NCERT Solutions Class 6 Maths Chapter 9 Symmetry Exercise 9.2

Exercise 9.2 focuses on rotational symmetry and order of symmetry. Students determine angles of symmetry (90°, 120°, 60°, etc.), find the order of rotational symmetry, colour sectors to create specific symmetry, and compare reflection vs rotational symmetry. It also includes reasoning-based questions, such as the smallest angle of symmetry, divisibility of 360°, and symmetry in real-life structures like the Parliament building and Ashoka Chakra.

Prepared by ALLEN experts, these NCERT Solutions for Class 6 Maths Chapter 9 Symmetry – Exercise 9.2 help students complete mirror images of figures across a line of symmetry. The clear, step-by-step explanations enhance visualisation skills, strengthen understanding of reflection symmetry, and support effective exam preparation.

1.0Download NCERT Solutions of Class 6 Maths Chapter 9 Symmetry Exercise 9.2

Download NCERT Solutions for Class 6 Maths Chapter 9 Symmetry Exercise 9.2 and get accurate step-by-step answers. These solutions are a great way to develop a strong understanding of symmetry thinking through practical drawing and visual problems.

2.0Key Concepts Covered in Exercise 9.2 Class 6 Maths

• Reflection: The concept of reflection as a transformation involves flipping a figure over a line (the line of reflection or mirror line). 
• Drawing Symmetrical Figures: One practice is completing an incomplete symmetrical figure by using the reflection of the figure across a given line of reflection. 
• Reflection of Points: This is where students learn how to find the reflection of points across a line, especially on a grid. 
• Properties of Reflection: Students can understand the properties of reflection, such as the distance of a point from the line of reflection is equal to distance of its image point from the line of reflection; and the line segment linking a point to its image point is perpendicular to the line of reflection. 
• Symmetry on a Grid: Since working with grids allows students to draw reflecting points and lines, students can accurately place points and lines on a grid. 
• Real-life Problems: Using real-life examples, students can identify and create symmetrical designs and images and connect their mathematical learning to designs.

3.0NCERT Exercise Solutions Class 6 Chapter 9 Symmetry : All Exercises 

4.0NCERT Class 6 Maths Chapter 9 Symmetry Exercise 9.2 : Detailed Solutions

9.2 Rotational Symmetry

1. Find the angles of symmetry for the given figures about the point marked ( $\cdot$ ).
   
   Sol. (a) $90^{\circ },180^{\circ },270^{\circ },360^{\circ }$ (b) $360^{\circ }$ (c) $180^{\circ },360^{\circ }$
2. 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) $360^{\circ }$
3. Give the order of rotational symmetry for each figure.
   
   Sol. (a) 2 (b) 1 (c) 6 (d) 3 (e) 4 (f) 5
4. 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.
   
   (iii) Possible angles of symmetry are $60^{\circ },90^{\circ },120^{\circ }$.
5. Draw two figures other than a circle and a square that have both reflection symmetry and rotational symmetry. Sol.
   
6. 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.
   
7. 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 $360^{\circ }$.
8. In a figure, $60^{\circ }$ is an angle of symmetry. Sol. The figure will have $20^{\circ }$ angles of symmetry.
9. 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 $17^{\circ }$.)
10. This is a picture of the new Parliament Building in Delhi.
    
    Sol. a. Yes, outer boundary have reflection symmetry.
    
    b. $120^{\circ }$
11. 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.
12. 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
13. 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.
14. How many lines of symmetry and angles of symmetry does Ashoka Chakra have? Sol. 24 lines of symmetry

5.0Key Features and Benefits Class 6 Maths Chapter 9 Symmetry Exercise 9.2

• Provides clear and well-explained NCERT Solutions that help students understand symmetry concepts step by step in a simple and structured way.
• Improves observation and drawing skills as students learn to identify and draw lines of symmetry in different shapes and figures.
• Uses relatable real-life examples that make learning symmetry interesting, engaging, and easier to understand.
• Builds a strong conceptual foundation that helps students apply symmetry in more advanced geometry topics in higher classes.
• Regular practice increases confidence and helps students solve symmetry-related questions accurately during exams.