CBSE Class 6 Mathematics Symmetry Practice Paper Worksheet Set 09 with Answers

CBSE Class 6 Maths Ganita Prakash Chapter 9 Symmetry Practice Paper 25 is a 40-mark test of 20 questions spread over Sections A to E, solved here step by step. It covers lines of symmetry of the square, rectangle, regular hexagon, isosceles and scalene triangles, the order of rotational symmetry and smallest angle of rotation of regular polygons, folding and punching a square sheet, and case studies on a regular decagon floor design and a twelve-bladed garden windmill.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. (a) Write the number of lines of symmetry of a regular hexagon.
(b) Write one such line.
Answer:
(a) A regular hexagon has 6 lines of symmetry: 3 lines join opposite vertices and 3 lines join the midpoints of opposite sides.
(b) One line of symmetry is the line joining two opposite vertices, passing through the centre. (The line joining the midpoints of two opposite sides is also correct.)

In simple words: A regular hexagon can be folded into matching halves in 6 different ways.

Teacher's Note:
1. For a regular polygon, the number of lines of symmetry equals the number of sides.
2. Every line of symmetry of a regular polygon passes through its centre.

Question 12. (a) Write the order of rotational symmetry of a square.
(b) Write its smallest angle of rotation.
Answer:
(a) Turning a square about its centre, it looks the same after 90°, 180°, 270° and 360°. That is 4 times, so the order is 4.
(b) Smallest angle of rotation = 360° ÷ 4 = 90°.
In simple words: A square matches itself after every quarter turn, 4 times in a full turn.

Teacher's Note:
1. A quarter turn is 90°.
2. Order × smallest angle = 360°: 4 × 90° = 360°.

Question 13. (a) Write the order of rotational symmetry of an equilateral triangle.
(b) Write its smallest angle of rotation.
Answer:
(a) An equilateral triangle matches itself after 120°, 240° and 360°, so its order of rotational symmetry is 3.
(b) Smallest angle of rotation = 360° ÷ 3 = 120°.

In simple words: An equilateral triangle looks the same after every one-third turn.

Teacher's Note:
1. A one-third turn is 360° ÷ 3 = 120°.
2. Its order (3) equals its number of sides and its number of lines of symmetry.

Question 14. (a) Write the number of lines of symmetry of a rectangle.
(b) Write its order of rotational symmetry.
Answer:
(a) A rectangle has 2 lines of symmetry: the vertical and the horizontal lines through the midpoints of opposite sides. Its diagonals are not lines of symmetry.
(b) A rectangle looks the same only after 180° and 360°, so its order of rotational symmetry is 2.

In simple words: A rectangle folds into mirror halves in 2 ways and looks the same after a half turn.

Teacher's Note:
1. Fold a paper rectangle along a diagonal to see that the halves do not match.
2. Smallest angle of rotation of a rectangle is 180°.

Section C: Short Answer Questions (3 Marks Each)

Question 15. A regular octagon is drawn.
(a) Write its number of sides
(b) Write its number of lines of symmetry
(c) Write its smallest angle of rotation
Answer:
(a) 'Octa' means eight, so a regular octagon has 8 sides.
(b) A regular polygon has as many lines of symmetry as sides, so it has 8 lines of symmetry (4 through opposite vertices and 4 through midpoints of opposite sides).
(c) Its order of rotational symmetry is 8, so the smallest angle of rotation = 360° ÷ 8 = 45°.

In simple words: A regular octagon has 8 sides, 8 lines of symmetry and matches itself after every 45° turn.

Teacher's Note:
1. For any regular polygon with n sides: n lines of symmetry, order n, smallest angle 360° ÷ n.
2. Check: 8 × 45° = 360°.

Question 16. A square sheet is folded along both diagonals.
(a) Write number of folds
(b) Write number of equal regions formed
(c) Write the number of holes seen on unfolding if one hole is punched through the folded sheet
Answer:
(a) A square has 2 diagonals, so there are 2 folds.
(b) The two diagonals cross at the centre and cut the square into 4 equal triangles.
(c) After two folds the sheet has 4 layers, so one punch makes a hole in each layer. On unfolding we see 4 holes, one in each triangle; each hole is the mirror image of the next one in a diagonal.

In simple words: Two diagonal folds make 4 layers, so one punch gives 4 symmetrically placed holes.

Teacher's Note:
1. Each fold doubles the number of layers: 1 → 2 → 4.
2. The holes are reflections of one another in the fold lines.

Question 17. A ceiling fan has three identical blades.
(a) Write the centre of rotation
(b) Write order of rotational symmetry
(c) Write the smallest angle of rotation
Answer:
(a) The fan turns about the central point of its hub (where the blades are joined), so that is the centre of rotation.
(b) With 3 identical, equally spaced blades, the fan looks the same 3 times in one full turn, so the order is 3.
(c) Smallest angle of rotation = 360° ÷ 3 = 120°.
In simple words: A three-bladed fan looks the same after every 120° turn about its centre.

Teacher's Note:
1. The centre of rotation is the one point that does not move during the turn.
2. Equal spacing of identical blades is what gives rotational symmetry.

Section D: Long Answer Question (5 Marks)

Question 18. A regular polygon has 8 equal sides.
(a) Write its name
(b) Write number of lines of symmetry
(c) Write order of rotational symmetry
(d) Write smallest angle of rotation
(e) Write one real-life object showing similar symmetry
Answer:
(a) A polygon with 8 equal sides (and equal angles) is a regular octagon.
(b) Lines of symmetry = number of sides = 8.
(c) It matches itself 8 times in one full turn, so the order of rotational symmetry is 8.
(d) Smallest angle of rotation = 360° ÷ 8 = 45°.
(e) Any object made of 8 identical, equally spaced parts, for example an umbrella with 8 identical panels seen from above or an octagonal floor tile.

In simple words: A regular octagon has 8 lines of symmetry and order 8, and it matches after every 45° turn.

Teacher's Note:
1. Name, lines, order and angle all come from the number of sides: 8.
2. For (e), choose an object whose 8 parts are identical and equally spaced.
3. Always check: order × smallest angle = 360°.

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

Question 19. Case Study 1: School Hall Floor Design
During a school celebration, students create a floor design in the shape of a regular decagon. Each side and angle is equal. Rotating the decagon about its centre, it matches itself ten times. Folding along axes through the centre produces identical mirror halves. Teachers explain that symmetry makes the design visually balanced and attractive. Students count the overlapping rotations and symmetry lines to understand geometry in real-life objects.
Based on the above, answer the following questions:
(a) Write the number of sides of the decagon
(b) Write the order of rotational symmetry
(c) Write the smallest angle of rotation
(d) Write the number of lines of symmetry
Answer:
(a) 'Deca' means ten, so a decagon has 10 sides.
(b) The decagon matches itself 10 times in one full turn, so the order of rotational symmetry is 10.
(c) Smallest angle of rotation = 360° ÷ 10 = 36°.
(d) A regular decagon has as many lines of symmetry as sides: 10.

In simple words: The regular decagon design has 10 sides, order 10, a 36° smallest turn and 10 lines of symmetry.

Teacher's Note:
1. The lines of symmetry of a decagon: 5 through opposite vertices and 5 through midpoints of opposite sides.
2. Check: 10 × 36° = 360°.

Question 20. Case Study 2:
A decorative windmill in a garden has twelve identical blades. When air blows, it rotates smoothly. Students observe that after each equal turn, the windmill looks the same. Folding along any line does not produce mirror halves. They count how many times the pattern repeats in one full rotation. The windmill demonstrates rotational symmetry in everyday objects and is visually attractive.
Based on the above, answer the following questions:
(a) Write the type of symmetry
(b) Write the order of rotational symmetry
(c) Write the smallest angle of rotation
(d) Write whether it has any line of symmetry
Answer:
(a) The windmill looks the same after equal turns, so it has rotational symmetry (only).
(b) 12 identical blades means the pattern repeats 12 times in one full turn, so the order is 12.
(c) Smallest angle of rotation = 360° ÷ 12 = 30°.
(d) Folding along any line does not give mirror halves, so it has no line of symmetry.

In simple words: The windmill matches itself after every 30° turn, 12 times in all, but cannot be folded into mirror halves.

Teacher's Note:
1. The blades all lean the same way; that is why a mirror would reverse them and no fold works.
2. Rotational symmetry can exist without reflection symmetry.