CBSE Class 6 Maths Important Questions Chapter 9 - Symmetry

1. What is a line of symmetry?

Ans: A line of symmetry divides a shape into two identical, mirror-image halves.

2. How many lines of symmetry does a square have?

Ans: A square has 4 lines of symmetry.

3. What is mirror symmetry?

Ans: Mirror symmetry is when one side of a shape reflects exactly onto the other side.

4. Does a circle have symmetry?

Ans: Yes, a circle has infinite lines of symmetry.

5. Give an example of symmetry in nature.

Ans: A butterfly has symmetry, with each wing mirroring the other.

6. In the following figures, identify the figure that has:

(i) line of symmetry

(ii) rotational symmetry

(iii) both lines of symmetry and rotational symmetry

(iv) Neither line of symmetry nor rotational symmetry

Ans:

(i) Figures (a) and (b) display line symmetry.

(ii) Figures (a) and (d) show rotational symmetry.

(iii) Figure (a) possesses both line symmetry and rotational symmetry.

(iv) Figure (c) lacks both line symmetry and rotational symmetry.

7. How many lines of symmetry do the following English alphabets have? 

(i) 

(ii) 

Ans: The letters H and I in the English alphabet each have two lines of symmetry, as illustrated. 

(i) 

(ii)

8. How many lines of symmetry do the following letters of the English alphabet have?

(i)

(ii) 

Ans: The letters F and J in the English alphabet have no lines of symmetry.

9. Write any five letters in the English alphabet such that they have one line of symmetry. Show the line of symmetry for each of them. 

Ans: 

10. Find the lines of symmetry and rotational symmetry of the following figure.

Ans: The figure has four lines of symmetry, as shown.

The rotational symmetry is as follows: 

The given figure returns to its original shape when rotated by 90°, 180°, 270°, and 360°. Therefore, it has 4 angles of symmetry: 90°, 180°, 270°, and 360°.

11. Minimum, how many unit squares will you colour so that the figure has: 

(i) Only one line of symmetry? 

(ii) two lines of symmetry? 

(iii) four lines of symmetry? 

(iv) Only a horizontal line of symmetry?

Ans:

(i) One unit square will be coloured to have only one line of symmetry.

(ii) Two unit squares will be coloured to have two lines of symmetry.

(iii) Four unit squares will be coloured to have four lines 

(iv) Two unit squares will be coloured to have only a horizontal line of symmetry.

12. Explain the process of identifying lines of symmetry in different geometric shapes. Provide examples of shapes with 1, 2, 4, and infinite lines of symmetry.

Ans: To identify lines of symmetry, examine if a shape can be divided into two identical halves. For example, a rectangle has 2 lines of symmetry, a square has 4, a circle has infinite lines of symmetry, and a triangle (depending on the type) may have 1 line of symmetry.

13. Describe the difference between line symmetry and rotational symmetry with examples. 

Ans: Line symmetry divides a shape into mirror halves across a line, such as in a rectangle or butterfly. Rotational symmetry occurs when a shape looks the same after being rotated by a certain angle, like a square, which appears the same at 90°, 180°, and 270°.

14. How can symmetry be observed in nature? List five examples of natural objects or organisms that display symmetry and describe their type of symmetry. 

Ans: Symmetry in nature includes butterflies with line symmetry, starfish with radial symmetry, leaves with line symmetry, snowflakes with rotational symmetry, and flowers (like daisies) with radial symmetry. This natural symmetry helps maintain balance and appeal in structures.

15. How would you use symmetry to design a simple pattern? Describe the steps and explain how symmetry enhances the visual appeal of the design. 

Ans: To create a symmetrical pattern, start by drawing a base shape, such as a square. Divide it with lines of symmetry (horizontal, vertical, or diagonal) and replicate designs in each section to mirror across the lines. Symmetry provides balance and uniformity, making the pattern visually pleasing and harmonious.

Practise Extra Questions on Symmetry

1. How many lines of symmetry do these shapes have?

Ans: 

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

Ans: 

3. 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. 

Ans: 

4. This is a picture of the new Parliament Building in Delhi.

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

Ans: The outer boundary exhibits rotational symmetry around its centre. 

The smallest angle of rotation is calculated as 360° ÷ 3 = 120°. 

Additional angles of rotation are 240° and 360°.

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

Ans: The outer boundary displays reflection symmetry, featuring 3 lines of symmetry.

5. How many lines of symmetry and angles of symmetry does Ashoka Chakra have?

Ans: The Ashoka Chakra features 24 spokes that are evenly distributed. These 24 spokes form 12 pairs. A line drawn through each opposite pair represents a line of symmetry, resulting in a total of 12 lines of symmetry. The smallest angle of symmetry is calculated as 360° ÷ 12 = 30°. The other angles of symmetry are multiples of this angle up to 360°. These include 60°, 120°, 150°, and so on, totaling 12 angles.

This page offers CBSE Class 6 Maths Important Questions and extra questions for Chapter 9 Symmetry. At Vedantu, we create short answer questions after reviewing the previous test papers so students can easily rely on our guide.

This page also contains some extra questions to give students more practise to score well in upcoming exams.

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