NCERT Solutions Class 6 Maths Chapter 9 Symmetry Exercise 9.2

In general, exercise 9.2 Welcome NCERT Solutions for Class 6 Maths Chapter 9 Symmetry act as extensions of the line symmetry as stated in Exercise 9.1. Exercise 9.1 worked on recognizing lines of symmetry in a variety of figures, and exercise 9.2 involves drawing symmetrical figures or finishing a symmetrical pattern and reflecting on it. 

This exercise is important in students making the shift from recognizing line symmetry (as in exercise 9.1) to actively applying the notion of line symmetry via construction. Essentially, it allows for visualizing what is happening to the shapes when we look at reflected images and properties that are unchanged under reflection.

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.

Key Concepts of Exercise 9.2

• 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.

2.0NCERT Exercise Solutions Class 6 Chapter 9 Symmetry : All Exercises 

3.0NCERT 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

4.0Key Features and Benefits Class 6 Maths Chapter 9 Symmetry Exercise 9.2

• Provides easy and practical learning through clear and detailed NCERT Solutions. 
• Improves observation and drawing skills. 
• Provides real-life examples that make geometry fun and exciting. 
• Provides students with a strong foundation to apply their learning in advanced geometric problems. 
• Makes students feel more confident in solving symmetry-related problems when preparing for exams.