Class 6 Maths Chapter 9 Symmetry – Revision Notes

Quick revision notes for Class 6 Maths Chapter 9 (Symmetry) — covering line symmetry and rotational symmetry, the two halves of this chapter. These Class 6 Mathematics Chapter 9 notes are ideal for quick revision just before exams.

Key Definitions

• Symmetrical figure: a figure whose parts repeat in a definite, balanced pattern.
• Line of symmetry (axis of symmetry): a line along which a figure can be folded so both halves match exactly (mirror halves).
• Rotational symmetry: a figure looks exactly the same after being rotated by some angle strictly between 0° and 360° about a fixed point.
• Centre of rotation: the fixed point about which the figure is rotated.
• Angle of symmetry: an angle of rotation that brings the figure back to its original appearance.
• Order of rotational symmetry: the total number of angles of symmetry a figure has (how many times it matches itself in one full turn).

Key Rules

• 360° is always an angle of symmetry for every figure — but this alone does not mean the figure has rotational symmetry.
• The smallest angle of symmetry must be a whole-number factor of 360°.
• All other angles of symmetry are whole-number multiples of the smallest one.
• A regular polygon with n sides has exactly n lines of symmetry and rotational symmetry of order n (angle of symmetry = 360°/n).
• A circle has infinite lines of symmetry and infinite angles of symmetry.

Quick Reference Table: Lines of Symmetry

• Line segment: 2
• Isosceles triangle: 1
• Equilateral triangle: 3
• Scalene triangle: 0
• Square: 4
• Rectangle (non-square): 2
• Rhombus (non-square): 2
• Regular pentagon: 5
• Regular hexagon: 6
• Circle: infinite

Worked Real-World Examples

• New Parliament Building, Delhi: 3 lines of symmetry; rotational symmetry order 3 (angles: 120°, 240°, 360°).
• Ashoka Chakra (24 spokes): 12 lines of symmetry; smallest angle of symmetry = 15° (360° ÷ 24).

Common Mistakes to Avoid

• Don’t assume every rectangle’s diagonal is a line of symmetry — only a square’s diagonals work.
• Don’t confuse “matches at 360°” with “has rotational symmetry” — a smaller angle must also work.
• Don’t assume a triangle can have exactly 2 lines of symmetry — it’s impossible (2 forces a 3rd).
• Remember: a circle has infinite (not a large finite number of) lines and angles of symmetry.

One-Line Summary

Symmetry in Class 6 covers two related ideas — mirror-image line symmetry and turn-based rotational symmetry — and ties both back to shapes you already know (squares, regular polygons) and to real Indian examples like the Ashoka Chakra and the new Parliament Building.

Written by Satish

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