Class 6 Maths Ganita Prakash Chapter 9 Solutions (NCERT 2026–27) – Symmetry

These Class 6 Maths Ganita Prakash Chapter 9 solutions cover Symmetry from the new NCF-2023 textbook (Reprint 2026–27). Every Figure it Out question, Math Talk and Try This task is solved step by step — lines of symmetry, reflection symmetry, rotational symmetry, angles of symmetry and order of rotation — so you can master the chapter and revise it quickly.

Class: 6 Subject: Mathematics Book: Ganita Prakash Chapter: 9 Exercises: Figure it Out (9.1 Line of Symmetry), Figure it Out (9.2 Rotational Symmetry) Session: 2026–27
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Chapter 9 Overview

Chapter 9 of Ganita Prakash, Symmetry, begins with beautiful symmetrical objects — a flower, a butterfly, a rangoli, a pinwheel, the Taj Mahal and a gopuram — and asks what is special about them. It then builds two big ideas. The first is the line of symmetry (also called reflection symmetry): a line that cuts a figure into two parts that exactly overlap when folded along it. The second is rotational symmetry: when a figure looks exactly the same after being turned by an angle about a fixed centre of rotation. You explore how many lines and how many angles of symmetry different shapes have — squares, triangles, hexagons, circles, radial-arm figures and the Ashoka Chakra. The Class 6 Maths Ganita Prakash Chapter 9 solutions below work through every Figure it Out, Math Talk and Try This question step by step.

Key Concepts & Definitions

Symmetry: when a figure is made up of parts that repeat in a definite pattern, we say the figure has symmetry and is symmetrical. The clouds picture in the chapter is not symmetrical.

Line of symmetry (axis of symmetry): a line that cuts a plane figure into two parts that exactly overlap when the figure is folded along that line. The two halves are called mirror halves.

Reflection symmetry: a figure that has a line (or lines) of symmetry is said to have reflection symmetry — each side is the mirror image of the other across the line.

Centre of rotation: the fixed point about which a figure is turned when checking for rotational symmetry.

Angle of symmetry (angle of rotational symmetry): an angle through which a figure can be rotated so that it looks exactly the same as before.

Rotational symmetry: a figure has rotational symmetry if it has an angle of symmetry strictly between 0° and 360°. (360° alone is not counted, because every figure looks the same after a full turn.)

Order of rotational symmetry: the number of angles of symmetry a figure has, i.e. how many times it looks the same in one full turn (including the 360° turn).

Important Rules & Patterns (Chapter 9)

Lines of symmetry of regular shapes: a regular polygon with n sides has exactly n lines of symmetry (square 4, equilateral triangle 3, regular hexagon 6, etc.).

360° is always an angle of symmetry: a full turn brings every figure back to its original position.

Smallest angle rule: all angles of symmetry are multiples of the smallest angle of symmetry. If the smallest angle is a, the angles are a, 2a, 3a, …, 360°.

Number of angles: if the smallest angle of symmetry is a, the order (number of angles up to 360°) is 360° ÷ a.

Factor rule: if the smallest angle of symmetry is a whole number of degrees, it must be a factor of 360 (e.g. 45° works, 17° does not).

Radial-arms figure: a figure made of k equally-spaced radial arms has k angles of symmetry, each a multiple of (360° ÷ k).

Circle: every angle is an angle of symmetry and every diameter is a line of symmetry — the most symmetric figure.

Figure it Out — Line of Symmetry (Section 9.1)

Questions are reproduced verbatim from the NCERT Ganita Prakash textbook; the worked solutions are original and verified against the answers given in the book. Figure-only items are answered in words/tables since the textbook diagrams cannot be reproduced.

1. Do you see any line of symmetry in the figures at the start of the chapter? What about in the picture of the cloud?

SOLUTION Yes — the opening figures are symmetrical. The flower has 6 lines of symmetry, the rangoli has 4 lines of symmetry, and the butterfly has 1 line of symmetry (the vertical line down its body). The pinwheel looks symmetrical but has no line of symmetry (its arms curve the same way, so the halves do not fold onto each other). The picture of the cloud is irregular, so it has no line of symmetry.

2. For each of the following figures, identify the line(s) of symmetry if it exists.

SOLUTION For each figure, fold (in imagination) along a line and check whether the two halves overlap exactly. Typical answers for the figures shown: An isosceles triangle has 1 vertical line of symmetry; a letter such as H has 2 (one vertical, one horizontal); a plus / star-type figure can have several. A figure with no matching halves (e.g. a scalene shape) has 0 lines of symmetry. (Figure-based question — the line(s) are drawn wherever folding makes the two halves coincide.)

[Page 221] Is there any other way to fold the square so that the two halves overlap? How many lines of symmetry does the square shape have?

SOLUTION No, there is no other way to fold the square — the four folds already found (vertical, horizontal and the two diagonals) are all of them. ∴ the square shape has 4 lines of symmetry.

[Page 221] We saw that the diagonal of a square is also a line of symmetry. Let us take a rectangle that is not a square. Is its diagonal a line of symmetry?

SOLUTION No. When a non-square rectangle is folded along its diagonal, the two triangular halves do not overlap (one is longer and thinner than the other). ∴ a rectangle’s diagonal is not a line of symmetry. (A non-square rectangle has only 2 lines of symmetry — the horizontal and vertical lines through its centre.)

[Page 222] What if we reflect along the diagonal from A to C? Where do points A, B, C and D go? What if we reflect along the horizontal line of symmetry?

SOLUTION The square has corners A (top-left), B (top-right), C (bottom-right), D (bottom-left). Reflecting along the diagonal A–C: A and C lie on the line, so they stay in place; B and D swap — D moves to the position earlier occupied by B (and B moves to D’s position). Reflecting along the horizontal line of symmetry: the top and bottom swap — D and C move to the positions earlier occupied by A and B respectively (and A, B move down to D, C).

[Page 223] Punching Game — 1. In each of the following figures, a hole was punched in a folded square sheet of paper and then the paper was unfolded. Identify the line along which the paper was folded. Figure (d) was created by punching a single hole. How was the paper folded?

SOLUTION The fold line is the line of symmetry joining the matching holes — the punched holes are mirror images across the fold. (a), (b), (c): the fold is the line of symmetry that lies exactly halfway between each pair of matching holes (it may be vertical, horizontal or diagonal depending on how the holes are placed). (d) shows a single hole, so the paper was folded twice — first vertically and then horizontally (or vice versa) — and the punch passed through the point common to both folds, giving just one hole on opening.

2. Given the line(s) of symmetry, find the other hole(s):

SOLUTION For each given line of symmetry, reflect every existing hole across that line; the reflected positions are the missing holes (they lie at the same distance from the line, on the opposite side). When two lines of symmetry are given, reflect across both — each hole then has up to three matching holes (across line 1, across line 2 and across both), forming a symmetric pattern. (Figure-based construction.)

4. After each of the following cuts, predict the shape of the hole when the paper is opened. After you have made your prediction, make the cutouts and verify your answer.

SOLUTION When a folded paper is cut, the opened hole is the cut shape reflected across each fold line. So a cut made on a once-folded sheet opens into a shape that is symmetric about that single fold. A cut on a twice-folded sheet opens into a shape symmetric about both fold lines. For example, a small notch cut at the folded corner of a sheet folded twice opens into a complete small shape (square / diamond) at the centre. (Predict, then verify by actually cutting — the prediction matches.)

5. Suppose you have to get each of these shapes with some folds and a single straight cut. How will you do it? a. The hole in the centre is a square. b. The hole in the centre is a square. Note: For the above two questions, check if the 4-sided figures in the centre satisfy both the properties of a square.

SOLUTION a. First fold the paper in half horizontally, then fold again vertically. Now cut a small square at the centre (folded corner) so that all sides are closed; on opening, the centre hole is a full square. b. Again fold horizontally then vertically. This time, at the closed (folded) corner, make a single straight slanting cut. On opening, the slanting cut from the corner produces a square hole turned at 45° (a “diamond”) at the centre. In both cases the four-sided centre hole has equal sides and equal (right) angles, so it satisfies both properties of a square.

6. How many lines of symmetry do these shapes have? a. (the figure shown) b. A triangle with equal sides and equal angles. c. A hexagon with equal sides and equal angles.

SOLUTION a. Count the fold lines that make the two halves overlap for the shape drawn — for the regular figure shown it has the same number of lines of symmetry as its number of equal sides. b. A triangle with equal sides and equal angles is an equilateral triangle: it has 3 lines of symmetry (one from each vertex to the midpoint of the opposite side). c. A hexagon with equal sides and equal angles is a regular hexagon: it has 6 lines of symmetry (3 through opposite vertices and 3 through midpoints of opposite sides).

7. Trace each figure and draw the lines of symmetry, if any:

SOLUTION Trace each figure, then test folds. Draw a line wherever the fold makes the two halves coincide; if no fold makes them overlap, the figure has no line of symmetry. Letters and simple shapes give: a vertical line, a horizontal line, both, or none, according to the figure. (Figure-based — lines are drawn on the traced copy.)

8. Find the lines of symmetry for the kolam below.

SOLUTION A kolam is usually drawn on a square dot-grid and is highly symmetric. Fold it along the vertical, horizontal and both diagonal lines through the centre. A typical square kolam has 4 lines of symmetry (vertical, horizontal and the two diagonals), matching the symmetry of a square. (Exact number depends on the kolam shown; draw each line where the two halves coincide.)

9. Draw the following. a. A triangle with exactly one line of symmetry. b. A triangle with exactly three lines of symmetry. c. A triangle with no line of symmetry. Is it possible to draw a triangle with exactly two lines of symmetry?

SOLUTION a. An isosceles triangle (two equal sides) has exactly one line of symmetry. b. An equilateral triangle (all sides equal) has exactly three lines of symmetry. c. A scalene triangle (all sides different) has no line of symmetry. No, it is not possible to draw a triangle with exactly two lines of symmetry. A triangle can have only 0, 1 or 3 lines of symmetry.

10. Draw the following. In each case, the figure should contain at least one curved boundary. a. A figure with exactly one line of symmetry. b. A figure with exactly two lines of symmetry. c. A figure with exactly four lines of symmetry.

SOLUTION a. A heart shape or a semicircle has exactly one line of symmetry (vertical), and both have curved boundaries. b. A leaf-shaped figure (two equal arcs, like an ellipse / oval) has exactly two lines of symmetry — the long axis and the short axis — with curved sides. c. A figure like a four-petalled flower (or a square with rounded/curved petals on each side) has exactly four lines of symmetry and curved boundaries.

11. Copy the following on squared paper. Complete them so that the blue line is a line of symmetry. Problem (a) has been done for you. Hint: For (c) and (f), see if rotating the book helps!

SOLUTION For each figure, reflect every square / segment across the blue line. Each shaded square at a distance d on one side gets a matching shaded square at the same distance d on the other side. After mirroring all parts, the completed figure folds exactly onto itself along the blue line. (Figure-based — complete the drawing on squared paper as in the worked example (a).)

12. Copy the following drawing on squared paper. Complete each one of them so that the resulting figure has the two blue lines as lines of symmetry.

SOLUTION Reflect the given part across the first blue line, then reflect the whole result across the second blue line. This usually creates four matching copies arranged symmetrically about the point where the two lines cross. The finished figure overlaps itself when folded along either blue line. (Figure-based construction on squared paper.)

13. Copy the following on a dot grid. For each figure draw two more lines to make a shape that has a line of symmetry.

SOLUTION For each figure, add two more line segments so that the completed shape can be folded into two matching halves. Choose the new lines so they mirror the existing ones across a chosen axis (vertical, horizontal or diagonal). After adding the two lines, the shape has at least one line of symmetry. (Figure-based — drawn on the dot grid.)

Math Talk & Try This — Answered

These are the in-text exploratory and short tasks in the chapter; the determinate ones are answered, and the open ones are guided.

Math Talk — Symmetries of famous structures What are the symmetries that you see in the Taj Mahal and the gopuram? Answer. Both have reflection symmetry about a vertical line down the centre — the left half is the mirror image of the right half (the matching domes/minarets of the Taj Mahal, the matching tiers of the gopuram). They have a single vertical line of symmetry and no rotational symmetry.
Try This — Ink Blot Devils Fold a paper in half, spill a few drops of ink on one half, press and open. What do you see? Is the figure symmetric? Where is the line of symmetry? Answer. The ink prints a mirror image on the other half, so the figure is symmetric. The fold line is the line of symmetry. Usually there is no other line of symmetry, because random ink blots are not symmetric in any other direction.
Try This — Paper folding and cutting A sheet is folded and a cut is made along a dotted line. Draw how the paper looks when unfolded. Do you see a line of symmetry? Answer. On unfolding, the cut appears as a shape that is the mirror image across the fold. The fold line is the line of symmetry of the cut-out design.
Math Talk — Angles of symmetry of the windmill / square How many angles of symmetry does the paper windmill have? What about a square? Answer. The windmill looks the same after a quarter turn, so its angles of symmetry are 90°, 180°, 270° and 360° — that is 4 angles. A square also returns to itself after 90°, so it has the same 4 angles of symmetry (order 4).
Math Talk — The strip example Find the angles of symmetry of the given strip. Answer. Rotating the strip by 180° does not give the original; only a full turn of 360° brings it back. So 360° is its only angle of symmetry, which means the strip has no rotational symmetry.
Math Talk — Three radial arms must be 120° If a figure with three radial arms has rotational symmetry, what must each angle be? Answer. The three equal angles share a full turn equally, so each angle = 360° ÷ 3 = 120°. The figure then has angles of symmetry 120°, 240° and 360° (order 3).
Try This — 5 and 6 angles of symmetry (radial arms) Can you draw a figure with radial arms that has a) exactly 5 angles of symmetry, b) 6 angles of symmetry? Find the angles in each case. Answer. (a) Use 5 equally-spaced arms; smallest angle = 360° ÷ 5 = 72°. Angles of symmetry = 72°, 144°, 216°, 288°, 360°. (b) Use 6 equally-spaced arms; smallest angle = 360° ÷ 6 = 60°. Angles of symmetry = 60°, 120°, 180°, 240°, 300°, 360°.
Try This — 7 angles of symmetry A radial-arms figure has exactly 7 angles of symmetry. What is its smallest angle of symmetry? Is it a whole number? If not, express it as a mixed fraction. Answer. Smallest angle = 360° ÷ 7 = 513⁄7° (since 7 × 51 = 357, remainder 3). It is not a whole number of degrees.
Math Talk — Multiples of the smallest angle In each case the angles are the multiples of the smallest angle. Will this always happen? What do you think? Answer. Yes. The angles of symmetry are always multiples of the smallest angle of symmetry — the second angle is twice the smallest, the third is three times, and so on up to 360°.
True or False (page 236) • Every figure will have 360 degrees as an angle of symmetry. • If the smallest angle of symmetry of a figure is a natural number in degrees, then it is a factor of 360. Answer. Both statements are True. A full 360° turn always returns any figure to itself; and since all angles are multiples of the smallest angle and 360° must be one of them, the smallest whole-number angle must divide 360 exactly (be a factor of 360).

Figure it Out — Rotational Symmetry (Section 9.2)

1. Find the angles of symmetry for the given figures about the point marked •. (a)   (b)   (c)

SOLUTION Rotate each figure about the marked point and note the turns that bring it back onto itself. (a) Looks the same after a quarter turn → angles of symmetry = 90°, 180°, 270°, 360°. (b) Comes back only after a full turn → angle of symmetry = 360° (so it has no rotational symmetry). (c) Looks the same after a half turn → angles of symmetry = 180°, 360°.

2. Which of the following figures have more than one angle of symmetry?

SOLUTION A figure has “more than one angle of symmetry” when it returns to itself at some turn smaller than a full 360° (i.e. it has rotational symmetry). So the figures with rotational symmetry — those that look the same after a quarter, half or third turn (like a windmill, a regular shape or a radial-arm figure) — have more than one angle of symmetry. Figures that come back only after a full 360° turn have just one.

3. Give the order of rotational symmetry for each figure:

SOLUTION The order of rotational symmetry = the number of angles of symmetry (the number of times the figure looks the same in one full turn). For example: a figure that matches at 90°, 180°, 270°, 360° has order 4; one that matches at 120°, 240°, 360° has order 3; one that matches at 180°, 360° has order 2; and a figure that returns only at 360° has order 1 (no rotational symmetry). Read each figure’s order from its smallest matching turn.

[Section 9.2, page 238] 1. Colour the sectors of the circle below so that the figure has i) 3 angles of symmetry, ii) 4 angles of symmetry, iii) what are the possible numbers of angles of symmetry you can obtain by colouring the sectors in different ways?

SOLUTION The circle is divided into 12 equal sectors, so each sector is 30°. (i) To get 3 angles of symmetry, colour the sectors in a pattern that repeats every 120° (every 4 sectors), giving angles 120°, 240°, 360°. (ii) To get 4 angles of symmetry, colour a pattern that repeats every 90° (every 3 sectors), giving angles 90°, 180°, 270°, 360°. (iii) The possible orders are the divisors of 12 — so 1, 2, 3, 4, 6 and 12 angles of symmetry can be obtained (up to 12, when all sectors are coloured the same).

2. Draw two figures other than a circle and a square that have both reflection symmetry and rotational symmetry.

SOLUTION Any regular polygon works. Two good examples: Equilateral triangle: number of lines of symmetry = 3, order of rotational symmetry = 3. Regular pentagon (or a regular hexagon): a regular pentagon has 5 lines of symmetry and order 5; a regular hexagon has 6 lines of symmetry and order 6. Each has both reflection and rotational symmetry.

3. Draw, wherever possible, a rough sketch of: a. A triangle with at least two lines of symmetry and at least two angles of symmetry. b. A triangle with only one line of symmetry but not having rotational symmetry. c. A quadrilateral with rotational symmetry but no reflection symmetry. d. A quadrilateral with reflection symmetry but not having rotational symmetry.

SOLUTION a. An equilateral triangle — it has 3 lines of symmetry and 3 angles of symmetry (so “at least two” of each is satisfied). b. An isosceles triangle — it has 1 line of symmetry and no rotational symmetry (only 360°). c. A parallelogram (that is not a rectangle or rhombus) — it has rotational symmetry of order 2 (angles 180°, 360°) but no line of symmetry. d. A kite — it has 1 line of symmetry (its axis) but no rotational symmetry (returns only at 360°).

4. In a figure, 60° is the smallest angle of symmetry. What are the other angles of symmetry of this figure?

SOLUTION All angles of symmetry are multiples of the smallest angle (60°) up to 360°. Multiples of 60° up to 360°: 60°, 120°, 180°, 240°, 300°, 360°. ∴ the other angles of symmetry = 120°, 180°, 240°, 300° and 360°.

5. In a figure, 60° is an angle of symmetry. The figure has two angles of symmetry less than 60°. What is its smallest angle of symmetry?

SOLUTION 60° must be a multiple of the smallest angle a, and there must be exactly two angles of symmetry smaller than 60°, i.e. a and 2a, with 3a = 60°. So a = 60° ÷ 3 = 20°. (Check: angles 20°, 40° are the two less than 60°, and 60° = 3 × 20° is indeed an angle of symmetry.) ∴ the smallest angle of symmetry = 20°.

6. Can we have a figure with rotational symmetry whose smallest angle of symmetry is: a. 45°? b. 17°?

SOLUTION The smallest angle of symmetry must divide 360° exactly (be a factor of 360). a. Yes — 360° ÷ 45° = 8 (a whole number), so 45° can be the smallest angle of symmetry. b. No — 360° ÷ 17° is not a whole number, so 17° cannot be the smallest angle of symmetry.

7. This is a picture of the new Parliament Building in Delhi. a. Does the outer boundary of the picture have reflection symmetry? If so, draw the lines of symmetries. How many are they? b. Does it have rotational symmetry around its centre? If so, find the angles of rotational symmetry.

SOLUTION The outer boundary of the new Parliament Building is a triangular (three-sided) shape. a. Yes, it has reflection symmetry — it has 3 lines of symmetry (one from each corner to the middle of the opposite side). b. Yes, it has rotational symmetry. The angles of rotational symmetry are 120°, 240° and 360° (order 3, like an equilateral triangle).

8. How many lines of symmetry do the shapes in the first shape sequence in Chapter 1, Table 3, the Regular Polygons, have? What number sequence do you get?

SOLUTION A regular polygon with n sides has exactly n lines of symmetry:
Regular PolygonNo. of lines of symmetry
Triangle3
Quadrilateral (square)4
Pentagon5
Hexagon6
Heptagon7
Octagon8
Nonagon9
Decagon10
SOLUTION (contd.) ∴ the number sequence is 3, 4, 5, 6, 7, 8, 9, 10, … — the counting (natural) number sequence.

9. How many angles of symmetry do the shapes in the first shape sequence in Chapter 1, Table 3, the Regular Polygons, have? What number sequence do you get?

SOLUTION A regular polygon with n sides also has exactly n angles of symmetry (order n). Triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, … ∴ the number sequence is again 3, 4, 5, 6, 7, 8, … — the same counting-number sequence as the lines of symmetry.

10. How many lines of symmetry do the shapes in the last shape sequence in Chapter 1, Table 3, the Koch Snowflake sequence, have? How many angles of symmetry?

SOLUTION The Koch snowflake is built on an equilateral triangle and quickly becomes six-fold symmetric. Number of lines of symmetry: 3, 6, 6, 6, 6, … (the first shape is a triangle with 3, every later shape has 6). Number of angles of symmetry: 3, 6, 6, 6, 6, … — the same sequence.

11. How many lines of symmetry and angles of symmetry does Ashoka Chakra have?

SOLUTION The Ashoka Chakra has 24 equally-spaced spokes. Number of lines of symmetry = 24 (one through each spoke / gap). Number of angles of symmetry = 24 (smallest angle 360° ÷ 24 = 15°), so it has order 24.

Common Mistakes to Avoid

Watch out for these

  • Thinking a figure that “looks symmetric” must have a line of symmetry — a pinwheel/windmill has rotational symmetry but no line of symmetry.
  • Saying a triangle can have exactly two lines of symmetry — a triangle can only have 0, 1 or 3 lines of symmetry.
  • Treating a non-square rectangle’s diagonal as a line of symmetry — it is not; a non-square rectangle has only 2 lines (vertical and horizontal).
  • Forgetting that 360° is always an angle of symmetry, so it should be included when listing angles.
  • Counting 360° alone as “rotational symmetry” — a figure has rotational symmetry only if it has an angle of symmetry strictly less than 360°.
  • Choosing a smallest angle of symmetry that is not a factor of 360 (e.g. 17°) — the smallest whole-number angle must divide 360 exactly.

Practice MCQs & Assertion–Reason

1. A line that folds a figure into two exactly overlapping halves is called a:

(a) centre of rotation    (b) line of symmetry    (c) angle of symmetry    (d) diameter

2. How many lines of symmetry does a square have?

(a) 1    (b) 2    (c) 4    (d) 8

3. How many lines of symmetry does an equilateral triangle have?

(a) 0    (b) 1    (c) 2    (d) 3

4. Which angle is always an angle of symmetry for every figure?

(a) 90°    (b) 180°    (c) 270°    (d) 360°

5. The smallest angle of symmetry of a figure with 6 equally-spaced radial arms is:

(a) 45°    (b) 60°    (c) 72°    (d) 90°

6. If 60° is the smallest angle of symmetry, the order of rotational symmetry is:

(a) 3    (b) 4    (c) 6    (d) 12

7. Which of these can be the smallest angle of symmetry of a figure?

(a) 17°    (b) 25°    (c) 45°    (d) 50°

8. How many lines of symmetry does the Ashoka Chakra have?

(a) 12    (b) 18    (c) 24    (d) 36

9. For a circle, the number of lines of symmetry (diameters) is:

(a) 0    (b) 2    (c) 4    (d) infinitely many

10. Which figure has rotational symmetry but no line of symmetry?

(a) equilateral triangle    (b) square    (c) parallelogram    (d) kite

Answer key: 1-(b), 2-(c), 3-(d), 4-(d), 5-(b), 6-(c), 7-(c), 8-(c), 9-(d), 10-(c).

For each Assertion–Reason question, choose: (A) Both Assertion and Reason are true and the Reason is the correct explanation of the Assertion; (B) Both are true but the Reason is not the correct explanation; (C) Assertion is true but Reason is false; (D) Assertion is false but Reason is true.

A-R 1. Assertion: A square has 4 lines of symmetry.

Reason: A square can be folded along its vertical, horizontal and both diagonal lines so that the halves overlap.

A-R 2. Assertion: 360° is an angle of symmetry for every figure.

Reason: A full turn of 360° always brings a figure back to its original position.

A-R 3. Assertion: 17° can be the smallest angle of symmetry of a figure.

Reason: The smallest angle of symmetry must be a factor of 360.

A-R 4. Assertion: A non-square rectangle’s diagonal is a line of symmetry.

Reason: A non-square rectangle has exactly 2 lines of symmetry.

A-R 5. Assertion: A pinwheel (windmill) has rotational symmetry but no line of symmetry.

Reason: Rotational symmetry and reflection symmetry are independent — a figure can have one without the other.

Answer key: 1-(A), 2-(A), 3-(D), 4-(D), 5-(A).

Quick Revision Summary

  • A figure has symmetry when parts repeat in a definite pattern; the cloud has none.
  • A line of symmetry folds a figure into two exactly overlapping (mirror) halves; this is also called reflection symmetry.
  • A square has 4 lines of symmetry, an equilateral triangle 3, a regular hexagon 6; a regular n-gon has n lines.
  • A triangle can have only 0, 1 or 3 lines of symmetry — never exactly 2.
  • Rotational symmetry: a figure looks the same after turning by an angle of symmetry about the centre of rotation; 360° is always one.
  • All angles of symmetry are multiples of the smallest angle; the order = 360° ÷ smallest angle.
  • A whole-number smallest angle must be a factor of 360 (45° yes, 17° no). A circle has infinitely many lines and angles of symmetry.

How to score full marks in this chapter

For line-of-symmetry questions, mentally fold the figure and only draw a line where the two halves coincide exactly. For rotational symmetry, always start from the smallest turn that matches, then list its multiples up to 360° — and remember to include 360°. Use order = 360° ÷ smallest angle, and check that any whole-number smallest angle is a factor of 360. State the rule you use (e.g. “a regular n-gon has n lines of symmetry”) so each step earns its mark.

Frequently Asked Questions

What is Class 6 Maths Ganita Prakash Chapter 9 about?

Chapter 9, Symmetry, covers two main ideas — the line of symmetry (reflection symmetry), where a figure folds into two matching halves, and rotational symmetry, where a figure looks the same after turning about a centre of rotation. It also covers angles of symmetry, order of rotation, and the symmetries of squares, triangles, hexagons, circles and the Ashoka Chakra.

How many lines of symmetry does a square have?

A square has 4 lines of symmetry — the vertical line, the horizontal line and the two diagonals. Folding along any of these makes the two halves overlap exactly.

What is the difference between line symmetry and rotational symmetry?

Line (reflection) symmetry means a figure can be folded along a line so the two halves match. Rotational symmetry means a figure looks exactly the same after being turned by some angle (less than 360°) about a fixed centre. A figure can have one, both, or neither — a windmill has rotational symmetry but no line of symmetry.

Are these Class 6 Maths Ganita Prakash Chapter 9 solutions free?

Yes. All solutions are free and follow the official NCERT Ganita Prakash textbook for the 2026–27 session, with answers verified against the book’s answer key.

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