Class 6 Maths Chapter 9 Symmetry – Extra Questions with Answers

Line symmetry and rotational symmetry combine in Chapter 9, and this question set tests how well the two ideas can be told apart and applied together.

Last Updated: September 23, 2026

Very Short Answer Questions (1 mark)

Q1. How many lines of symmetry does a regular hexagon have?
Ans: 6.

Q2. What is the order of rotational symmetry of an equilateral triangle?
Ans: 3 (angle of symmetry = 120°).

Q3. Name a quadrilateral that has rotational symmetry but no line of symmetry.
Ans: A parallelogram that is neither a rectangle nor a rhombus — it has 180° rotational symmetry (order 2) but no line of symmetry.

Q4. What is the smallest angle of symmetry possible for a figure whose order of rotational symmetry is 5?
Ans: 360° ÷ 5 = 72°.

Q5. Does a scalene triangle have any line of symmetry?
Ans: No, since all three sides and angles are different, no fold line can create matching halves.

Short Answer Questions (2–3 marks)

Q6. A rhombus and a square both have 4 equal sides. Do they have the same number of lines of symmetry? Explain.
Ans: No. A square has 4 lines of symmetry (2 through opposite sides’ midpoints, plus 2 diagonals), but a non-square rhombus has only 2 lines of symmetry (its two diagonals) — its side-to-side folds do not produce matching halves because its angles are not all equal.

Q7. Explain why 100° cannot be the smallest angle of rotational symmetry of any figure.
Ans: The smallest angle of symmetry must divide 360° exactly (be a whole-number factor of 360). Since 360 ÷ 100 = 3.6, which is not a whole number, 100° cannot be a valid smallest angle of symmetry.

Q8. A figure has angles of symmetry at 72°, 144°, 216°, 288°, and 360°. What is its order of rotational symmetry, and what regular polygon is it likely to resemble?
Ans: The order is 5 (five angles of symmetry), matching a regular pentagon, which also has 5 lines of symmetry.

Q9. Give one real-life example each of an object with (a) only line symmetry, (b) only rotational symmetry, (c) both.
Ans: (a) The letter “A” — one vertical line of symmetry, no rotational symmetry. (b) A pinwheel with curved, slanted blades — rotational symmetry but no line of symmetry. (c) A regular hexagon-shaped floor tile — both line symmetry (6 lines) and rotational symmetry (order 6).

Higher-Order Thinking / Application Questions

Q10. The Ashoka Chakra has 24 spokes. If a similar wheel design had 36 equally spaced spokes instead, what would be its smallest angle of symmetry and how many lines of symmetry would it have?
Ans: Smallest angle of symmetry = 360° ÷ 36 = 10°. Since 36 is even, the spokes pair up across the centre, giving 36 ÷ 2 = 18 lines of symmetry.

Q11. A student says, “Since a rectangle has 2 lines of symmetry and a square has 4, a square is ‘more symmetric.'” Do you agree? Explain using rotational symmetry as well.
Ans: Yes, a square is more symmetric than a general rectangle in both respects: a square has 4 lines of symmetry versus a rectangle’s 2, and a square has rotational symmetry of order 4 (angles of symmetry at 90°, 180°, 270°, 360°) while a non-square rectangle only has order 2 (angles of symmetry at 180°, 360°).

Q12. Sketch (in your own notebook) a quadrilateral that has rotational symmetry of order 2 but no line of symmetry, and explain your reasoning.
Ans: A “Z”-shaped or slanted parallelogram (not a rectangle or rhombus) works: rotating it by 180° about its centre maps it onto itself (order 2 rotational symmetry), but no straight fold line produces two matching mirror halves, since its opposite sides are parallel but not positioned symmetrically about any single line.

Frequently Asked Questions

How many lines of symmetry does a square have, and where are they located?
A square has four lines of symmetry: two connecting the midpoints of opposite sides, and two diagonal lines connecting opposite corners, each dividing the square into two mirror-image halves.

Does every shape with rotational symmetry also have line symmetry?
No, some shapes have rotational symmetry without any line of symmetry, such as certain pinwheel-like shapes that look the same after rotation but cannot be folded along any line to match.

Written by Satish

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