CBSE Class 6 Mathematics Symmetry Practice Paper Assignment Set 03 with Answers

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Practice Paper 26 for CBSE Class 6 Mathematics (Ganita Prakash) Chapter 9 Symmetry is a full 40-mark paper with 20 questions in Sections A to E, and every question below has a worked answer. It tests finding the smallest angle of rotation from the order (and the reverse), identifying a regular hexagon and a regular decagon from their symmetry, rotation-only figures like the windmill, an eight-bladed ceiling fan, and case studies on a hexagonal floor design and a twelve-bladed garden pinwheel.

Section A: Multiple Choice Questions (1 Mark Each)

Question 1: A regular polygon has an order of rotational symmetry of 8. What is the smallest angle of rotation?
(a) 30°
(b) 36°
(c) 40°
(d) 45°
Show Answer & Explanation

Answer: (d) 45°

Explanation:
1. The figure matches itself 8 times in one complete turn of 360°, at equal steps.
2. Size of each step = 360° ÷ 8.
3. 360° ÷ 8 = 45° (this is the regular octagon).

Teacher's Note:
1. Divide the full turn by the order to get the smallest angle.
2. 30° goes with order 12, 36° with order 10 and 40° with order 9.

Question 2: A rectangle is folded along its vertical centre line. Which statement is correct?
(a) Two unequal parts
(b) Two mirror halves
(c) Only rotational symmetry
(d) No symmetry
Show Answer & Explanation

Answer: (b) Two mirror halves

Explanation:
1. The vertical centre line cuts the top and bottom sides exactly in the middle.
2. When we fold along it, every point on the left lands on a matching point on the right.
3. So the fold gives two mirror halves, and the vertical centre line is a line of symmetry.

Teacher's Note:
1. The horizontal centre line of a rectangle works in the same way.
2. A rectangle has reflection symmetry as well as rotational symmetry of order 2, so (c) is wrong.

Question 3: A figure overlaps itself 6 times in one full rotation. Which figure is it?
(a) Equilateral triangle
(b) Regular hexagon
(c) Square
(d) Rectangle
Show Answer & Explanation

Answer: (b) Regular hexagon

Explanation:
1. Find the number of overlaps for each option: equilateral triangle 3, square 4, rectangle 2.
2. A regular hexagon matches after every 360° ÷ 6 = 60°, so it overlaps itself 6 times.
3. The figure is a regular hexagon.

Teacher's Note:
1. For regular polygons, overlaps in one full turn = number of sides.
2. The rectangle is not regular, so it has only 2 overlaps though it has 4 sides.

Question 4: Which figure has rotational symmetry but no reflection symmetry?
(a) Windmill
(b) Square
(c) Equilateral triangle
(d) Regular hexagon
Show Answer & Explanation

Answer: (a) Windmill

Explanation:
1. The square, the equilateral triangle and the regular hexagon can each be folded into mirror halves, so they do have reflection symmetry.
2. The blades of a windmill all slant in the same direction. A turn keeps the shape the same, but a mirror would make the blades slant the other way.
3. So the windmill has rotational symmetry but no line of symmetry.

Teacher's Note:
1. To test reflection symmetry, imagine placing a mirror along the fold line.
2. Every regular polygon has both types of symmetry.

Question 5: If a regular decagon has 10 lines of symmetry, what is its smallest angle of rotation?
(a) 30°
(b) 36°
(c) 40°
(d) 45°
Show Answer & Explanation

Answer: (b) 36°

Explanation:
1. For a regular polygon, the number of lines of symmetry, the number of sides and the order of rotational symmetry are all the same.
2. So the regular decagon has order 10.
3. Smallest angle of rotation = 360° ÷ 10 = 36°.

Teacher's Note:
1. Lines of symmetry = order of rotation only for regular polygons; a rectangle has 2 of each, but a windmill has 0 lines.
2. Check: 10 × 36° = 360°.

Question 6: Which shape has exactly one line of symmetry?
(a) Isosceles triangle
(b) Square
(c) Equilateral triangle
(d) Regular hexagon
Show Answer & Explanation

Answer: (a) Isosceles triangle

Explanation:
1. Count the lines: square 4, equilateral triangle 3, regular hexagon 6.
2. A triangle with exactly two equal sides can be folded into matching halves only along the line from the vertex between the equal sides to the middle of the third side.
3. So the answer is the isosceles triangle.

Teacher's Note:
1. The fold line of an isosceles triangle also cuts its base into two equal parts at a right angle.
2. An equilateral triangle is a special isosceles triangle with 3 lines, so (c) is not 'exactly one'.

Question 7: A regular polygon has smallest angle of rotation equal to 72°. How many sides does it have?
(a) 5
(b) 6
(c) 8
(d) 10
Show Answer & Explanation

Answer: (a) 5

Explanation:
1. Order of rotational symmetry = 360° ÷ smallest angle = 360° ÷ 72° = 5.
2. For a regular polygon, the order equals the number of sides.
3. So it has 5 sides; it is a regular pentagon.

Teacher's Note:
1. Check by multiplying: 5 × 72° = 360°.
2. 6 sides would give 60°, 8 sides 45° and 10 sides 36°.

Question 8: Which rotation always maps any figure onto itself?
(a) 120°
(b) 180°
(c) 270°
(d) 360°
Show Answer & Explanation

Answer: (d) 360°

Explanation:
1. 120°, 180° or 270° turns map only some figures onto themselves (for example 180° works for a rectangle but not for an equilateral triangle).
2. A 360° turn is a complete turn, which brings every figure back to exactly where it started.
3. So the answer is 360°.

Teacher's Note:
1. Because every figure matches after 360°, we say a figure has rotational symmetry only if it matches before completing the full turn.
2. A figure that matches only at 360° has no rotational symmetry.

Question 9:
Assertion (A): A scalene triangle has no line of symmetry.
Reason (R): All sides and angles are unequal.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Assertion: whichever line we fold a scalene triangle along, the two parts do not cover each other. So it has no line of symmetry. A is true.
2. Reason: by definition, a scalene triangle has three sides of different lengths, and its three angles are also different. R is true.
3. For a fold to work, a side must land on an equal side. As no two sides are equal, this never happens, so R correctly explains A.

Teacher's Note:
1. Number of lines of symmetry of a triangle: 0 (scalene), 1 (isosceles), 3 (equilateral).
2. Try folding a paper scalene triangle to check.

Question 10:
Assertion (A): A square has four lines of symmetry.
Reason (R): Folding along any diagonal or centre line produces two mirror halves.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Assertion: the four lines of symmetry of a square are its 2 diagonals and the 2 lines joining the midpoints of opposite sides. A is true.
2. Reason: folding along any of these four lines makes one half lie exactly on the other. R is true.
3. Since there are 2 diagonals and 2 centre lines, R tells us exactly where the four lines come from, so R is the correct explanation of A.

Teacher's Note:
1. Draw a square and mark all four lines to see them.
2. Only the square (not the rectangle) has its diagonals as lines of symmetry.

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 equal sides and 6 equal angles, so it has 6 lines of symmetry.
(b) One line of symmetry: the line through the centre joining a pair of opposite vertices. (A line through the centre joining the midpoints of a pair of opposite sides is also a line of symmetry.)
In simple words: The regular hexagon has 6 fold lines, each passing through its centre.

Teacher's Note:
1. Of the 6 lines, 3 go vertex to vertex and 3 go side-midpoint to side-midpoint.
2. Number of lines of symmetry of a regular polygon = number of sides.

 

Question 12. (a) Write the order of rotational symmetry of a square.
(b) Write its smallest angle of rotation.
Answer:
(a) Rotate a square about its centre. It looks exactly the same at 90°, 180°, 270° and 360°, which is 4 positions. Order = 4.
(b) Smallest angle = 360° ÷ 4 = 90° (a quarter turn).
O 90° 180° 270° 360° A Vertex A reaches the next corner every 90°
In simple words: A square matches itself after every quarter turn, so its order is 4.

Teacher's Note:
1. The marked angles 90°, 180°, 270°, 360° are all multiples of 90°.
2. Check: 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 looks the same at 3 positions in one full turn (120°, 240°, 360°), so its order is 3.
(b) Smallest angle = 360° ÷ 3 = 120°.
In simple words: An equilateral triangle matches itself every one-third of a turn, which is 120°.

Teacher's Note:
1. Turning by 120° sends each vertex to the next vertex.
2. An equilateral triangle also has 3 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 line joining the midpoints of its two longer sides and the line joining the midpoints of its two shorter sides.
(b) It matches itself only at 180° and 360° in a full turn, so its order of rotational symmetry is 2.
The two lines of symmetry of a rectangle
In simple words: A rectangle has 2 fold lines and matches itself twice in one full turn.

Teacher's Note:
1. The diagonals of a rectangle are not lines of symmetry: the folded corners do not match.
2. A rotation of 90° turns a long side into a short side, so a rectangle does not match at 90°.

 

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) An octagon has 8 sides.
(b) Being regular, it has as many lines of symmetry as sides: 8 lines of symmetry.
(c) It matches itself 8 times in one full turn, so the smallest angle of rotation = 360° ÷ 8 = 45°.
The 8 lines of symmetry of a regular octagon
In simple words: A regular octagon: 8 sides, 8 lines of symmetry, smallest turn 45°.

Teacher's Note:
1. 4 lines pass through opposite vertices and 4 through midpoints of opposite sides.
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) One fold for each diagonal: 2 folds.
(b) The two diagonals divide the square into 4 equal triangles meeting at the centre.
(c) The first fold makes 2 layers and the second makes 4 layers. A single punch goes through all 4 layers, so on opening the sheet there are 4 holes, which are mirror images of one another in the diagonals.
The 4 holes are reflections of each other in the diagonals
In simple words: Folding twice gives 4 layers, so one punch makes 4 matching holes.

Teacher's Note:
1. Number of layers doubles with each fold.
2. This is a quick way to make a symmetric paper design.

 

Question 17. A ceiling fan has eight identical blades.
(a) Write the centre of rotation
(b) Write the order of rotational symmetry
(c) Write the smallest angle of rotation
Answer:
(a) The centre of rotation is the central point of the fan's hub, the fixed point about which all the blades turn.
(b) The 8 identical blades are equally spaced, so the fan looks the same 8 times in one full turn. Order = 8.
(c) Smallest angle of rotation = 360° ÷ 8 = 45°.
In simple words: An eight-bladed fan looks the same after every 45° turn about its centre.

Teacher's Note:
1. The number of identical, equally spaced blades gives the order.
2. 45° is the angle between two neighbouring blades.

 

Section D: Long Answer Question (5 Marks)

Question 18. A regular polygon has 10 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 10 equal sides and equal angles is a regular decagon.
(b) It has 10 lines of symmetry (5 joining opposite vertices and 5 joining midpoints of opposite sides).
(c) It matches itself 10 times in one full turn, so the order of rotational symmetry is 10.
(d) Smallest angle of rotation = 360° ÷ 10 = 36°.
(e) Any object with 10 identical, equally spaced parts, for example a flower with 10 identical petals or a ten-sided decorative floor tile.
36° O A A 36° turn moves vertex A to the next vertex
In simple words: A regular decagon has 10 lines of symmetry, order 10 and a smallest turn of 36°.

Teacher's Note:
1. All four numerical answers come from the number of sides, 10.
2. Check: 10 × 36° = 360°.
3. For (e), the parts must be identical and evenly spaced.

 

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

Question 19. Case Study 1: School Hall Floor Design
Students create a floor design in the shape of a regular hexagon. Each side is equal and angles identical. Rotating the hexagon about its centre, it matches itself six times in one full rotation. Folding along axes through the centre produces identical mirror halves. The design appears balanced and visually appealing. Teachers explain that symmetry in rotation and reflection makes the design attractive and helps students recognize symmetry in real-life objects.
Based on the above, answer the following questions:
(a) Write the number of sides of the hexagon
(b) Write the order of rotational symmetry
(c) Write the smallest angle of rotation
(d) Write the number of lines of symmetry
Answer:
(a) 'Hexa' means six, so the hexagon has 6 sides.
(b) It matches itself 6 times in one full rotation, so the order of rotational symmetry is 6.
(c) Smallest angle of rotation = 360° ÷ 6 = 60°.
(d) A regular hexagon has 6 lines of symmetry.
Regular hexagon: 6 lines of symmetry
In simple words: The hexagonal floor design has 6 sides, order 6, a 60° smallest turn and 6 lines of symmetry.

Teacher's Note:
1. 3 lines of symmetry join opposite corners and 3 join midpoints of opposite sides.
2. Check: 6 × 60° = 360°.

 

Question 20. Case Study 2:
A decorative garden pinwheel has twelve identical blades fixed around a central point. When wind blows, it rotates smoothly. After each equal turn, the pinwheel looks exactly the same. Folding along any line does not produce mirror halves. Students count the number of times it repeats in one full rotation. The pinwheel demonstrates rotational symmetry in real-life objects.
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 pinwheel looks the same after equal turns about its centre, so it shows rotational symmetry.
(b) With 12 identical blades, it repeats 12 times in one full rotation: order = 12.
(c) Smallest angle of rotation = 360° ÷ 12 = 30°.
(d) No. Folding along any line does not give mirror halves, so it has no line of symmetry.
30° Pinwheel with 12 curved blades: matches every 30°
In simple words: The pinwheel repeats every 30° (12 times a turn) but has no line of symmetry.

Teacher's Note:
1. The blades curl the same way round, so a mirror image would curl the opposite way.
2. A figure can have rotational symmetry with no line of symmetry.

 

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Chapter Assignment & Practice Material for Class 6 Mathematics Chapter 09 Symmetry

Revision Assignment: Chapter 09 Symmetry (CBSE)

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