---
title: "NCERT Solutions for Class 6 Maths Chapter 9 Symmetry (2026-27)"
url: https://www.swavid.com/maths/class/6/chapter/symmetry/ncert-solutions
dateModified: 2026-10-07T14:54:07+00:00
---

# NCERT Solutions for Class 6 Maths Chapter 9 Symmetry (2026-27)

This chapter's questions cover concepts of symmetry, including lines of symmetry for various geometric shapes, paper folding and cutting, reflection symmetry, and rotational symmetry.

Free PDF (16 pages): https://www.swavid.com/api/seo/pdf/ncert/maths/class-6/swavid-ncert-solutions-class-6-maths-chapter-9-symmetry-04e44dc149.pdf

## Figure it Out (Page 219)

### Question 1

*2 marks · Very short answer*

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**

1. The figures of the flower, rangoli, and butterfly have 6, 4, and 1 lines of symmetry respectively.
2. The pinwheel and cloud figures have no line of symmetry.

**Answer:** There are 6, 4, and 1 lines of symmetry in the flower, rangoli, and butterfly respectively, while the pinwheel and cloud have none.

> Common mistake: Confusing rotational symmetry with line of symmetry for the pinwheel.

### Question 2

*3 marks · Short answer*

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

**Solution**

1. A line of symmetry is a line that cuts a figure into two parts that exactly overlap when folded along that line.
2. Observing the given figures from left to right, the first figure (pentagon) has 1 vertical line of symmetry.
3. The second figure (rhombus) has 2 lines of symmetry (both diagonals).
4. The third figure (an L-shape), fourth figure, and fifth figure do not have any lines of symmetry as folding them does not result in overlapping halves.

**Answer:** The first figure has 1 line of symmetry, the second figure has 2 lines of symmetry, and the remaining figures have no lines of symmetry.

> Common mistake: Confusing diagonal lines of a rectangle or irregular shapes as lines of symmetry without checking if they form exact mirror halves.

## Figure it Out (Page 223)

### Question 1

*3 marks · Short answer*

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?

**Part a (1 mark)**

1. Observe the symmetry of the two holes in the unfolded square.
2. The fold is along the vertical or horizontal line of symmetry passing through the center.

Answer a: Vertical or horizontal line

**Part b (1 mark)**

1. Observe the two punched holes situated symmetrically across a diagonal of the square.
2. The paper was folded along the diagonal line of symmetry.

Answer b: Diagonal line

**Part d (1 mark)**

1. Examine the four holes placed near the corners of the unfolded square.
2. To get four holes from a single punch, the paper must be folded twice: first vertically and then horizontally (or vice versa).

Answer d: Folded vertically and then horizontally (or vice versa)

**Answer:** Figure (a) was folded vertically or horizontally, figure (b) along a diagonal, figure (c) horizontally or vertically, and figure (d) vertically and then horizontally or vice versa.

> Common mistake: Confusing diagonal folds with vertical or horizontal folds.

### Question 2

*3 marks · Short answer*

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

**Part a (1 mark)**

1. Locate the given hole on one side of the diagonal dotted line of symmetry.
2. Reflect the hole perpendicularly across the diagonal to find the matching position on the other side.

Answer a: Hole on the opposite side of the diagonal

**Part c (1 mark)**

1. Identify the vertical line of symmetry in the triangle.
2. Reflect the hole near the left edge across the vertical line to the right side.

Answer c: Hole reflected across the vertical axis

**Part e (1 mark)**

1. Note the circular boundary and the dotted line of symmetry passing through the center.
2. Reflect the given hole across the diameter to locate the position of the other hole.

Answer e: Hole on the opposite end of the diameter

**Answer:** The other hole is obtained by reflecting the given hole across the dotted line of symmetry.

> Common mistake: Placing the reflected hole at an incorrect distance from the line of symmetry.

### Question 3

*3 marks · Short answer*

Here are some questions on paper cutting. Consider a vertical fold. We represent it this way:

**Solution**

1. A vertical fold brings the left and right halves of a sheet of paper together.
2. It is represented by a rectangular strip with an arrow showing the direction of the fold.
3. The fold acts as a line of symmetry for subsequent cuts.

**Answer:** A vertical fold brings the two sides of the paper together along a vertical line of symmetry.

> Common mistake: Confusing the direction of vertical and horizontal folds.

### Question 4

*3 marks · Short answer*

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.

**Part a (1 mark)**

1. Observe the dotted lines along the folded vertical strip.
2. When the paper is opened, the cutouts reflect across the vertical line of symmetry to form a butterfly-like symmetric shape.

Answer a: A symmetric shape resembling butterfly wings

**Part b (2 marks)**

1. Note the triangular and diagonal cuts made on the folded paper.
2. Unfolding reveals a symmetric polygonal hole in the center.

Answer b: A symmetric geometric hole

**Answer:** When unfolded, the cutouts form symmetric shapes along the fold lines.

> Common mistake: Failing to account for both sides of the fold when predicting the shape.

### Question 5

*3 marks · Short answer*

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.

**Part a (1.5 marks)**

1. First fold the paper horizontally then vertically.
2. Cut a small square at the center where all sides have closed corners to get a square hole in the middle when unfolded.

Answer a: Fold horizontally then vertically, and cut a square at the center.

**Part b (1.5 marks)**

1. First fold the paper horizontally then vertically.
2. At the closed corner, make a slanting straight cut to get a square hole turned diagonally (diamond shape) when unfolded.

Answer b: Fold horizontally then vertically, and make a slanting cut at the closed corner.

**Answer:** The shapes are obtained by folding the paper horizontally then vertically, and making a straight cut at the center or the closed corner.

> Common mistake: Making cuts on the open edges instead of the closed folds.

### Question 6

*3 marks · Short answer*

How many lines of symmetry do these shapes have? 
a. 
b. A triangle with equal sides and equal angles. 
c. A hexagon with equal sides and equal angles.

**Part a (1 mark)**

1. Examine the given star polygon shape.
2. Count the lines passing through vertices and opposite indentations.
3. There are 4 lines of symmetry.

Answer a: 4 lines of symmetry

**Part b (1 mark)**

1. Consider an equilateral triangle (triangle with equal sides and equal angles).
2. Draw lines from each vertex to the midpoint of the opposite side.
3. There are 3 lines of symmetry.

Answer b: 3 lines of symmetry

**Part c (1 mark)**

1. Consider a regular hexagon (hexagon with equal sides and equal angles).
2. Count the lines joining opposite vertices and opposite sides' midpoints.
3. There are 6 lines of symmetry.

Answer c: 6 lines of symmetry

**Answer:** The number of lines of symmetry depends on the geometry of each shape.

> Common mistake: Counting only vertical and horizontal lines while ignoring diagonal or vertex-to-vertex lines.

### Question 7

*3 marks · Short answer*

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

**Solution**

1. Trace each given figure carefully onto paper.
2. Identify the lines along which each figure can be folded so that the two halves coincide exactly.
3. Draw the lines of symmetry as shown in the textbook solution (Fig. 9.7).

**Answer:** The lines of symmetry are drawn through the respective centres of the given figures.

> Common mistake: Drawing incorrect diagonal or oblique lines that do not divide the figure into exact mirror halves.

### Question 8

*3 marks · Short answer*

Find the lines of symmetry for the kolam below.

**Solution**

1. Observe the given complex kolam pattern carefully.
2. Locate the lines passing through the centre that divide the pattern into identical mirror halves.
3. Draw the vertical, horizontal, and diagonal lines of symmetry as shown in the textbook.

**Answer:** The kolam has multiple lines of symmetry passing through its central point.

> Common mistake: Missing diagonal lines of symmetry in circularly arranged patterns.

### Question 9

*3 marks · Short answer*

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?

**Part a (1 mark)**

1. Draw an isosceles triangle with two equal sides.
2. Draw the median from the vertex between the equal sides to the base.
3. This median acts as the single line of symmetry.

Answer a: An isosceles triangle with exactly one line of symmetry.

**Part b (1 mark)**

1. Draw an equilateral triangle with all three sides equal.
2. Draw lines from each vertex to the midpoint of the opposite side.
3. These three lines form the lines of symmetry.

Answer b: An equilateral triangle with exactly three lines of symmetry.

**Part c (1 mark)**

1. Draw a scalene triangle with all three sides of different lengths.
2. Check that no line can fold the triangle onto itself.
3. State that a triangle with exactly two lines of symmetry is not possible.

Answer c: A scalene triangle with no line of symmetry; a triangle cannot have exactly two lines of symmetry.

**Answer:** Triangles can have 1, 3, or 0 lines of symmetry, and it is impossible to draw a triangle with exactly 2 lines of symmetry.

> Common mistake: Assuming all triangles have lines of symmetry.

### Question 10

*3 marks · Short answer*

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.

**Part a (1 mark)**

1. Draw a shape resembling a bell or tear-drop containing a curved boundary.
2. Draw a single vertical line passing down the middle.
3. Verify that both halves overlap completely upon folding along this line.

Answer a: A figure with a curved boundary and exactly one line of symmetry.

**Part b (1 mark)**

1. Draw an oval or capsule-like shape with curved ends.
2. Draw both a vertical and a horizontal line through the centre.
3. Verify that these two perpendicular lines are the only lines of symmetry.

Answer b: A figure with a curved boundary and exactly two lines of symmetry.

**Part c (1 mark)**

1. Draw a symmetrical four-petalled flower or a curved cross shape.
2. Draw vertical, horizontal, and two diagonal lines through the centre.
3. Verify that all four lines divide the figure into identical overlapping parts.

Answer c: A figure with a curved boundary and exactly four lines of symmetry.

**Answer:** Figures containing curved boundaries with exactly 1, 2, and 4 lines of symmetry can be constructed.

> Common mistake: Omitting the curved boundary requirement specified in the question.

### Question 11

*3 marks · Short answer*

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.

**Solution**

1. Copy the given squared paper drawings labeled (b) to (f) carefully.
2. Use the blue line as the axis of reflection (line of symmetry).
3. Plot corresponding points at equal perpendicular distances on the opposite side of the blue line and connect them to complete the figure.

**Answer:** The figures are completed symmetrically across the given blue line.

> Common mistake: Counting grid squares incorrectly while reflecting points across a diagonal or horizontal line.

### Question 12

*3 marks · Short answer*

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**

1. Copy the given drawings (a) to (f) along with the two intersecting blue lines of symmetry.
2. Reflect the existing partial drawing across the first blue line.
3. Reflect the resulting shape across the second blue line to complete the symmetrical figure in all four quadrants.

**Answer:** The figures are completed such that both blue lines serve as lines of symmetry.

> Common mistake: Failing to reflect across both axes symmetrically, resulting in an asymmetrical completion.

### Question 13

*3 marks · Short answer*

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**

1. Observe the given partial figure and the dotted line of symmetry on the dot grid.
2. Draw two more line segments on the opposite side of the line of symmetry such that each point and line is reflected symmetrically.
3. Verify that folding along the line of symmetry makes the two halves completely overlap.

**Answer:** The shapes are completed by drawing two more lines to form figures symmetric about the given dotted line.

> Common mistake: Drawing lines incorrectly by not mirroring the exact grid distances from the line of symmetry.

## Figure it Out (Page 235)

### Question 1

*3 marks · Short answer*

Find the angles of symmetry for the given figures about the point marked •.

**Part a (1 mark)**

1. The figure is a cross shape with 4 radial arms, which repeats every quarter turn.
2. The angles of symmetry are multiples of $90^\circ$, giving $90^\circ, 180^\circ, 270^\circ, 360^\circ$.

Answer a: Angles of symmetry = $90^\circ, 180^\circ, 270^\circ, 360^\circ$

**Part b (1 mark)**

1. The figure is an asymmetrical line segment passing through the centre point.
2. It only matches its original position after a full turn, so the only angle of symmetry is $360^\circ$.

Answer b: Angle of symmetry = $360^\circ$

**Part c (1 mark)**

1. The figure is a straight line segment with perpendicular segments on opposite sides.
2. It matches its original position after a half turn and a full turn, giving angles of $180^\circ$ and $360^\circ$.

Answer c: Angles of symmetry = $180^\circ, 360^\circ$

**Answer:** The angles of symmetry are (a) $90^\circ, 180^\circ, 270^\circ, 360^\circ$, (b) $360^\circ$, and (c) $180^\circ, 360^\circ$.

> Common mistake: Forgetting to include $360^\circ$ as an angle of symmetry for every figure.

### Question 2

*3 marks · Short answer*

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

**Solution**

1. A figure has more than one angle of symmetry if its order of rotational symmetry is greater than 1.
2. The first figure (circle with perpendicular diameters), second figure (equilateral triangle split into three sectors), third figure (4-armed pinwheel), fourth figure (cross), and fifth figure (regular pentagram/star) all have more than one angle of symmetry.
3. Thus, all these five figures have more than one angle of symmetry.

**Answer:** The first, second, third, fourth, and fifth figures have more than one angle of symmetry.

> Common mistake: Confusing line symmetry with rotational symmetry.

### Question 3

*3 marks · Short answer*

Give the order of rotational symmetry for each figure:

**Part a (0.5 marks)**

1. Count the number of times the figure looks the same in one full turn of $360^\circ$.
2. The line segment looks the same 2 times, so its order of rotational symmetry is 2.

Answer a: Order of rotational symmetry = 2

**Part b (0.5 marks)**

1. Count the number of times the intersecting lines look the same in one full turn.
2. It coincides with itself 4 times, so its order is 4.

Answer b: Order of rotational symmetry = 4

**Part c (0.5 marks)**

1. Count the number of points on the star polygon.
2. The six-pointed star looks the same 6 times in a full turn, so its order is 6.

Answer c: Order of rotational symmetry = 6

**Part d (0.5 marks)**

1. Count the number of identical bent arms in the triskelion figure.
2. It looks the same 3 times in a full turn, so its order is 3.

Answer d: Order of rotational symmetry = 3

**Part e (0.5 marks)**

1. Count the number of identical arms on the cross shape.
2. It looks the same 4 times in a full turn, so its order is 4.

Answer e: Order of rotational symmetry = 4

**Part f (0.5 marks)**

1. Count the number of sides of the regular pentagon.
2. It coincides with itself 5 times in a full turn, so its order is 5.

Answer f: Order of rotational symmetry = 5

**Answer:** The orders of rotational symmetry are (a) 2, (b) 4, (c) 6, (d) 3, (e) 4, and (f) 5.

> Common mistake: Confusing the order of rotational symmetry with the number of lines of symmetry.

## True or False (Page 236)

### Question 1

*1 mark · True or false*

Every figure will have 360 degrees as an angle of symmetry.

**Solution**

1. When any figure is rotated by $360^\circ$, it always comes back to its original position.
2. Therefore, $360^\circ$ is always an angle of symmetry for every figure.

**Answer:** True

> Common mistake: Thinking that only figures with complex symmetry patterns have a $360^\circ$ angle of symmetry.

### Question 2

*1 mark · True or false*

If the smallest angle of symmetry of a figure is a natural number in degrees, then it is a factor of 360.

**Solution**

1. The angles of rotational symmetry are multiples of the smallest angle of symmetry.
2. Since $360^\circ$ is always an angle of symmetry, the smallest angle of symmetry must divide $360^\circ$ completely, making it a factor of $360$.

**Answer:** True

> Common mistake: Confusing factors of $360$ with multiples of the smallest angle of symmetry.

## Figure it Out (Page 238)

### Question 1

*3 marks · Case-based*

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?

**Part (i)**

1. Total number of sectors in the given circle is 12.
2. To obtain 3 angles of symmetry, we colour groups of sectors repeating after every $360^\circ / 3 = 120^\circ$ (or every 4 sectors).
3. Thus, colouring 4 adjacent sectors out of 12 gives 3 angles of symmetry.

Answer (i): Colour 4 adjacent sectors out of 12.

**Part (ii)**

1. Total number of sectors in the given circle is 12.
2. To obtain 4 angles of symmetry, we colour groups of sectors repeating after every $360^\circ / 4 = 90^\circ$ (or every 3 sectors).
3. Thus, colouring 3 adjacent sectors out of 12 gives 4 angles of symmetry.

Answer (ii): Colour 3 adjacent sectors out of 12.

**Part (iii)**

1. The total number of equal sectors is 12.
2. The number of angles of symmetry must divide 12 completely to form a symmetric repeating pattern around the centre.
3. Therefore, the possible numbers of angles of symmetry are the factors of 12, which are 1, 2, 3, 4, 6, and 12.

Answer (iii): 1, 2, 3, 4, 6, and 12

**Answer:** Sectors can be coloured to obtain 3 angles of symmetry, 4 angles of symmetry, and possible numbers of angles of symmetry that are factors of 12.

> Common mistake: Forgetting that the number of angles of symmetry obtained by colouring sectors must be a factor of the total number of sectors.

### Question 2

*3 marks · Short answer*

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

**Solution**

1. Recall figures that possess both lines of reflection symmetry and rotational symmetry.
2. Draw a regular hexagon and a figure with 4 radial arms (like a plus sign with equal arms).
3. State that both figures have lines of symmetry and rotational symmetry with an order greater than 1.

**Answer:** Regular hexagon and a figure with 4 radial arms

> Common mistake: Drawing a scalene triangle which has neither reflection nor rotational symmetry.

### Question 3

*3 marks · Case-based*

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.

**Part a**

1. An equilateral triangle has 3 lines of symmetry and 3 angles of symmetry.
2. Since $3 \ge 2$, an equilateral triangle satisfies the given conditions.

Answer a: An equilateral triangle.

**Part b**

1. An isosceles triangle that is not equilateral has exactly one line of symmetry along the median to the unequal side.
2. It has no rotational symmetry except for $360^\circ$, meaning it does not have rotational symmetry.

Answer b: An isosceles triangle (not equilateral).

**Part c**

1. A parallelogram (that is not a rectangle or rhombus) has no line of reflection symmetry.
2. However, it has rotational symmetry of order 2 with angles $180^\circ$ and $360^\circ$.

Answer c: A parallelogram.

**Part d**

1. An isosceles trapezoid has one line of symmetry passing through the midpoints of the parallel sides.
2. It does not have rotational symmetry.

Answer d: An isosceles trapezoid.

**Answer:** Sketches drawn according to the given symmetry conditions for triangles and quadrilaterals.

> Common mistake: Confusing line symmetry with rotational symmetry in quadrilaterals like parallelograms and trapezoids.

### Question 4

*3 marks · Short answer*

In a figure, $60^{\circ}$ is the smallest angle of symmetry. What are the other angles of symmetry of this figure?

**Solution**

1. Identify the smallest angle of symmetry as given, which is $60^\circ$.
2. Recall that the angles of symmetry are always the multiples of the smallest angle of symmetry.
3. List the multiples of $60^\circ$ up to $360^\circ$: $120^\circ, 180^\circ, 240^\circ, 300^\circ, 360^\circ$.

**Answer:** Other angles of symmetry = $120^\circ, 180^\circ, 240^\circ, 300^\circ, 360^\circ$

> Common mistake: Forgetting to include $360^\circ$ in the list of angles of symmetry.

### Question 5

*3 marks · Short answer*

In a figure, $60^{\circ}$ is an angle of symmetry. The figure has two angles of symmetry less than $60^{\circ}$. What is its smallest angle of symmetry?

**Solution**

1. State the given angle of symmetry as $60^\circ$.
2. Read that the figure has two angles of symmetry less than $60^\circ$, meaning the angles are formed by dividing $60^\circ$ equally.
3. Since there are two angles less than $60^\circ$, divide $60^\circ$ by 3 to find the smallest angle: $60^\circ \div 3 = 20^\circ$.

**Answer:** The smallest angle of symmetry = $20^\circ$

> Common mistake: Dividing by 2 instead of considering the three equal parts.

### Question 6

*3 marks · Short answer*

Can we have a figure with rotational symmetry whose smallest angle of symmetry is: 
a. $45^{\circ}$? 
b. $17^{\circ}$?

**Part a (1.5 marks)**

1. Check if $45^\circ$ is a factor of $360^\circ$ by dividing $360^\circ$ by $45^\circ$.
2. $360^\circ \div 45^\circ = 8$, which is a whole number, so such a figure is possible.

Answer a: Yes, as $360^\circ$ is a multiple of $45^\circ$

**Part b (1.5 marks)**

1. Check if $17^\circ$ is a factor of $360^\circ$ by dividing $360^\circ$ by $17^\circ$.
2. $360^\circ \div 17^\circ$ does not yield a whole number, so such a figure is not possible.

Answer b: No, as $360^\circ$ is not a multiple of $17^\circ$

**Answer:** (a) Yes, as $360^\circ$ is a multiple of $45^\circ$. (b) No, as $360^\circ$ is not a multiple of $17^\circ$.

> Common mistake: Assuming any arbitrary angle can be the smallest angle of rotational symmetry without checking if it divides $360^\circ$.

### Question 7

*3 marks · Short answer*

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.

**Part a (1 mark)**

1. Observe the outer boundary shape of the new Parliament Building from the figure in the textbook (Page 239).
2. Fold the shape along the lines passing through each vertex and the midpoint of the opposite side.
3. The outer boundary has reflection symmetry with 3 lines of symmetry.

Answer a: Yes, the outer boundary has 3 lines of symmetry.

**Part b (2 marks)**

1. Consider the centre of the outer boundary of the building.
2. Rotate the figure about its centre to find when it overlaps with itself.
3. The angles of rotational symmetry are multiples of $120^\circ$, which are $120^\circ, 240^\circ, 360^\circ$.

Answer b: Yes, it has rotational symmetry with angles $120^\circ, 240^\circ, 360^\circ$.

**Answer:** The outer boundary has 3 lines of reflection symmetry and rotational symmetry with angles $120^\circ, 240^\circ, 360^\circ$.

> Common mistake: Confusing the number of sides with the number of lines of symmetry in a regular polygon.

### Question 8

*3 marks · Short answer*

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**

1. Recall the shapes in the first shape sequence (Regular Polygons) from Chapter 1, Table 3: triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon.
2. A regular polygon of $n$ sides has $n$ lines of symmetry.
3. Thus, the number of lines of symmetry for the sequence are 3, 4, 5, 6, 7, 8, 9, 10, which forms a counting number sequence.

**Answer:** The number of lines of symmetry are 3, 4, 5, 6, 7, 8, 9, 10, forming a counting number sequence.

> Common mistake: Forgetting that a regular polygon has as many lines of symmetry as its number of sides.

### Question 9

*3 marks · Short answer*

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**

1. A regular polygon with $n$ sides has an order of rotational symmetry equal to $n$.
2. The smallest angle of symmetry is $\frac{360^\circ}{n}$, and the other angles are its multiples up to $360^\circ$.
3. The number sequence for the order of rotational symmetry of the regular polygons is 3, 4, 5, 6, 7, 8, 9, 10.

**Answer:** The number of angles of symmetry for the regular polygons are 3, 4, 5, 6, 7, 8, 9, 10, forming a counting number sequence.

> Common mistake: Listing only the smallest angle instead of counting the total number of angles of symmetry.

### Question 10

*3 marks · Short answer*

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**

1. Examine the shapes in the last shape sequence (Koch Snowflake sequence) from Chapter 1, Table 3.
2. Count the lines of symmetry for each shape in the sequence, which gives the sequence of numbers.
3. Count the angles of symmetry for each shape, which corresponds to the same values.

**Answer:** Number of lines of symmetry: 3, 6, 6, 6, 6; Number of angles of symmetry: 3, 6, 6, 6, 6.

> Common mistake: Assuming all steps in the snowflake sequence have an increasing number of symmetry lines without checking.

### Question 11

*3 marks · Short answer*

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

**Solution**

1. Observe the Ashoka Chakra from the figure in the textbook (Page 239) which has 24 equally spaced spokes.
2. Any line passing through the centre and bisecting opposite spokes acts as a line of reflection symmetry, giving 24 lines of symmetry.
3. Rotating the Ashoka Chakra by an angle of $\frac{360^\circ}{24} = 15^\circ$ and its multiples brings it back onto itself, giving 24 angles of symmetry.

**Answer:** The Ashoka Chakra has 24 lines of symmetry and 24 angles of symmetry.

> Common mistake: Confusing the number of spokes with the degree measure instead of counting total symmetry angles.

## Frequently asked questions

### How many total questions and exercises are in NCERT Solutions for Class 6 Maths Chapter 9 Symmetry?

This chapter in the new NCERT book for the 2026-27 session contains a total of 31 questions across multiple sections. You get 2 questions on page 219, 13 questions on page 223, 3 questions on page 235, 2 true or false questions on page 236, and 11 questions on page 238. SwaVid's free PDF and step-by-step solutions are on this page only to help you complete all these exercises easily.

### Which important topics and concepts are covered in the Class 6 Maths Chapter 9 questions?

The questions cover core concepts like the line of symmetry, completing figures on dot grids and squared paper, and counting lines of symmetry in regular and irregular shapes. Other advanced topics include angles of symmetry, order of rotational symmetry, and smallest angles of symmetry in circles and regular polygons. SwaVid's free PDF and step-by-step solutions are on this page only to help you master every single concept.

### Which question types are the hardest in this chapter and how should students approach them?

Questions involving rotational symmetry, angles of symmetry, and factors of 360 as the smallest angle of symmetry on pages 235 and 238 are often considered tricky by students. To approach them, first understand how a shape rotates about its center and identify the exact degree measure before counting the order of rotation. SwaVid's free PDF and step-by-step solutions are on this page only to guide you through these difficult problems.

### How can students write answers for full marks in Class 6 Maths Chapter 9 Symmetry exam questions?

To secure full marks, students must clearly define terms like the line of symmetry or rotational symmetry and state exact angles when dealing with regular polygons. Drawing neat diagrams with dotted lines for symmetry and showing proper working for multiples and factors of 360 will ensure maximum score. SwaVid's free PDF and step-by-step solutions are on this page only to show you the correct presentation method.

### Is the free PDF available for Class 6 Maths Chapter 9 Symmetry based on the new NCERT syllabus?

Yes, the complete chapter solutions aligned with the new NCERT book under the NCF 2023 framework for the 2026-27 session are ready for student use. SwaVid's free PDF and step-by-step solutions are on this page only so you can download and study offline without any hassle.

## Related pages

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