Symmetry Class 6 (Ganita Prakash)

Master Symmetry Class 6 (Ganita Prakash) with comprehensive NCERT Solutions, Practice Questions, MCQs, Sample Papers, Case Based Questions, and Video lessons.

NCERT Solutions

Symmetry Class 6 (Ganita Prakash) – NCERT Solutions

Each question below opens its complete step-by-step Teachoo solution.

Figure it out - Page 224 - 229

13 questions

Question 1

(a) 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?To find line of symmetry,
We join points, and draw a line perpendicular to it
Then, we check if it is line of symmetry
We fold the paper along the vertical line
Question 1 (b) 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?To find line of symmetry,
We join points, and draw a line perpendicular to it
Then, we check if it is line of symmetry
We fold the paper along the diagonal
Question 1 (c) 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?To find line of symmetry,
We join points, and draw a line perpendicular to it
Then, we check if it is line of symmetry
We fold the paper along the horizontal line
Question 1 (d) 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?To find line of symmetry,
We join points, and draw a line perpendicular to it
Then, we check if it is line of symmetry
We fold the paper vertically and then horizontally (or vice versa)

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Question 2

(a) Given the line(s) of symmetry, find the other hole(s):To find the other hole,
We draw a perpendicular of line of symmetry from the given hole
At an equal distance from 1st hole would be the other hole
Question 2 (b) Given the line(s) of symmetry, find the other hole(s):Answer:
Question 2 (c) Given the line(s) of symmetry, find the other hole(s):Answer:
Question 2 (d) Given the line(s) of symmetry, find the other hole(s):Question 2 (e) Given the line(s) of symmetry, find the other hole(s):Answer:

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Question 3

Here are some questions on paper cutting. Consider a vertical fold. We represent it this way: Similarly, a horizontal fold is represented as follows:Here, we are just shown how to represent Horizontal and Vertical Folds for the questions in Question 4 and 5

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Question 4

(a) 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.The paper is folded vertically. The cut is a zig-zag.
When opened, the hole will be a symmetrical bow-tie shape
Question 4 (b) 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.The paper is folded vertically. The cut is like an 'M' shape into fold.
When opened, the hole will look like a 'W' or a crown.
Question 4 (c) 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.Here
The paper is folded vertically, then horizontally.
Two squares are cut from the corner where all folded edges meet.
When opened, this will create a shape like
Question 4 (d) 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.Here
The paper is folded vertically.
Two rectangles are cut from the folded edge.
When opened, the hole will look like an "I-beam" or a dumbbell shape

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Question 5

(a) 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. Note: For the above two questions, check if the 4-sided figures in the centre satisfy both the properties of a square.To do this, we follow these steps
Fold the paper horizontally then vertically.
Now cut a small square at the center (all sides closed corner).
Fold Horizontally
Fold Vertically
Cut a small square from left corner (the folded corner)
Question 5 (b) Suppose you have to get each of these shapes with some folds and a single straight cut. How will you do it? (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.To do this, we follow these steps
Fold the paper horizontally then vertically.
Make a single straight, slanting cut across that corner. When unfolded, this will create a diamond or tilted square.
Fold Horizontally
Fold Vertically
Make a small slanting cut from left corner (the folded corner)

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Question 6

(a) How many lines of symmetry do these shapes have? Let’s do this one-by-one
Thus, this figure has 4 lines of symmetry
Thus, this figure has 8 lines of symmetry
Question 6 (b) A triangle with equal sides and equal angles.Let’s do this

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Question 7

Trace each figure and draw the lines of symmetry, if any:Let’s do this one by one
Figure 1
Thus, this figure has 1 line of symmetry
Figure 2
Thus, this figure has 2 lines of symmetry
Figure 3
Thus, this figure has 2 lines of symmetry
Figure 4
Thus, this figure has 2 lines of symmetry
Figure 5
Thus, this figure has 4 lines of symmetry
Figure 6
Thus, this figure has 2 lines of symmetry
Figure 7
Thus, this figure has 1 line of symmetry
Figure 8
Thus, this figure has 4 lines of symmetry

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Question 8

Find the lines of symmetry for the kolam below.Let’s enlarge the image and make lines of symmetry
Thus, this figure has 6 lines of symmetry

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Question 9

(a) Draw the following. (a) A triangle with exactly one line of symmetry. Isosceles Triangle has 1 Lines of Symmetry
Question 9 (b) Draw the following. (b) A triangle with exactly three lines of symmetry. Equilateral Triangle has 3 Lines of Symmetry
Question 9 (c) Draw the following. (c) A triangle with no line of symmetry. Scalene Triangle has 0 Lines of Symmetry
Question 9 (d) Is it possible to draw a triangle with exactly two lines of symmetry?It is not possible for a triangle to have two lines of symmetry

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Question 10

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

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Question 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.Let’s do this one by one
Question 11 (a) This one is already done for us
Basically we need to reflect the red shape across the blue line

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Question 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.Let’s do this one by one
Question 12 (a) Question 12 (b) Question 12 (c) Question 12 (d) Question 12 (e) Question 12 (f)

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Question 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.Question 13(a) Line of Symmetry
Question 13(b) Line of Symmetry
Question 13(c) Line of Symmetry
Question 13(d) Line of Symmetry
Question 13(e) Line of Symmetry
Question 13(f) Line of Symmetry
Question 13(f) Line of Symmetry

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Figure it out - Page 235

3 questions

Question 1

(a) Find the angles of symmetry for the given figures about the point marked •.To check its Rotational Symmetry, we
Mark its end points as 1, 2, 3, 4
At center marked •, we rotate it 90°
Thus, in 1 full turn (i.e 360°)
The figure is same as that of initial 4 times
So, we say that figure has
Rotational Symmetry of order 4

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Question 2

Which of the following figures have more than one angle of symmetry?Let’s do it one by one
Figure 1To check its Rotational Symmetry, we
Mark its end points as 1, 2, 3, 4
At center marked •, we rotate it 90°
Thus, in 1 full turn (i.e 360°)
The figure is same as that of initial 4 times
So, we say that figure has
Rotational Symmetry of order 4

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Question 3

Give the order of rotational symmetry for each figure:Let’s do it one by one
To check its Rotational Symmetry, we
Mark its end points as 1, 2
At center marked •, we rotate it 180°
Thus, in 1 full turn (i.e 360°)
The figure is same as that of initial 2 times
So, we say that figure has
Rotational Symmetry of order 2
This is same as last question

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Figure it out - Page 238, 239

11 questions

Question 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?The circle has 12 sectors.
This figure has 12 angles of symmetry (also called the "order" of symmetry)

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Question 2

Draw two figures other than a circle and a square that have both reflection symmetry and rotational symmetry.Let’s take
Lines of Symmetry = 4
Order of Rotational Symmetry = 4
Cross
Lines of Symmetry = 6
Order of Rotational Symmetry = 6
Flower Petal (with 6 petals)

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Question 3

(a) Draw, wherever possible, a rough sketch of: A triangle with at least two lines of symmetry and at least two angles of symmetry.Equilateral Triangle

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Question 4

In a figure, 60° is the smallest angle of symmetry. What are the other angles of symmetry of this figure?Since figure has 60° as smallest angle of symmetry
The other angle of symmetry would be its multiples

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Question 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?Since figure has two angles of symmetry less than 60°
It means 60° is the 3rd angle of symmetry

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Question 6

(a) Can we have a figure with rotational symmetry whose smallest angle of symmetry is: (a) 45°?The rule here
360° should be a multiple of Smallest angle of symmetry

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Question 7

(a) 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?Let’s enlarge it and check
Question 7 (b) This is a picture of the new Parliament Building in Delhi. (b) Does it have rotational symmetry around its centre? If so, find the angles of rotational symmetry.We mark its center and check rotational symmetry
Checking Rotational Symmetry

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Question 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?The table looks like
Regular Polygons – Lines of symmetry

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Question 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?The table looks like
Regular Polygons – Angles of symmetry

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Question 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?The table looks like
Koch Snowflake – Lines of Symmetry

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Question 11

How many lines of symmetry and angles of symmetry does Ashoka Chakra have?The Ashoka Chakra is the wheel in the center of the Indian flag. It has 24 spokes

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Why Learn This With Teachoo?

Learn Symmetry Class 6 with clear explanations of line symmetry, reflection symmetry, rotational symmetry and circle symmetry, together with Ganita Prakash solutions and practice resources on Teachoo.

Symmetry is Chapter 9 of the current NCERT Ganita Prakash Class 6 Mathematics book. A figure is symmetrical when its parts match through a specific transformation, such as reflection or rotation. Symmetry appears in flowers, butterflies, rangoli patterns, architecture, logos and geometrical figures.

The chapter teaches students to identify symmetry accurately rather than deciding only that a figure “looks balanced.” A valid symmetry must follow a testable rule.

Line Symmetry

A figure has line symmetry if it can be folded along a line so that its two parts overlap exactly. The fold line is called the line of symmetry or axis of symmetry.

Students identify figures with:

  • No line of symmetry

  • Exactly one line of symmetry

  • Two or more lines of symmetry

  • Infinitely many lines of symmetry, as in a circle

The orientation of the line matters. A figure may have a vertical line of symmetry but no horizontal line, or vice versa.

Figures with More Than One Line of Symmetry

Regular shapes often have multiple symmetry lines. A square has four; an equilateral triangle has three. Students examine how the number and position of symmetry lines depend on the figure’s properties.

They should verify every proposed line through mental or physical folding. A line passing through the centre is not automatically a symmetry line.

Reflection Symmetry

Reflection symmetry is often described as mirror symmetry. Every point on one side has a corresponding point on the other side at the same perpendicular distance from the mirror line.

Students complete half-drawn shapes and create reflected images on grids. Counting squares from the symmetry line prevents distorted reflections.

Generating Symmetrical Shapes

The chapter includes activities for producing shapes with specified lines of symmetry. Paper folding and cutting provide physical demonstrations, while grid drawings develop accuracy.

Students learn that adding one feature to a figure may destroy an existing symmetry unless the corresponding feature is added in the correct reflected position.

Rotational Symmetry

A figure has rotational symmetry if it matches its original position after a rotation of less than one complete turn.

Important ideas include:

  • Centre of rotation

  • Angle of rotation

  • Order of rotational symmetry

The order tells how many times the figure matches itself during one complete rotation. A square has rotational symmetry of order 4 because it matches at rotations of (90^\circ), (180^\circ), (270^\circ) and (360^\circ).

Symmetries of a Circle

A circle has infinitely many lines of symmetry because every diameter divides it into two matching halves. It also matches itself through rotation by any angle around its centre.

Designs drawn inside a circle may have fewer symmetries than the circle itself. Students must examine the complete figure, not only its outer boundary.

What Teachoo Covers

Teachoo’s chapter page includes the definition of symmetry, line symmetry, figures with multiple symmetry lines, reflection symmetry, generating symmetrical shapes, rotational symmetry, circle symmetry and the Ganita Prakash “Figure it Out” questions from pages 224–229, 235, 236 and 238–239.

What Students Should Be Able to Do

Students should be able to:

  • Define line and rotational symmetry.

  • Identify and draw lines of symmetry.

  • Verify a symmetry line through folding or reflection.

  • Complete reflected figures on a grid.

  • Create shapes with a specified number of symmetry lines.

  • Identify the centre and angle of rotation.

  • Determine the order of rotational symmetry.

  • Describe the line and rotational symmetries of a circle.

How to Study Symmetry

Use tracing paper, a small mirror or paper folding. These tools turn an abstract claim into a direct test. When working on a grid, reflect each vertex or key point separately rather than copying the overall appearance.

For rotational symmetry, mark one point on the figure and track where it moves. Test equal rotations until the complete figure, including internal markings, matches its starting position.

Why Is This Chapter Important?

Symmetry connects geometry with art, design, nature and transformations. Later, students use reflection and rotation in coordinate geometry, constructions, congruence and visual reasoning.

Common Mistakes in Symmetry Questions

A line through the centre is not necessarily a line of symmetry; the two sides must match point for point. Students sometimes check only the outer boundary and ignore colours, holes or internal markings. Those details are part of the figure and can remove a symmetry. In grid reflections, the image must be the same perpendicular distance from the mirror line. For rotational symmetry, a complete turn is always a match, but the chapter asks whether the figure matches before completing the full turn. Test the smallest successful rotation to determine the order correctly.

Deeper reasoning and concept connections

A student has understood Symmetry only when the idea can be moved between words, diagrams, examples and mathematical notation. Start with a concrete example, identify what changes and what remains fixed, represent the relationship clearly and then state the rule. This movement between representations is important because school and competency questions often present a familiar idea in an unfamiliar form.

The chapter should also be connected to earlier and later mathematics. Definitions supply the language, worked examples reveal the method, and mixed questions test whether the method can be selected without a hint. Instead of memorising the appearance of a solved question, ask what information triggered the method, which condition made it valid and how the answer could be checked. That makes learning transferable to later chapters rather than limited to one exercise.

How to solve unfamiliar and competency-based questions

Read the complete problem before calculating. Underline the quantities, conditions and command word—find, compare, construct, justify, estimate or prove. Rephrase the task in one sentence and choose a representation such as a table, labelled figure, number line, expression or graph. Solve in small steps, keeping units and labels visible.

For an application question, the final line must answer the situation, not only display a number. For an assertion–reason question, test the assertion and reason separately before deciding whether one explains the other. For an MCQ, eliminate options using definitions, signs, size estimates or boundary cases before performing long calculations. If the answer is visual, check it against the stated scale or construction conditions rather than the appearance of the drawing.

What complete mastery looks like

For Symmetry, a student should be able to define the central ideas in simple language, recognise them in different representations, solve routine questions accurately and explain the method used. They should also be able to correct a flawed solution, create an example satisfying given conditions and combine two ideas from the chapter in one problem. A reliable mastery test is to solve one direct question, one application question and one reasoning question without looking at notes, then explain all three aloud or in writing.

Keep a compact error log with four labels: concept, interpretation, calculation and presentation. Reattempt each error after a gap instead of rereading the answer immediately. Improvement comes from correcting the decision that caused the mistake, not from repeating questions whose method is already known.

Additional frequently asked questions

What should a student know before starting Symmetry?

Revise the definitions, number operations, diagrams or notation used at the beginning of the chapter. The prerequisite list should be short: if an earlier skill blocks progress, repair that skill with two or three focused questions and return to the chapter.

How can a student check an answer in Symmetry?

Use an independent check whenever possible: substitute the result, reverse the operation, estimate its size, compare it with the figure, test a simpler case or solve using another representation. A check should examine the mathematical condition, not merely repeat the same arithmetic.

How many questions are enough for strong preparation?

There is no fixed number. Stop counting questions and track coverage: every concept, every standard method, at least one mixed problem, one competency-based problem and every previously incorrect type should be solved independently. Ten varied, analysed questions are more valuable than fifty copied solutions.

How should Teachoo solutions be used without becoming dependent on them?

Attempt the question first and mark the exact step where progress stops. Read only enough of the solution to repair that step, close it and restart the question. Finally, solve a similar problem without help. This turns a solution into feedback rather than a substitute for thinking.

Frequently Asked Questions

What is a line of symmetry?

It is a line that divides a figure into two matching halves that overlap exactly when folded.

What is rotational symmetry?

A figure has rotational symmetry if it matches its original appearance after a rotation smaller than one full turn.

How many lines of symmetry does a circle have?

A circle has infinitely many lines of symmetry; every diameter is one.

Does Teachoo provide Class 6 Symmetry solutions?

Yes. The chapter provides explanations and solutions for the listed Ganita Prakash questions.

Choose a symmetry topic, test the figure through folding, reflection or rotation and then verify your conclusion with the solution.