Class 6 Maths Symmetry Notes

Class 6 Maths – Chapter: Symmetry

1. Introduction

Symmetry is when a figure can be divided into two identical parts such that one part is the mirror image of the other.

• The line along which the figure is divided is called the line of symmetry.

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2. Types of Symmetry

1. Line Symmetry (Reflection Symmetry)
   • A figure has line symmetry if it can be folded along a line and both halves match perfectly.
   • Examples: Square, Rectangle, Circle, Equilateral Triangle
2. Rotational Symmetry
   • A figure has rotational symmetry if it looks the same after rotation by less than 360°.
   • Order of rotation: Number of times it looks the same in one full rotation
   • Examples: Pentagon (order 5), Star (order 5), Circle (infinite)
3. Point Symmetry (Central Symmetry)
   • A figure has point symmetry if every part has a matching part opposite to a central point.
   • Example: Letter “S”, “Z”

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3. Properties of Symmetry

• Line of symmetry divides the figure into two equal parts.
• Number of lines of symmetry varies by shape:
  • Square → 4
  • Rectangle → 2
  • Circle → Infinite
  • Equilateral triangle → 3
  • Isosceles triangle → 1

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4. Examples

1. Line Symmetry:

• Fold a rectangle → Two halves match
• Fold an equilateral triangle → 3 lines of symmetry

2. Rotational Symmetry:

• Square → Rotate 90°, 180°, 270° → Looks same → Order 4

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5. Practice Questions (50 Mixed)

Part A – MCQs – 15 Questions

1. A square has how many lines of symmetry?
2. An equilateral triangle has how many lines of symmetry?
3. Which of these has rotational symmetry of order 5? Circle, Pentagon, Rectangle, Triangle
4. Which figure has infinite lines of symmetry?
5. A rectangle has how many lines of symmetry?
6. Letter “S” has what type of symmetry?
7. Letter “Z” has what type of symmetry?
8. Line symmetry is also called?
9. What is the order of rotational symmetry for a circle?
10. Which letter has line symmetry but not point symmetry?
11. Which shape has point symmetry but no line symmetry?
12. A regular pentagon has how many lines of symmetry?
13. A star has rotational symmetry of order?
14. Mirror divides a figure into?
15. Line of symmetry passes through?

Part B – Fill in the Blanks – 10 Questions

16. Line of symmetry divides a figure into ___ identical parts
17. Circle has ___ lines of symmetry
18. Square has ___ lines of symmetry
19. Rotational symmetry means the figure looks ___ after rotation
20. Order of rotational symmetry of equilateral triangle = ___
21. Letter “O” has ___ lines of symmetry
22. Letter “H” has ___ lines of symmetry
23. Point symmetry is also called ___ symmetry
24. Rectangle has ___ lines of symmetry
25. Letter “T” has ___ line of symmetry

Part C – True/False – 5 Questions

26. A rectangle has 4 lines of symmetry (False)
27. Circle has infinite rotational symmetry (True)
28. Letter “N” has point symmetry (True)
29. Rotational symmetry is only for circular figures (False)
30. Equilateral triangle has 3 lines of symmetry (True)

Part D – Match the Following – 5 Questions

Column A	Column B
31. Square	a) 4 lines of symmetry
32. Rectangle	b) 2 lines of symmetry
33. Circle	c) Infinite lines of symmetry
34. Equilateral triangle	d) 3 lines of symmetry
35. Pentagon	e) 5 lines of symmetry

Part E – Short Answer / Problem Solving – 15 Questions

36. Draw a square and mark all lines of symmetry
37. Draw an equilateral triangle and mark lines of symmetry
38. Draw letter “H” and show lines of symmetry
39. Draw letter “S” and show point symmetry
40. Draw a rectangle and mark lines of symmetry
41. Draw letter “O” and mark lines of symmetry
42. Draw a regular pentagon and mark lines of symmetry
43. Draw letter “T” and mark line of symmetry
44. Draw letter “Z” and show point symmetry
45. Find the order of rotational symmetry of a square
46. Find the order of rotational symmetry of an equilateral triangle
47. Find the order of rotational symmetry of a regular hexagon
48. Identify if letter “X” has line and point symmetry
49. Draw a star and find order of rotational symmetry
50. Draw letter “N” and show point symmetry

Answers – Class 6 Maths: Symmetry

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Part A – MCQs (Answers)

1. 4
2. 3
3. Pentagon
4. Circle
5. 2
6. Point symmetry
7. Point symmetry
8. Reflection symmetry
9. Infinite
10. Letter “H”
11. Letter “S”
12. 5
13. 5
14. Two identical halves
15. Through vertex, midpoint, or center depending on figure

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Part B – Fill in the Blanks (Answers)

16. Two
17. Infinite
18. 4
19. Same
20. 3
21. Infinite
22. 2
23. Central symmetry
24. 2
25. 1

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Part C – True/False (Answers)

26. False
27. True
28. True
29. False
30. True

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Part D – Match the Following (Answers)

Column A	Column B
31. Square	a) 4 lines of symmetry
32. Rectangle	b) 2 lines of symmetry
33. Circle	c) Infinite lines of symmetry
34. Equilateral triangle	d) 3 lines of symmetry
35. Pentagon	e) 5 lines of symmetry

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Part E – Short Answer / Problem Solving (Answers)

36. Square: Draw square → 2 diagonals + vertical + horizontal lines → 4 lines of symmetry
37. Equilateral Triangle: Draw triangle → 3 lines from vertices to opposite sides’ midpoints → 3 lines of symmetry
38. Letter “H”: Draw vertical line → symmetrical on both sides → 1 line of symmetry
39. Letter “S”: Point symmetry about center → every part matches opposite side
40. Rectangle: Draw vertical and horizontal lines → 2 lines of symmetry
41. Letter “O”: Circle → infinite lines of symmetry
42. Regular Pentagon: Draw lines from each vertex to opposite side midpoint → 5 lines of symmetry
43. Letter “T”: Draw vertical line through center → 1 line of symmetry
44. Letter “Z”: Rotated 180° → point symmetry, no line symmetry
45. Order of rotational symmetry – square: 4
46. Order of rotational symmetry – equilateral triangle: 3
47. Order of rotational symmetry – regular hexagon: 6
48. Letter “X”: 2 lines of symmetry (diagonals) + point symmetry
49. Star: Rotate 72° → looks same → Order = 5
50. Letter “N”: Point symmetry about center, no line symmetry