NCERT Solutions Class 6 Maths Chapter 9 Symmetry

This chapter 9 Symmetry from Class 6 Maths introduces the concept of symmetry and how shapes or figures can be divided into identical halves. Students learn about lines of symmetry and explore how symmetry appears in geometric shapes, patterns, and everyday objects. The chapter helps students recognise symmetrical designs and understand how symmetry is used in mathematics, art, and nature.

In NCERT Solution for Class 6 Maths Symmetry, students will learn to recognize the patterns in different shapes and objects. The solutions help students understand different types of symmetry including line symmetry and rotational symmetry. These solutions are designed step-by-step to simplify the intricate problems of Chapter Symmetry, Class 6, enabling students to understand the important role of symmetry and its real-life applications. 

1.0Download NCERT Solutions Class 6 Maths Chapter 9 Symmetry

ALLEN'S Experts lucidly curated the solutions to improve the students' problem-solving abilities. For a more precise idea about Integers NCERT Solutions, students can download the below NCERT Solution for Class 6 Maths chapter 9 pdf solution.

2.0Key Concepts Covered in Chapter 9 - Symmetry

This chapter explains how shapes and patterns can be divided or rotated to produce identical parts. It helps students recognize symmetrical designs in mathematics, nature, and art.

• Understanding the concept of symmetry in shapes and patterns.
• Identifying lines of symmetry (reflection symmetry) in different figures.
• Learning how paper folding and mirror reflections demonstrate symmetry.
• Exploring rotational symmetry and angles of rotation.
• Determining the order of rotational symmetry in geometric figures.
• Applying symmetry concepts to polygons, patterns, and real-life designs.

3.0Class 6 Maths Chapter 9 Symmetry: All Exercises

Exercise 9.1 - Line of Symmetry

This exercise focuses on identifying lines of symmetry in shapes and everyday objects such as butterflies, flowers, and rangoli designs. Students analyse figures to determine whether they are symmetrical and locate the axis that divides them into identical halves. Activities like paper folding and hole punching help demonstrate how symmetrical patterns are formed.

Key Concepts Covered:

• Identifying line(s) of symmetry

• Paper folding and hole punching symmetry

• Completing figures using symmetry line

• Lines of symmetry in regular polygons

• Drawing figures with given symmetry conditions

Exercise 9.2 - Rotational Symmetry

This exercise introduces rotational symmetry and explains how a figure can match its original position after rotating by certain angles. Students identify angles of symmetry, determine the order of rotational symmetry, and explore figures like polygons and patterns that exhibit rotational symmetry. These problems help students understand symmetry beyond reflection.

Key Concepts Covered:

• Angles of rotational symmetry

• Order of rotational symmetry

• Smallest angle concept

• Relationship with 360° divisibility

• Comparing reflection and rotational symmetry

4.0NCERT Class 6 Maths Chapter 9 Symmetry: Detailed Solutions

9.1 - Line of Symmetry

• Do you see any line of symmetry in the figures at the start of the chapter? What about in the picture of the cloud? Sol. The butterfly, flower, pinwheel, and rangoli at the start of the chapter exhibit symmetry.

• The cloud does not have symmetry as it lacks a definite pattern.

• For each of the following figures, identify the line(s) of symmetry if it exists.

• Sol. Below are the symmetrical figures and their lines of symmetry:

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.

Sol. Do it yourself!

• 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?

• Sol.

• Given the line(s) of symmetry, find the other hole(s).

• Sol. Based on the symmetry given, the holes will appear as reflections across the fold line.

• Here are some questions on paper cutting. Consider a vertical fold. We represent it this way: Vertical Fold

• Similarly, a horizontal fold is represented as follows: Horizontal Fold

• Sol. Do it yourself!
• 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.

• Sol. Do it yourself!
• 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

• b. The hole in the centre is a square.

Sol. Do it yourself! 6. How many lines of symmetry do these shapes have? i.

ii. A triangle with equal sides and equal angles.

iii. A hexagon with equal sides and equal angles

Sol. i.

ii.

iii.

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

Sol.

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

Sol.

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. It is not possible to draw a triangle with exactly two lines of symmetry? Sol.

• 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. Sol. a.

• 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.

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

• 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.

• Sol.

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

• Sol.

• 9.2 ROTATIONAL SYMMETRY
• Find the angles of symmetry for the given figures about the point marked ( $\bullet$ ).

• Sol. (a) $90^{\circ },180^{\circ },270^{\circ },360^{\circ }$ (b) $360^{\circ }$ (c) $180^{\circ },360^{\circ }$
• Which of the following figures have more than one angle of symmetry?

• Sol. (a) $90^{\circ },180^{\circ },270^{\circ },360^{\circ }$ (b) $120^{\circ },240^{\circ },360^{\circ }$ (c) $120^{\circ },240^{\circ },360^{\circ }$ (d) $90^{\circ },180^{\circ },270^{\circ },360^{\circ }$ (e) $90^{\circ },180^{\circ },270^{\circ },360^{\circ }$ (f) $72^{\circ },144^{\circ },216^{\circ },288^{\circ },360^{\circ }$ (g) $360^{\circ }$
• Give the order of rotational symmetry for each figure.

• Sol. (a) 2 (b) 1 (c) 6 (d) 3 (e) 4 (f) 5
• 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?

• Sol. (i)

• (iii) Possible angles of symmetry are $60^{\circ },90^{\circ },120^{\circ }$.
• Draw two figures other than a circle and a square that have both reflection symmetry and rotational symmetry. Sol.

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

• c.

• d.

• In a figure, $60^{\circ }$ is the smallest angle of symmetry. What are the other angles of symmetry of this figure? Sol. If $60^{\circ }$ is the smallest, other angles will be $120^{\circ },180^{\circ },240^{\circ },300^{\circ }$, and $360^{\circ }$.
• In a figure, $60^{\circ }$ is an angle of symmetry. Sol. The figure will have $20^{\circ }$ angles of symmetry.
• Can we have a figure with rotational symmetry whose smallest angle of symmetry is: Sol. a. $45^{\circ }$ ? (Yes, a figure with 8 -fold symmetry octagon) b. $17^{\circ }$ ? (No, as $360^{\circ }$ is not evenly divisible by $17^{\circ }$.)
• This is a picture of the new Parliament Building in Delhi.

• Sol. a. Yes, outer boundary have reflection symmetry.

• b. $120^{\circ }$
• 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? Sol. Do it by yourself.
• 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? Sol. Do it by yourself.
• 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? Sol. Do it by yourself.
• How many lines of symmetry and angles of symmetry does Ashoka Chakra have? Sol. 24 lines of symmetry.

5.0Key Features and Benefits of Chapter 9: Symmetry

• The chapter - symmetry introduces the concept of through everyday objects and patterns, helping students easily relate mathematical ideas to real-life examples.
• It helps students identify lines of symmetry in geometric shapes and designs, improving their visual observation skills.
• Explains rotational symmetry and angles of rotation, allowing students to understand how figures repeat during rotation.
• Includes engaging activities like paper folding, drawing, and pattern analysis, making learning more interactive and practical.
• Develops spatial reasoning and pattern recognition, which are important skills for geometry.
• Builds a strong foundation for advanced geometry concepts involving symmetry and transformations.