Maths Class 6 Important Questions Chapter 9 Ganita Prakash

Symmetry

Short Answer Questions

1. What is symmetry?

Answer: Symmetry is when a figure is made of parts that repeat in a definite pattern.

2. What is a line of symmetry?

Answer: A line that divides a figure into two identical halves that overlap exactly when folded is called a line of symmetry.

3. Give one example of a symmetrical object.

Answer: A butterfly is a symmetrical object.

4. Does a cloud have symmetry?

Answer: No, a cloud does not have symmetry because it has no definite repeating pattern.

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

Answer: A square has 4 lines of symmetry.

6. Is the diagonal of a rectangle (not a square) a line of symmetry?

Answer: No, the diagonal of a rectangle is not a line of symmetry.

7. What is reflection symmetry?

Answer: When one half of a figure is the mirror image of the other half, it is called reflection symmetry.

8. What is rotational symmetry?

Answer: When a figure looks the same after rotation by a certain angle, it has rotational symmetry.

9. What is the centre of rotation?

Answer: The fixed point around which a figure rotates is called the centre of rotation.

10. What is always an angle of symmetry for any figure?

Answer: 360° is always an angle of symmetry.

Long Answer Questions

1. A figure has 4 angles of rotational symmetry. Find all the angles of symmetry.

Answer (Step-by-step):

1. Total angle in a full rotation = 360°.
2. Number of equal rotations = 4
3. Smallest angle = 360° ÷ 4 = 90°
4. Now list all multiples of 90° up to 360°:
   • 90°
   • 180°
   • 270°
   • 360°

Final Answer: Angles of symmetry = 90°, 180°, 270°, 360°

2. Explain why some figures have rotational symmetry but no line of symmetry.

Answer (Step-by-step):

1. A figure has rotational symmetry if it looks the same after rotation.
2. A figure has line symmetry only if it can be folded into two identical halves.
3. Some figures match after rotation but do not match when folded.
4. Example: A windmill shape looks the same after rotation but cannot be folded into equal halves.

Conclusion: Such figures have rotational symmetry but no line symmetry.

3. A figure has 2 angles of symmetry. Find those angles and explain.

Answer (Step-by-step):

1. Total rotation = 360°.
2. Number of angles of symmetry = 2
3. Smallest angle = 360° ÷ 2 = 180°
4. List the angles:
   • 180°
   • 360°

Final Answer: Angles of symmetry = 180° and 360°

4. In a figure, the smallest angle of symmetry is 60°. Find all other angles of symmetry.

Answer (Step-by-step):

1. Smallest angle = 60°
2. Keep adding 60° until 360°:
   • 60°
   • 120°
   • 180°
   • 240°
   • 300°
   • 360°

Final Answer: Angles of symmetry = 60°, 120°, 180°, 240°, 300°, 360°

5. Explain why 360° is always an angle of symmetry for every figure.

Answer (Step-by-step):

1. Rotating any figure by 360° means a full turn.
2. After a full turn, the figure returns to its original position.
3. Since it looks exactly the same, it satisfies the condition of symmetry.

Conclusion: Every figure has 360° as an angle of symmetry.