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Symmetry – Class 6 Mathematics notes, important questions and MCQs

NCERT Class 6 Mathematics, chapter 9. Notes, key terms, important questions with answers and MCQs.

Chapter overview

A figure has line symmetry if a line divides it into two mirror-image halves. Some figures also look the same after turning — rotational symmetry.

Line symmetry

The dividing line is the line (axis) of symmetry.
Square: 4 lines; rectangle: 2; equilateral triangle: 3; circle: infinitely many.
Letters like A, H, M, T have a vertical line of symmetry.

Rotational symmetry

A figure has rotational symmetry if it looks the same after a turn of less than 360°.
Order of rotational symmetry: number of times it looks the same in one full turn (square: 4).

Key terms

Line of symmetry: line that divides a figure into two matching halves
Mirror image: reflection of a figure as seen in a mirror
Order of rotational symmetry: number of matching positions in one full turn

Formulas

Regular polygon with n sides: n lines of symmetry

Important questions with answers

How many lines of symmetry does a rectangle have? Does it have rotational symmetry?2 marks

A rectangle has 2 lines of symmetry (joining mid-points of opposite sides). It has rotational symmetry of order 2.

Name three English capital letters with exactly one line of symmetry and one with none.3 marks

One line: A, B, C (also D, E, M, T, U, V, W, Y). No line: F (also G, J, L, N, P, Q, R, S, Z).

Compare a square, an equilateral triangle and a circle for (i) lines of symmetry and (ii) order of rotational symmetry.5 marks

Square: 4 lines of symmetry, rotational order 4 (turns of 90°). Equilateral triangle: 3 lines, rotational order 3 (turns of 120°). Circle: infinitely many lines (every diameter) and it looks the same after any turn, so it has rotational symmetry of every order.

Quick revision

Circle: infinite lines of symmetry.
Square: 4 lines, order 4.
Regular n-gon: n lines.

Exam tips

Fold a paper cut-out to test for line symmetry.
The letter S has rotational symmetry but no line symmetry.

Practice MCQs

How many lines of symmetry does a square have?
1. 1
2. 2
3. 4
4. 8
Show answer
Answer: (c) 4. Two diagonals and two mid-lines.
Which letter has a vertical line of symmetry?
1. F
2. A
3. G
4. J
Show answer
Answer: (b) A. A.
An equilateral triangle has how many lines of symmetry?
1. 1
2. 2
3. 3
4. 6
Show answer
Answer: (c) 3. Three.
A rectangle (not a square) has how many lines of symmetry?
1. 1
2. 2
3. 4
4. 0
Show answer
Answer: (b) 2. Two mid-lines.
Number of lines of symmetry of a regular hexagon is
1. 3
2. 4
3. 6
4. 12
Show answer
Answer: (c) 6. Equal to number of sides.
A regular hexagon has how many lines of symmetry?
1. 3
2. 4
3. 6
4. 12
Show answer
Answer: (c) 6. n = 6.
Which shape has infinitely many lines of symmetry?
1. square
2. circle
3. rhombus
4. pentagon
Show answer
Answer: (b) circle. Every diameter.
Which letter has both a horizontal and a vertical line of symmetry
1. A
2. H
3. B
4. E
Show answer
Answer: (b) H. H is symmetric both ways.

All chapters of Class 6 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.