NCERT Solutions Class 6 Maths Ganita Prakash Chapter 9 Symmetry

Have you ever seen how a butterfly’s wings look exactly the same on both sides? Or how a human face looks similar from left and right? This balance is called symmetry.

Many students find geometry confusing at first. When they move from simple shapes to new concepts, they may struggle to find where a shape can be folded into two equal parts. That is why having proper symmetry class 6 Ganita Prakash solutions is important to understand the topic clearly.

The main aim of Class 6 Ganita Prakash Chapter 9 Symmetry is to improve your spatial reasoning. Spatial reasoning means understanding shapes, patterns, and positions around you. Symmetry is present in nature, buildings, art, and many objects around us. In this guide, we provide clear and step-by-step Ganita Prakash class 6 symmetry solutions so that you can understand line symmetry and mirror reflection easily and score well in exams.

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Symmetry Class 6th Maths Chapter 9 Question and Answers

Below are the solutions for the NCERT Solutions for Class 6 Maths Ganita Prakash Chapter 9 Symmetry.

These solutions include step-by-step answers to help students understand the concepts of symmetry, line of symmetry and symmetrical figures.

Practicing these questions will strengthen your understanding and improve your performance in exams. 

9.1 Line of Symmetry Figure it Out (Page 219)

Question 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:
(a) Yes, there are six lines of symmetry.

(b) Yes, there is one line of symmetry.


(c) There are no lines of symmetry in the picture of clouds.

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

Solution:

 

Question 3.
Draw the following.
(a) A triangle with exactly one line of symmetry
Solution:

An isosceles triangle has one line of symmetry

(b) A triangle with exactly three lines of symmetry
Solution:

An equilateral triangle has one line 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 scalene triangle has no lines of symmetry.
No, it is not possible to draw a triangle with exactly two lines of symmetry.

Question 4.
Draw the following. In each case, the figure should contain at least one curved boundary.
(a) A figure with exactly one line of symmetry
Solution:

(b) A figure with exactly two lines of symmetry
Solution:

(c) A figure with exactly four lines of symmetry
Solution:

9.2 Rotational Symmetry Figure it Out (Page 238)

Question 1.
Color the sectors of the circle below so that the figure has
(a) 3 angles of sjjmmetry
(b) 4 angles of symmetry

Solution:
(a) Will look same after every rotation of 120°.

(b) Will look same after every rotation of 90°.

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

Question 3.
Draw wherever possible, a rough sketch of
(a) a triangle with atleast two lines of symmetry and atleast 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) A triangle with at least two lines of symmetry and at least two angles of symmetry.
Solution:
An equilateral triangle is the best example.

• It has 3 lines of symmetry (more than 2).

• It has 3 equal angles, which means it has rotational symmetry of order 3 and each angle acts symmetrically.
  So, it satisfies the condition.

(b) A triangle with only one line of symmetry but no rotational symmetry.
Solution:
An isosceles triangle (that is not equilateral) fits here.

• It has only one line of symmetry (from the vertex to the base's midpoint).

• It does not have rotational symmetry (it does not look the same when rotated other than full 360°).
  So, it satisfies the condition.

(c) A quadrilateral with rotational symmetry but no reflection symmetry.
Solution:
A parallelogram (that is not a rectangle or rhombus) works.

• It has rotational symmetry of order 2 (180° rotation).

• It does not have reflection symmetry (no line divides it into mirror halves).
  So, it satisfies the condition.

(d) A quadrilateral with reflection symmetry but not having rotational symmetry.
Solution:
A kite (where adjacent sides are equal but not all sides) is an example.

• It has one line of symmetry (vertical).

• It does not have rotational symmetry (it doesn't map onto itself at 180°).
  So, it satisfies the condition.

Question 4.

In a figure, 60° is the smallest angle of symmetry. What are the other angles of symmetry of this figure?
Solution:
It will also look the same by rotating at an angle of 120°, 180°, 240°, 300°, and 360° as these are the multiples of 60°.

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?
Solution:
Smallest angle of symmetry = 60° ÷ 3 = 20°.

Question 6. 

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

Solution:

To check if a figure can have a certain angle of rotational symmetry, we see if 360° is exactly divisible by that angle. This is because a full rotation is 360°, and symmetry means the shape looks the same after each turn.

(a) 45°

Let’s divide:
360° ÷ 45° = 8

Since 8 is a whole number, it means a figure can rotate 45° at a time and still look the same each time.
So, yes, 45° can be the smallest angle of symmetry of a figure.
(Example: a regular octagon has this property.)

(b) 17°

Now divide:
360° ÷ 17° = 21.176...

Since the result is not a whole number, you can’t evenly rotate the shape through 17° steps to complete a full 360°.
So, no, 17° cannot be the smallest angle of symmetry.

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?

Solution:
In Table 3 of Chapter 1, the shapes listed are regular polygons, such as:

• Equilateral triangle

• Square

• Regular pentagon

• Regular hexagon

• Regular heptagon

• Regular octagon, etc.

Each regular polygon has as many lines of symmetry as it has sides.

So, the number of lines of symmetry is:

• Equilateral triangle (3 sides) → 3 lines of symmetry

• Square (4 sides) → 4 lines

• Regular pentagon (5 sides) → 5 lines

• Regular hexagon (6 sides) → 6 lines

• Regular heptagon (7 sides) → 7 lines

• Regular octagon (8 sides) → 8 lines

Therefore, the number sequence is:
3, 4, 5, 6, 7, 8, ...

This is the natural number sequence starting from 3, where each number tells the lines of symmetry of a regular polygon with that many sides.

Question 9.
How many lines of symmetry do the shapes in the first shape sequence in Chapter 1, Table 3, the Koch Snowflake sequence, have? What angle of symmetry?
Solution:

The triangular shape has 3 lines of symmetry and 3 angles of symmetry.
In six-pointed stars, lines of symmetry are 12 and the angle of symmetry is 6.
The lines of symmetry and angle of symmetry for the rest three figures are the same as six-pointed stars.

Question 10.
How many lines of symmetry and angles of symmetry does Ashoka Chakra have?

Solution:
The Ashoka Chakra has 24 spokes spread equally.
24 spokes make 12 pairs.
Line through an opposite pair is a line of symmetry.
Hence, there are 12 lines of symmetry.
Smallest angle of symmetry = 360° ÷ 2 = 30°.
Other angles of symmetry are its multiple up to 360.
Other angles are 60°, 120°, 150°, ………… , 360°. (12 angles in all).

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What is Symmetry in Ganita Prakash?

In symmetry class 6 Ganita Prakash, a figure is called symmetrical if a line can divide it into two exactly equal parts. If you fold the shape along that line, both sides will match perfectly.

Key Concepts to Remember

• Line of Symmetry:
  This is the imaginary line that divides a shape into two equal halves. It is also called the axis of symmetry.

• Mirror Reflection:
  When you look into a mirror, your image looks similar but reversed. That is reflection, and it creates symmetry.

• Types of Symmetry:
  Some shapes have only one line of symmetry. Some have more. A circle is special because it has unlimited lines of symmetry.

Detailed Class 6 Maths Ganita Prakash Chapter 9 Solutions

To help you with your homework, we have broken down the core problems found in the class 6 Ganita Prakash Chapter 9 solutions.

 Identifying Lines of Symmetry

A major part of class 6 symmetry Ganita Prakash involves finding how many ways a shape can be divided.

• Equilateral Triangle: Has 3 lines of symmetry.

• Square: Has 4 lines of symmetry (Vertical, Horizontal, and two Diagonals).

• Regular Hexagon: Has 6 lines of symmetry.

Mirror Images and Reflection

In the Ganita Prakash class 6 symmetry solutions, you will often find questions where half of a picture is given and you have to complete the other half.

• Simple Rule:
  The image in the mirror is always at the same distance from the mirror line as the original object.

• Example:
  When you stand  in front of a mirror. Your reflection looks just like you but reversed. In the same way, if you draw the letter ‘B’ next to a vertical mirror line, the image will look flipped to the other side..

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Summary Table: Symmetry in Regular Polygons

Here is a quick table if you want to have a quick revision table for symmetry class 6 Ganita Prakash solutions:

Why Use Ganita Prakash Class 6 Symmetry Solutions?

If you use Class 6 Maths Ganita Prakash Chapter 9 solutions, you will be able to understand the symmetry better, and it also makes the chapter much easier. The solutions are easy to understand, concept-focused, and ideal for revision, homework help and exam preparation. Students can easily understand symmetry with the help of clear steps and examples. 

Tips to Learn Symmetry

• The Paper-Fold Test:
  Draw the shape, cut it out, and fold it. If both sides match perfectly, you have found a line of symmetry.

• Use a Mirror:
  Place a small mirror along the line. If the reflection completes the shape correctly, the line is correct.

• Watch the Vertices:
  In regular polygons, lines of symmetry usually pass through the corners or the middle of opposite sides

Read More: CBSE Class 6 Syllabus and Exam Pattern

NCERT Class 6 Maths Ganita Prakash Chapter 9 FAQs

1. How many lines of symmetry does a circle have?

In symmetry class 6 Ganita Prakash, a circle is unique because it has an infinite number of lines of symmetry. Any line passing through the centre of the circle will divide it into two equal halves.

2. What is the difference between a horizontal and vertical line of symmetry?

A horizontal line of symmetry runs from left to right (like the letter 'E'), while a vertical line runs from top to bottom (like the letter 'A'). Some shapes, like the letter 'H', have both!

3. Can a shape have no lines of symmetry?

Yes! Scalene triangles or irregular shapes often have zero lines of symmetry. These are called "asymmetrical" shapes in class 6 symmetry Ganita Prakash.

4. Is reflection the same as symmetry?

Reflection is the process that creates symmetry. The object and its mirror image together form a symmetrical pattern, with the mirror acting as the line of symmetry.

5. Where can I download class 6 Ganita Prakash Chapter 9 solutions?

You can find comprehensive, printable class 6 Maths Ganita Prakash chapter 9 solutions on the Physics Wallah (PW) website, tailored specifically for Class 6 students.