CBSE Important Questions Class 6 Maths Chapter 9 Symmetry

Symmetry means a figure has parts that repeat in a definite pattern. A figure can show reflection symmetry, rotational symmetry, or both depending on how its parts match.

Symmetry questions look visual, but most mistakes happen when students depend only on appearance. CBSE Important Questions Class 6 Maths Chapter 9 helps students prepare Symmetry from the 2026 NCERT Ganita Prakash syllabus through folding, reflection, rotation, paper cutting, radial arms and regular shapes. The chapter builds exam-ready understanding of lines of symmetry, mirror halves, centre of rotation, angles of symmetry, circles, squares, triangles, regular polygons, Ashoka Chakra and the new Parliament Building. NCERT defines symmetry as a definite repeated pattern in parts of a figure.

Key Takeaways

• Line of Symmetry: A line of symmetry divides a figure into two parts that overlap exactly when folded.
• Reflection Symmetry: Reflection symmetry occurs when one half of a figure mirrors the other half.
• Rotational Symmetry: Rotational symmetry occurs when a figure looks the same after rotation about a fixed point.
• Circle Symmetry: Every diameter of a circle is a line of symmetry, and every rotation angle is an angle of symmetry.

CBSE Important Questions Class 6 Maths Chapter 9 Structure 2026

Class 6 Maths Chapter 9 Important Questions with Answers

Students should first separate “looks balanced” from “mathematically symmetric.” These class 6 maths chapter 9 important questions test whether a figure can fold, reflect or rotate exactly.

1. What is symmetry in Class 6 Maths?

Symmetry means parts of a figure repeat in a definite pattern.

1. A symmetrical figure has matching parts.
2. The match may happen by folding or rotating.
3. Flowers, rangoli and butterflies often show symmetry.

Final Answer: Symmetry is a definite repeated pattern in a figure.

2. What is a symmetrical figure?

A symmetrical figure has parts that match exactly in a definite way.

1. One part may match the other after folding.
2. A figure may also match after rotation.
3. The matching must be exact.

Final Answer: A symmetrical figure has exact repeated parts.

3. Is a cloud always symmetrical?

No, a cloud is usually not symmetrical.

1. Cloud shapes are irregular.
2. Their parts do not repeat exactly.
3. Folding or rotating will not usually give a match.

Final Answer: A cloud is usually not symmetrical.

4. Why is a butterfly often used as an example of symmetry?

A butterfly is used because its left and right wings often look like mirror halves.

1. The body acts like a middle line.
2. The two wings have similar shapes.
3. Folding along the body can show reflection symmetry.

Final Answer: A butterfly can show one line of symmetry.

5. Why is rangoli useful for learning symmetry?

Rangoli is useful because its patterns often repeat around a centre.

1. Petals may repeat after equal turns.
2. Colours may follow a fixed order.
3. It can show reflection and rotational symmetry.

Final Answer: Rangoli helps students see repeated patterns.

Line of Symmetry Class 6 Questions

Line symmetry needs exact overlap, not just similar-looking halves. In line of symmetry class 6 questions, students should imagine folding the figure along the proposed line.

6. What is a line of symmetry?

A line of symmetry divides a figure into two parts that overlap exactly when folded.

1. Fold the figure along the line.
2. Check if both parts cover each other.
3. If they match, the line is a line of symmetry.

Final Answer: A line of symmetry creates two exact mirror halves.

7. What are mirror halves?

Mirror halves are two parts that match exactly on folding along a symmetry line.

1. One half reflects the other.
2. Both halves have the same shape.
3. Their positions must match exactly.

Final Answer: Mirror halves overlap exactly when folded.

8. Does every figure have a line of symmetry?

No, every figure does not have a line of symmetry.

1. Irregular figures may not fold into equal halves.
2. Some figures have rotational symmetry but no line symmetry.
3. A pinwheel is one such visual example.

Final Answer: Some figures have no line of symmetry.

9. Can a figure have more than one line of symmetry?

Yes, a figure can have more than one line of symmetry.

1. A square has multiple folding lines.
2. Some regular polygons also have many lines.
3. A circle has infinitely many lines of symmetry.

Final Answer: Many figures have multiple lines of symmetry.

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

A square has 4 lines of symmetry.

1. One vertical line divides it into mirror halves.
2. One horizontal line also divides it into mirror halves.
3. Its two diagonals are also lines of symmetry.

Final Answer: 4 lines of symmetry

11. How many lines of symmetry does a rectangle have?

A rectangle has 2 lines of symmetry when it is not a square.

1. One line passes vertically through the centre.
2. One line passes horizontally through the centre.
3. Its diagonals are not lines of symmetry.

Final Answer: 2 lines of symmetry

12. Is the diagonal of a square a line of symmetry?

Yes, each diagonal of a square is a line of symmetry.

1. Fold a square along a diagonal.
2. The two triangular halves overlap exactly.
3. A square has two such diagonals.

Final Answer: Yes

13. Is the diagonal of a rectangle a line of symmetry?

No, the diagonal of a rectangle is not a line of symmetry unless the rectangle is a square.

1. Fold a non-square rectangle along its diagonal.
2. The two parts do not overlap exactly.
3. So, the diagonal fails the fold test.

Final Answer: No

Reflection Symmetry Class 6 Important Questions

Reflection symmetry is easier when students track where points move after folding. These reflection symmetry class 6 questions use square corners, diagonals and mirror images.

14. What is reflection symmetry?

Reflection symmetry means one part of a figure is the mirror image of the other part.

1. A line acts like the mirror.
2. Points on one side reflect to the other side.
3. The reflected parts match exactly.

Final Answer: Reflection symmetry is mirror-image symmetry.

15. What happens to points on the line of symmetry?

Points on the line of symmetry remain in the same place after reflection.

1. They lie directly on the mirror line.
2. Reflection does not move them.
3. Other points switch to the opposite side.

Final Answer: Points on the symmetry line stay fixed.

16. In a square ABCD, what happens when reflected along diagonal AC?

Points A and C stay fixed, while B and D exchange positions.

1. A and C lie on the diagonal AC.
2. Points on the reflection line stay fixed.
3. B reflects to D, and D reflects to B.

Final Answer: A and C stay fixed; B and D swap

17. What happens when a square is reflected along its horizontal line of symmetry?

The upper points move to the lower positions, and lower points move to upper positions.

1. The horizontal line divides the square into top and bottom halves.
2. The top half reflects downward.
3. The bottom half reflects upward.

Final Answer: Top and bottom halves exchange positions.

18. Why do ink blot activities create symmetrical figures?

Ink blot activities create symmetry because folded paper transfers the same pattern to the other half.

1. Ink is placed on one half.
2. Folding presses it onto the other half.
3. The fold becomes the line of symmetry.

Final Answer: The fold creates matching mirror halves.

19. Why is paper folding useful in symmetry?

Paper folding tests whether two parts of a figure overlap exactly.

1. It gives a physical check.
2. It reveals mirror halves.
3. It helps students find lines of symmetry.

Final Answer: Paper folding verifies reflection symmetry.

Lines of Symmetry of Square Class 6 and Rectangle Questions

Squares and rectangles cause confusion because both have right angles. The difference appears when students test diagonal folds carefully.

20. Why does a square have more lines of symmetry than a rectangle?

A square has more lines of symmetry because all four sides are equal.

1. A rectangle has only opposite sides equal.
2. A square has all sides equal.
3. This makes its diagonals symmetry lines too.

Final Answer: Equal sides give the square two extra symmetry lines.

21. How many vertical and horizontal lines of symmetry does a square have?

A square has one vertical and one horizontal line of symmetry.

1. The vertical fold gives left and right mirror halves.
2. The horizontal fold gives top and bottom mirror halves.
3. The square also has two diagonal symmetry lines.

Final Answer: 2 straight centre folds and 2 diagonal folds

22. How many diagonal lines of symmetry does a square have?

A square has 2 diagonal lines of symmetry.

1. One diagonal joins one pair of opposite corners.
2. The other diagonal joins the remaining pair.
3. Both diagonals divide the square into matching halves.

Final Answer: 2 diagonal lines

23. Why does a non-square rectangle have no diagonal line of symmetry?

A non-square rectangle has unequal length and breadth, so diagonal folding does not match both halves exactly.

1. The diagonal creates two congruent triangles.
2. Their positions do not overlap under a fold.
3. Only centre vertical and horizontal folds work.

Final Answer: Its diagonal is not a symmetry line.

24. Can a triangle have exactly one line of symmetry?

Yes, an isosceles triangle can have exactly one line of symmetry.

1. It has two equal sides.
2. The symmetry line passes through the top vertex.
3. It also passes through the midpoint of the base.

Final Answer: Yes, an isosceles triangle has one line of symmetry

25. Can a triangle have exactly three lines of symmetry?

Yes, an equilateral triangle has exactly three lines of symmetry.

1. All sides are equal.
2. All angles are equal.
3. Each vertex-to-opposite-side fold creates mirror halves.

Final Answer: Yes, an equilateral triangle has three lines

26. Can a triangle have exactly two lines of symmetry?

No, a triangle cannot have exactly two lines of symmetry.

1. One line gives an isosceles triangle.
2. Three lines give an equilateral triangle.
3. No triangle has exactly two symmetry lines.

Final Answer: No

Symmetry Class 6 Questions on Paper Cutting and Punching

Paper-cutting questions test prediction. Students should track the folds first because every hole or cut gets reflected across each fold line.

27. What happens when a hole is punched in folded paper?

The hole appears in reflected positions when the paper opens.

1. One fold gives one matching hole.
2. Two folds can create more matching holes.
3. The fold lines become symmetry lines.

Final Answer: The punched hole repeats by reflection.

28. How can one punched hole create four holes?

One punched hole can create four holes when the paper is folded twice.

1. Fold the paper vertically.
2. Fold it horizontally.
3. Punch one hole through the folded layers.

Final Answer: Two folds can produce four matching holes.

29. What does the fold line represent in the punching game?

The fold line represents a line of symmetry.

1. Holes on one side reflect to the other.
2. Matching positions appear after unfolding.
3. The fold decides the mirror pattern.

Final Answer: The fold line is the symmetry line.

30. How can a square hole be cut at the centre using folding?

Fold the paper horizontally and vertically, then cut at the closed centre corner.

1. Two folds bring the centre into one corner.
2. A single cut gets reflected across both folds.
3. Opening the paper creates a central square hole.

Final Answer: Use two folds and one centre cut.

31. Why should students check if the centre hole is truly a square?

Students should check equal sides and right angles to confirm the hole is a square.

1. A square needs all sides equal.
2. It also needs all angles 90°.
3. A four-sided hole may only look square.

Final Answer: Equal sides and right angles prove it is a square.

Rotational Symmetry Class 6 Important Questions

Rotational symmetry does not need folding. Students must rotate the figure about a fixed centre and check when it looks exactly the same.

32. What is rotational symmetry?

Rotational symmetry means a figure looks the same after rotation about a fixed point.

1. The fixed point is the centre of rotation.
2. The figure turns around this point.
3. A match before 360° shows rotational symmetry.

Final Answer: Rotational symmetry is symmetry by turning.

33. What is the centre of rotation?

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

1. The figure turns around this point.
2. The centre may lie inside the figure.
3. A windmill rotates around its centre.

Final Answer: The centre of rotation is the fixed turning point.

34. What is an angle of symmetry?

An angle of symmetry is an angle through which a figure rotates and looks exactly the same.

1. Rotate the figure around its centre.
2. Check when it overlaps its original position.
3. That rotation angle is an angle of symmetry.

Final Answer: It is a rotation angle that gives an exact match.

35. Does every figure have 360° as an angle of symmetry?

Yes, every figure has 360° as an angle of symmetry.

1. A full turn brings any figure back.
2. 360° completes one rotation.
3. The original position returns.

Final Answer: Yes

36. When do we say a figure has rotational symmetry?

A figure has rotational symmetry when it matches itself after a rotation less than 360°.

1. 360° works for every figure.
2. Rotational symmetry needs another matching angle.
3. 90°, 120° or 180° may work for some figures.

Final Answer: It must match before a full turn.

37. Does a windmill have line symmetry?

No, a typical paper windmill does not have line symmetry.

1. Folding does not make its halves overlap.
2. Its arms turn around the centre.
3. It shows rotational symmetry instead.

Final Answer: No

38. What are the angles of symmetry of a windmill with four identical arms?

The angles are 90°, 180°, 270° and 360°.

1. Four equal arms divide a full turn equally.
2. 360° ÷ 4 = 90°.
3. So, each matching turn differs by 90°.

Final Answer: 90°, 180°, 270°, 360°

Angle of Symmetry Class 6 and Order of Rotational Symmetry Questions

Order and angle are linked. If a figure has 4 equal rotational matches in one full turn, its smallest angle is 90°.

39. What is the order of rotational symmetry?

The order of rotational symmetry is the number of times a figure matches itself in one full turn.

1. Count all matching positions in 360°.
2. Include the final 360° position.
3. That count is the order.

Final Answer: The order is the number of rotational matches.

40. What is the order of rotational symmetry of a square?

The order of rotational symmetry of a square is 4.

1. A square matches at 90°.
2. It also matches at 180° and 270°.
3. It returns again at 360°.

Final Answer: 4

41. What are the angles of symmetry of a square?

The angles of symmetry of a square are 90°, 180°, 270° and 360°.

1. A square has four equal sides.
2. Each quarter turn gives a match.
3. One full turn also gives a match.

Final Answer: 90°, 180°, 270°, 360°

42. What are the angles of symmetry when a figure has exactly 3 angles of symmetry?

The angles are 120°, 240° and 360°.

1. Divide 360° into 3 equal parts.
2. 360° ÷ 3 = 120°.
3. The angles are multiples of 120°.

Final Answer: 120°, 240°, 360°

43. What are the angles of symmetry when a figure has exactly 2 angles of symmetry?

The angles are 180° and 360°.

1. Divide 360° into 2 equal parts.
2. 360° ÷ 2 = 180°.
3. The figure matches at half turn and full turn.

Final Answer: 180°, 360°

44. If 60° is the smallest angle of symmetry, what are the other angles?

The other angles are 120°, 180°, 240°, 300° and 360°.

1. Angles of symmetry are multiples of the smallest angle.
2. Multiples of 60° up to 360° are listed.
3. 60° is already the smallest angle.

Final Answer: 120°, 180°, 240°, 300°, 360°

45. Can a figure have 45° as its smallest angle of symmetry?

Yes, a figure can have 45° as its smallest angle of symmetry.

1. 360° is divisible by 45°.
2. 360° ÷ 45° = 8.
3. Such a figure would have order 8.

Final Answer: Yes

46. Can a figure have 17° as its smallest angle of symmetry?

No, a figure cannot have 17° as its smallest angle of symmetry.

1. The smallest angle must divide 360° exactly.
2. 360° is not divisible by 17°.
3. So, 17° cannot work.

Final Answer: No

Radial Arms Symmetry Class 6 Questions

Radial arm questions help students connect rotation with equal angular gaps. If the gaps are unequal, the figure may look patterned but fail the rotation test.

47. What are radial arms in symmetry?

Radial arms are repeated arms arranged around a centre point.

1. Each arm starts near the centre.
2. The arms spread outward.
3. Equal spacing can create rotational symmetry.

Final Answer: Radial arms are repeated centre-based parts.

48. What angle is needed between 3 equal radial arms for rotational symmetry?

The angle between adjacent arms must be 120°.

1. A full turn is 360°.
2. There are 3 equal arms.
3. 360° ÷ 3 = 120°.

Final Answer: 120°

49. What are the angles of symmetry for 3 equal radial arms?

The angles are 120°, 240° and 360°.

1. The smallest matching turn is 120°.
2. The next matching turn is 240°.
3. A full turn gives 360°.

Final Answer: 120°, 240°, 360°

50. What is the smallest angle of symmetry for 5 equal radial arms?

The smallest angle of symmetry is 72°.

1. A full turn is 360°.
2. There are 5 equal arms.
3. 360° ÷ 5 = 72°.

Final Answer: 72°

51. What are the angles of symmetry for 5 equal radial arms?

The angles are 72°, 144°, 216°, 288° and 360°.

1. The smallest angle is 72°.
2. The other angles are multiples of 72°.
3. Continue until 360°.

Final Answer: 72°, 144°, 216°, 288°, 360°

52. What are the angles of symmetry for 6 equal radial arms?

The angles are 60°, 120°, 180°, 240°, 300° and 360°.

1. 360° ÷ 6 = 60°.
2. The smallest angle is 60°.
3. All matching angles are multiples of 60°.

Final Answer: 60°, 120°, 180°, 240°, 300°, 360°

53. What is the smallest angle for 7 equal radial arms?

The smallest angle is 51 3/7°.

1. A full turn is 360°.
2. Divide 360° by 7.
3. 360° ÷ 7 = 51 3/7°.

Final Answer: 51 3/7°

Symmetry of Circle Class 6 Questions

A circle is the most symmetric shape in this chapter. It behaves differently from polygons because every diameter and every rotation works.

54. How many lines of symmetry does a circle have?

A circle has infinitely many lines of symmetry.

1. Every diameter divides it into mirror halves.
2. A circle has infinitely many diameters.
3. Therefore, it has infinitely many symmetry lines.

Final Answer: Infinitely many

55. How many angles of symmetry does a circle have?

A circle has infinitely many angles of symmetry.

1. Rotate a circle by any angle around its centre.
2. It still coincides with itself.
3. Every rotation angle works.

Final Answer: Infinitely many

56. Why is every diameter of a circle a line of symmetry?

Every diameter is a line of symmetry because it divides the circle into two equal mirror halves.

1. A diameter passes through the centre.
2. It cuts the circle into two matching semicircles.
3. Folding along it gives exact overlap.

Final Answer: Every diameter gives mirror halves.

57. Does a circle have rotational symmetry?

Yes, a circle has rotational symmetry for every angle.

1. The centre stays fixed.
2. The circular boundary remains unchanged.
3. Any turn gives the same circle.

Final Answer: Yes

Symmetry in Regular Polygons Class 6 Questions

Regular polygons make symmetry predictable. A regular polygon with n equal sides usually has n lines of symmetry and n rotational matches.

58. How many lines of symmetry does an equilateral triangle have?

An equilateral triangle has 3 lines of symmetry.

1. All three sides are equal.
2. Each vertex gives one symmetry line.
3. Each line passes to the opposite side’s midpoint.

Final Answer: 3

59. How many angles of symmetry does an equilateral triangle have?

An equilateral triangle has 3 angles of symmetry.

1. It matches after 120° rotation.
2. It matches again after 240°.
3. It returns after 360°.

Final Answer: 3 angles of symmetry

60. How many lines of symmetry does a regular hexagon have?

A regular hexagon has 6 lines of symmetry.

1. It has 6 equal sides.
2. Its vertices and sides are evenly placed.
3. Six mirror lines divide it exactly.

Final Answer: 6

61. How many angles of symmetry does a regular hexagon have?

A regular hexagon has 6 angles of symmetry.

1. 360° ÷ 6 = 60°.
2. It matches at every 60° rotation.
3. It has 6 matching positions in one full turn.

Final Answer: 6

62. What is the symmetry pattern for regular polygons?

A regular polygon with n sides has n lines of symmetry and n angles of symmetry.

1. An equilateral triangle has 3.
2. A square has 4.
3. A regular pentagon has 5.

Final Answer: Regular polygons follow the side-count symmetry pattern.

Parliament Building Symmetry Class 6 and Ashoka Chakra Questions

Indian symbols and buildings make symmetry easier to remember. CBSE students should connect the chapter to familiar examples such as the Ashoka Chakra and the new Parliament Building.

63. Does the outer boundary of the new Parliament Building have reflection symmetry?

Yes, the outer boundary has 3 lines of symmetry.

1. Its boundary has a repeated triangular layout.
2. Three mirror lines pass through its centre.
3. The lines divide the boundary into matching parts.

Final Answer: Yes, 3 lines of symmetry

64. Does the new Parliament Building have rotational symmetry?

Yes, it has rotational symmetry around its centre.

1. It repeats after 120°.
2. It repeats again after 240°.
3. A full turn gives 360°.

Final Answer: Yes

65. What are the angles of rotational symmetry of the new Parliament Building?

The angles are 120°, 240° and 360°.

1. The outer boundary has 3 equal repeated parts.
2. 360° ÷ 3 = 120°.
3. Rotational matches occur at multiples of 120°.

Final Answer: 120°, 240°, 360°

66. How many lines of symmetry does the Ashoka Chakra have?

The Ashoka Chakra has 24 lines of symmetry.

1. It has 24 equally spaced spokes.
2. Each spoke can form a symmetry line.
3. Lines between opposite gaps also align with the repeated pattern.

Final Answer: 24 lines of symmetry

67. How many angles of symmetry does the Ashoka Chakra have?

The Ashoka Chakra has 24 angles of symmetry.

1. It has 24 equal repeated parts.
2. 360° ÷ 24 = 15°.
3. It matches at every 15° turn.

Final Answer: 24 angles of symmetry

Class 6 Maths Chapter 9 Extra Questions for CBSE Practice

These class 6 maths chapter 9 extra questions mix definitions, true-false, angle calculations and visual reasoning. They match the CBSE 2026 style for short answers and diagram-based tasks.

68. True or False: Every figure has reflection symmetry.

False, every figure does not have reflection symmetry.

1. Some figures do not fold into matching halves.
2. A cloud is generally irregular.
3. A pinwheel may have rotation but no reflection line.

Final Answer: False

69. True or False: Every figure has 360° as an angle of symmetry.

True, every figure has 360° as an angle of symmetry.

1. A full turn returns a figure to its original position.
2. This works for every figure.
3. 360° is always counted as a symmetry angle.

Final Answer: True

70. True or False: A figure can have rotational symmetry but no line of symmetry.

True, a figure can have rotational symmetry but no line of symmetry.

1. A windmill can match after rotation.
2. It may fail the folding test.
3. So both symmetries need not appear together.

Final Answer: True

71. True or False: A figure can have a line of symmetry but no rotational symmetry.

True, a figure can have line symmetry but no rotational symmetry before 360°.

1. Some shapes fold into mirror halves.
2. They do not match after smaller rotations.
3. Such figures have reflection symmetry only.

Final Answer: True

72. If a figure has order 8 rotational symmetry, what is its smallest angle?

The smallest angle is 45°.

1. A full turn is 360°.
2. Order = 8.
3. 360° ÷ 8 = 45°.

Final Answer: 45°

73. If the smallest angle of symmetry is 30°, what is the order?

The order is 12.

1. A full turn is 360°.
2. Divide 360° by 30°.
3. 360° ÷ 30° = 12.

Final Answer: 12

74. Name two figures that have both reflection and rotational symmetry.

A rectangle and an equilateral triangle have both reflection and rotational symmetry.

1. A rectangle has reflection lines and 180° rotational symmetry.
2. An equilateral triangle has 3 reflection lines.
3. It also has 120°, 240° and 360° symmetry.

Final Answer: Rectangle and equilateral triangle

75. Name one figure with infinitely many lines and angles of symmetry.

A circle has infinitely many lines and angles of symmetry.

1. Every diameter is a symmetry line.
2. Every rotation around its centre matches.
3. No polygon has this property.

Final Answer: Circle

Important Questions Class 6 Maths: