Class 6 Maths Chapter 9 Symmetry – Revision Notes

Chapter 9 splits neatly into two ideas — folding a figure along a line of symmetry, and turning it through an angle of rotational symmetry — both recapped in the notes below.

Last Updated: September 23, 2026

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.

Frequently Asked Questions

What does it mean for a shape to have line symmetry?
A shape has line symmetry if it can be folded along a straight line so both halves match up exactly, and that fold line is called the line of symmetry, with some shapes having more than one.

What is the difference between line symmetry and rotational symmetry?
Line symmetry involves a shape matching itself when folded along a line, while rotational symmetry involves a shape matching itself when rotated by an angle less than a full 360-degree turn.

Written by Satish

NCERTBooks.org is an independent educational resource run by a small team focused on making official NCERT textbooks easy to find, read, and download for students, parents, and teachers across India. We are not affiliated with NCERT or the Ministry of Education -- we organise publicly available NCERT content by class and subject, verify links against official sources, and build tools (like our in-browser reader) that make studying more convenient. Every guide we publish is written and reviewed by our team based on the actual NCERT curriculum and syllabus.