Vardaan
Class 7 Maths • Chapter 14

Symmetry

Vardaan Learning Institute • Detailed Notes with Practice Questions

🦋 1. Lines of Symmetry (Reflection / Bilateral Symmetry)

A figure has line symmetry if one half is the mirror image of the other half when folded along that line. The fold line is called the line of symmetry (or axis of symmetry).

Equilateral △3 lines of symmetry
Square4 lines of symmetry
Rectangle2 lines of symmetry
CircleInfinite lines of symmetry
Regular Pentagon5 lines of symmetry
Isosceles △1 line of symmetry
Shape Lines of Symmetry Remark
Scalene Triangle 0 No equal sides/angles
Isosceles Triangle 1 Along the angle bisector of apex
Equilateral Triangle 3 Each vertex to midpoint of opposite side
Square 4 2 from midpoints + 2 diagonals
Rectangle 2 From midpoints of opposite sides only
Rhombus 2 Both diagonals are axes of symmetry
Circle Infinite Any diameter is a line of symmetry
Regular Polygon (n sides) n A regular n-gon has exactly n lines

🔄 2. Rotational Symmetry

A figure has rotational symmetry if it looks the same after being rotated by some angle less than 360° about a fixed centre point.

Order of Rotational Symmetry: The number of times a figure looks the same during one complete rotation (360°).

Angle of rotation = 360° ÷ Order of symmetry

• Square: Order = 4, angle = 90°
• Equilateral triangle: Order = 3, angle = 120°
• Rectangle: Order = 2, angle = 180°
• Circle: Order = infinite (looks same at every angle)
• Scalene triangle: Order = 1 (only at 360° → no true rotational symmetry)
Centre of Rotation: The fixed point around which the figure is rotated.
Angle of Rotation: The angle through which the figure is rotated to look the same.
Note: Every figure has order 1 (at 360°). "True" rotational symmetry requires order ≥ 2.

📊 3. Combined Summary Table

Shape Lines of Symmetry Order of Rotational Symmetry
Scalene triangle 0 1
Isosceles triangle 1 1
Equilateral triangle 3 3
Square 4 4
Rectangle 2 2
Rhombus 2 2
Parallelogram 0 2
Regular hexagon 6 6
Circle Infinite Infinite
✏️ Practice Questions — Symmetry (24 Questions)

Section A — Basics Easy

Q1. How many lines of symmetry does a regular hexagon have?
Q2. Name a figure with only rotational symmetry but no line of symmetry.
Q3. What is the order of rotational symmetry of the letter H?
Q4. How many lines of symmetry does the letter O have?
Q5. A figure has rotational symmetry of order 5. Find the angle of rotation.
Q6. Which English capital letters have exactly 1 line of symmetry?
Q7. Does a scalene triangle have any line of symmetry or rotational symmetry?
Q8. Which quadrilateral has 2 lines of symmetry and rotational symmetry of order 2?

Section B — Medium Medium

Q9. A figure is rotated by 60° and looks same. What is its order of symmetry?
Q10. How many lines of symmetry does a regular octagon have?
Q11. Draw and show lines of symmetry for the letter 'B'.
Q12. A shape has 4 lines of symmetry and order 4 rotation. Name the shape.
Q13. State whether true or false: A rectangle has 4 lines of symmetry.
Q14. What is the angle of rotation for a regular hexagon?
Q15. A windmill has order 4 rotational symmetry. What angles does it look the same at?
Q16. The word "MOM" has line symmetry. Which axis?

Section C — Applied / Challenge Hard

  1. Q17. Name all English capital letters with 2 lines of symmetry.
  2. Q18. Can a figure have an infinite number of lines of symmetry but finite rotational order? Explain.
  3. Q19. A regular polygon has 6 lines of symmetry. How many sides does it have? What is its name?
  4. Q20. A flag design is a rectangle with an equilateral triangle on one side. Describe all symmetry axes of this combined figure.
  5. Q21. Explain why a parallelogram has no line of symmetry but has rotational symmetry of order 2.
  6. Q22. An artist rotates a design by these angles and it looks the same each time: 72°, 144°, 216°, 288°, 360°. What is the order of symmetry? Is it a polygon? If so, which?
  7. Q23. Which of these have line symmetry: a) peacock b) human face c) Eiffel tower d) bicycle wheel?
  8. Q24. A shape has 0 lines of symmetry but rotational symmetry of order 3. Can you design such a shape? (Hint: Think of a modified triangle with curved arms like a triskelion.)
✅ Key Answers: Q1:6 | Q2:Parallelogram (no line symmetry but order 2 rotational) | Q3:order 2 | Q4:2 (horizontal and vertical) | Q5:72° | Q9:order 6 | Q10:8 | Q12:Square | Q13:FALSE (rectangle has only 2 lines) | Q14:60° | Q19:6 sides → Regular hexagon | Q22:order 5 → regular pentagon

📝 Quick Revision

  1. Line symmetry: figure can be folded so both halves match exactly. The fold line = axis of symmetry
  2. Regular polygon with n sides → n lines of symmetry
  3. Rotational symmetry order = number of times figure looks same in one full (360°) rotation
  4. Angle of rotation = 360° ÷ order
  5. Square: 4 lines, order 4 | Rectangle: 2 lines, order 2 | Rhombus: 2 lines, order 2
  6. Parallelogram: NO lines of symmetry, but order 2 rotational
  7. Circle: infinite lines of symmetry, infinite rotational symmetry