1749622064332

(ii) 4 angles of symmetry will appear after each 90-degree rotation

1749622067123

(iii) We can obtain four possible numbers of symmetry angles by colouring the sectors in different ways.
1749622068900

Question 2: Draw two figures other than a circle and a square that have both reflection symmetry and rotational symmetry.

Solution:

Equilateral Triangle

1749622068725

Regular Hexagon

1749622068272

Question 3: Draw, wherever possible, a rough sketch of:
a. A triangle with at least two lines of symmetry and at least two angles of symmetry.
b. A triangle with only one line of symmetry but not having rotational symmetry.
c. A quadrilateral with rotational symmetry but no reflection symmetry.
d. A quadrilateral with reflection symmetry but not having rotational symmetry.

Solution:

A triangle with at least two lines of symmetry and at least two angles of symmetry

1749622067562

A triangle with only one line of symmetry but not having rotational symmetry.

1749622064467

A quadrilateral with rotational symmetry but no reflection symmetry.

1749622062957

A quadrilateral with reflection symmetry but not having rotational symmetry.

1749622064203

Question 4: In a figure, 60° is the smallest angle of symmetry. What are the other angles of symmetry of this figure?

Solution:

Since 60° is the smallest angle of symmetry, any angle that is a multiple of 60° up to 360° is also an angle of symmetry.
The other angles of symmetry would be multiples of 60∘, i.e. 120°,180°,240°,300° and 360°.

Question 5: In a figure, 60° is an angle of symmetry. The figure has two angles of symmetry less than 60°. What is its smallest angle of symmetry?

Solution:

Smallest angle of symmetry = 60°3=20°

Question 6: Can we have a figure with rotational symmetry whose smallest angle of symmetry is:

a. 45°?

b. 17°?

Solution:

(a) 360°÷45°=8.

Since 45∘ divides 360∘ perfectly, it's possible to have a figure with rotational symmetry whose smallest angle of symmetry is 45∘.

(b) 360°÷17°=21.18

Since 17° doesn't evenly divide 360°, it is impossible to have a figure with rotational symmetry whose smallest angle of symmetry is 17°.

Question 7: This is a picture of the new Parliament Building in Delhi.
1749622065197

a. Does the outer boundary of the picture have reflection symmetry? If so, draw the lines of symmetries. How many are they?

b. Does it have rotational symmetry around its centre? If so, find the angles of rotational symmetry.

Solution:

a. Yes, the outer boundary of the picture has reflection symmetry. There are three lines of symmetry, and it is shown in the figure below.
1749622067692

b. Yes, the figure has rotational symmetry around its centre.

The smallest angle of rotational symmetry =360∘3=120∘.
Therefore, the angles of rotational symmetry of the figure are 120∘,240∘ and 360∘.


1749622066530

Question 8: How many lines of symmetry do the shapes in the first shape sequence in Chapter 1, Table 3, the Regular Polygons, have? What number sequence do you get?
1749622068193

Solution:

In a regular polygon, the number of lines of symmetry equals the number of its sides.

Therefore, Number of lines of symmetry in a triangle (3-sided polygon) = 3

Number of lines of symmetry in a quadrilateral (4-sided polygon) =4

Number of lines of symmetry in a pentagon (5-sided polygon) =5

Number of lines of symmetry in a hexagon (6-sided polygon) = 6

Number of lines of symmetry in a heptagon (7-sided polygon) =7

Number of lines of symmetry in an octagon (8-sided polygon) =8

Number of lines of symmetry in a nonagon (9-sided polygon) =9

Number of lines of symmetry in a decagon (10-sided polygon) = 10

Number sequence: 3,4,5,6,7,8,9,10…..

Question 9: How many angles of symmetry do the shapes in the first shape sequence in Chapter 1, Table 3, the Regular Polygons, have? What number sequence do you get?

1749622068085

Solution:

In a regular polygon, the number of angles of symmetry is equal to the number of lines of symmetry.

Therefore,

Number of angles of symmetry in a triangle (3-sided polygon) =3

Number of angles of symmetry in a quadrilateral (4-sided polygon) =4

Number of angles of symmetry in a pentagon (5-sided polygon) =5

Number of angles of symmetry in a hexagon (6-sided polygon) =6

Number of angles of symmetry in a heptagon (7-sided polygon) =7

Number of angles of symmetry in an octagon (8-sided polygon) =8

Number of angles of symmetry in a nonagon (9-sided polygon) = 9

Number of angles of symmetry in a decagon (10-sided polygon) = 10

Number sequence: 3,4,5,6,7,8,9,10…..

Question 10: How many lines of symmetry do the shapes in the last shape sequence in Chapter 1, Table 3, the Koch Snowflake sequence, have? How many angles of symmetry?

Solution:

1749622066219

The triangular shape has 3 lines of symmetry and 3 angles of symmetry.

In six-pointed stars, lines of symmetry is 12 and the angle of symmetry is 6.

The lines of symmetry and angle of symmetry for the remaining three figures are the same as six-pointed star.

Question 11: How many lines of symmetry and angles of symmetry does the Ashoka Chakra have?

1749622066909

Solution:

The Ashoka Chakra has 24 spokes spread equally.

24 spokes make 12 pairs.

A line through an opposite pair is a line of symmetry.

Hence, there are 12 lines of symmetry.

Smallest angle of symmetry =360°12=30°

Other angles of symmetry are its multiples up to 360°.

Other angles are 60°,120°,150°, 360°. (12 angles in all).

NCERT Solutions for Class 6 Maths Chapter 9 Symmetry - Notes

Understanding symmetry is like seeing the world in a mirror—orderly and elegant. These notes will surely help students to solve problems related to this chapter efficiently.

Symmetry: Symmetry refers to a part or parts of a figure that are repeated in some definite pattern.

Symmetry | Definition | Solved Examples | Geometry- Cuemath

In the above image, we see that the pattern is repeated after a fixed interval. This is a symmetrical pattern.

Line of Symmetry: A line of symmetry is the one that differentiates an object into 2 equal halves, such that the right-hand side is equal to the left-hand side or the image in the top matches that in the bottom. A line that cuts a figure into two parts that exactly overlap when folded along that line is called a line of symmetry of the figure.

Symmetry - Definition, Types, Examples, and Diagrams

Reflection: Reflection of an object is defined as the exact copy of that object. It is the same object that completely overlaps the first one. A figure that has a line or lines of symmetry is thus also said to have reflection symmetry.

Reflection Symmetry - Definition, Examples, and Diagrams

Rotational Symmetry: When we define rotational symmetry, we can say that it is defined on a fixed point known as centre of rotation. The angle through which it is rotated is known as the angle of rotation. Eg windmill.

Symmetry Class 6 Maths Chapter 9 - Topics

The topics discussed in the NCERT Solutions for class 6, chapter 9, Symmetry, are:

  • Line of Symmetry
  • Reflection
  • Rotational Symmetry

NCERT Solutions for Class 6 Maths Chapter 9 Symmetry - Points to Remember

Symmetry: Symmetry refers to a part or parts of a figure that are repeated in some pattern.

Line of Symmetry: A line that cuts a figure into two parts that exactly overlap when folded along that line is called a line of symmetry of the figure.

Reflection: Reflection of an object is defined as the exact copy of that object. It is the same object that completely overlaps the first one.

Rotational Symmetry: When we define rotational symmetry, we can say that it is defined on a fixed point known as the centre of rotation. The angle through which it is rotated is known as the angle of rotation.

NCERT Solutions for Class 6 Maths Chapter Wise

Students can check out the NCERT Solutions for Class 6 Maths chapter-wise using the links below.

NCERT Solutions for Class 6 Subject Wise

NCERT Solutions for Class 6 provide detailed and accurate answers to all subjects covered in the CBSE curriculum. These solutions help students build strong foundational concepts through step-by-step explanations. Students can access the NCERT Solutions subject-wise for Class 6 using the links below.

Students can also check the NCERT Books and the NCERT Syllabus for Class 6 here:

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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 .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

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

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

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

Option 3)

Fraction of solute present in water

Option 4)

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)

558.5 × 6.023 × 1023

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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