CBSE Class 6 Mathematics Symmetry Practice Paper Worksheet Set 10 with Answers

Here is CBSE Class 6 Maths Ganita Prakash Chapter 9 Symmetry Practice Paper 27: 20 questions worth 40 marks, arranged in Sections A to E, each followed by a clear step-by-step answer. This paper focuses on rotational symmetry: finding the order from the smallest angle, deciding whether a regular hexagon, decagon or pentagon matches after a given turn, the infinite order of a circle, the angle reached after several matching positions of an octagon, and case studies on hexagonal wall tiles and a pentagon-shaped school logo.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. (a) Find smallest angle of rotational symmetry of regular octagon.
(b) Find its order.
Answer:
(a) A regular octagon has 8 sides, so its smallest angle = 360° ÷ 8 = 45°.
(b) Order = 360° ÷ 45° = 8.
In simple words: A regular octagon matches every 45°, which happens 8 times in a full turn.

Teacher's Note:
1. Order and smallest angle always multiply to 360°.
2. 8 × 45° = 360°.

Question 12. (a) Find number of symmetry lines in regular decagon.
(b) Find order of rotational symmetry.
Answer:
(a) A regular decagon has 10 equal sides, so it has 10 lines of symmetry.
(b) It matches itself after every 36°, 10 times in a full turn, so the order is 10.
In simple words: A regular decagon has 10 lines of symmetry and order 10.

Teacher's Note:
1. For regular polygons: lines of symmetry = order = number of sides.
2. Smallest angle for a decagon: 360° ÷ 10 = 36°.

Question 13. (a) A shape matches itself after a smallest rotation of 120°. Find order.
(b) Total matches in full turn.
Answer:
(a) Order = 360° ÷ smallest angle = 360° ÷ 120° = 3.
(b) It matches at 120°, 240° and 360°, so there are 3 matches in a full turn.

In simple words: A shape that first matches at 120° matches 3 times in a full turn.

Teacher's Note:
1. The order and the number of matches in a full turn are the same thing.
2. An equilateral triangle is a shape of this kind.

Question 14. (a) Find order of square symmetry.
(b) Find smallest rotation angle.
Answer:
(a) A square matches at 90°, 180°, 270° and 360°, so its order of rotational symmetry is 4.
(b) Smallest rotation angle = 360° ÷ 4 = 90°.
In simple words: A square matches 4 times, every 90°.

Teacher's Note:
1. The square also has 4 lines of symmetry.
2. 4 × 90° = 360°.

Section C: Short Answer Questions (3 Marks Each)

Question 15. (a) Find smallest rotation angle of regular pentagon.
(b) Find order.
(c) Total matches in full turn.
Answer:
(a) A regular pentagon has 5 sides, so its smallest rotation angle = 360° ÷ 5 = 72°.
(b) Order = 360° ÷ 72° = 5.
(c) It matches at 72°, 144°, 216°, 288° and 360°: 5 matches in a full turn.

In simple words: A regular pentagon matches every 72°, 5 times in all.

Teacher's Note:
1. List the multiples of 72° up to 360° to count the matches.
2. 5 × 72° = 360°.

Question 16. (a) Find symmetry lines in square.
(b) Find rotational symmetry order.
(c) Find smallest angle.
Answer:
(a) A square has 4 lines of symmetry: 2 diagonals and 2 lines joining the midpoints of opposite sides.
(b) It looks the same 4 times in a full turn, so its rotational symmetry order is 4.
(c) Smallest angle = 360° ÷ 4 = 90°.

In simple words: A square has 4 lines of symmetry, order 4 and a smallest angle of 90°.

Teacher's Note:
1. The square is the regular polygon with 4 sides, so all its numbers are 4.
2. Its diagonals are lines of symmetry, unlike those of a rectangle.

Question 17. (a) Find rotational order of regular hexagon.
(b) Find smallest angle.
(c) Find matches.
Answer:
(a) A regular hexagon has 6 equal sides, so its rotational order is 6.
(b) Smallest angle = 360° ÷ 6 = 60°.
(c) It matches at 60°, 120°, 180°, 240°, 300° and 360°: 6 matches in one full turn.
In simple words: A regular hexagon matches every 60°, 6 times in one full turn.

Teacher's Note:
1. The number of matches in a full turn equals the order.
2. 6 × 60° = 360°.

Section D: Long Answer Question (5 Marks)

Question 18. A regular octagon is rotated step-by-step.
(a) Find order of symmetry
(b) Find smallest angle
(c) Find matches in full rotation
(d) Find angle after 3 matches
(e) Find angle after 5 matches
Answer:
(a) A regular octagon has 8 sides, so its order of rotational symmetry is 8.
(b) Smallest angle = 360° ÷ 8 = 45°.
(c) It matches 8 times in one full rotation.
(d) Each match needs a further 45°, so after 3 matches the angle turned = 3 × 45° = 135°.
(e) After 5 matches the angle turned = 5 × 45° = 225°.

In simple words: Each step of an octagon is 45°, so 3 steps give 135° and 5 steps give 225°.

Teacher's Note:
1. Angle after k matches = k × smallest angle.
2. After 8 matches the angle is 8 × 45° = 360°, a full turn.
3. In the figure, read the labels at the 3rd and 5th vertices.

Section E: Case Study Based Questions (4 Marks Each)

Question 19. Case Study 1: School Hall Floor Design
In a school corridor, decorative tiles shaped like regular hexagons are used to create attractive wall patterns. Each tile is carefully rotated while placing so that the design appears uniform from all viewing angles. Students observe that when the tile is rotated step-by-step, it matches itself multiple times before completing one full turn. The art teacher explains that this matching property is due to rotational symmetry. Students measure angles of rotation and count how many times the tile appears identical during one full rotation. This activity helps them connect mathematics with real-life artistic design and understand symmetry clearly.
Based on the above, answer the following questions:
(a) Find the order of rotational symmetry
(b) Find the smallest rotation angle
(c) Find the number of matches
(d) Find whether it matches after 180°
Answer:
(a) The tile is a regular hexagon with 6 sides, so its order of rotational symmetry is 6.
(b) Smallest rotation angle = 360° ÷ 6 = 60°.
(c) It matches 6 times in one full rotation.
(d) 180° ÷ 60° = 3, a whole number, so 180° is 3 steps of 60°. Yes, it matches after 180°.

In simple words: A hexagonal tile matches every 60°, so it matches 6 times, including at 180°.

Teacher's Note:
1. To check a given angle, divide it by the smallest angle.
2. A regular hexagon matches after a half turn because 6 is an even number.

Question 20. Case Study 2:
A school designs its logo in the shape of a regular pentagon with identical sides and angles. The logo is printed on badges, notebooks, and uniforms. When students rotate the badge slowly around its center, they notice the logo matches itself several times before completing one full turn. They carefully observe and count matching positions and calculate the rotation angle needed for matching. Their mathematics teacher explains that regular polygons show rotational symmetry and that the number of matching positions depends on number of sides. Students enjoy learning this concept through the real example of their school identity.
Based on the above, answer the following questions:
(a) Find the order of symmetry
(b) Find the smallest angle
(c) Find whether it matches after 144°
(d) Find the number of matches in 360°
Answer:
(a) The logo is a regular pentagon (5 sides), so its order of rotational symmetry is 5.
(b) Smallest angle = 360° ÷ 5 = 72°.
(c) 144° ÷ 72° = 2, a whole number (144° = 2 × 72°). Yes, it matches after 144°.
(d) In a full turn of 360° it matches 5 times (at 72°, 144°, 216°, 288°, 360°).

In simple words: The pentagon logo matches every 72°, so it matches at 144° and 5 times in all.

Teacher's Note:
1. Number of matching positions = number of sides for a regular polygon.
2. Any multiple of 72° up to 360° gives a match.