NCERT Solutions for Class 6 Maths Ganita Prakash Chapter 9 are designed according to the updated CBSE Class 6 Maths syllabus helping students build a strong understanding of the topic Symmetry. These solutions explain key concepts like lines of symmetry, symmetrical figures, and patterns clearly and step-by-step.
By practicing questions from Class 6 Maths Chapter 9, students can improve their visual and logical thinking skills.
Class 6 Maths Ganita Prakash Chapter 9 Symmetry
Class 6 Maths Chapter 9 Symmetry introduces students to the concept of balanced and proportionate figures, where one part is the mirror image of the other. In this chapter students learn about line of symmetry, symmetrical shapes and how to identify or draw symmetrical figures.
The chapter also explores the practical use of symmetry in patterns, art, and nature. Through simple activities and visual understanding, learners grasp how symmetry plays a role in design and everyday objects. This chapter builds a strong foundation for geometry and helps students develop visual and spatial reasoning skills.
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
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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
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Regular hexagon (6 sides) → 6 lines
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Regular heptagon (7 sides) → 7 lines
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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).
NCERT Solutions for Class 6 Maths Chapter 9 PDF Download
Students can download the NCERT Class 6th Maths Chapter 9 PDF from the link given below for easy and offline access to solutions. NCERT Solutions for Class 6 Maths Ganita Prakash Chapter 9 PDF Download includes accurate and step-by-step answers to all textbook questions based on the topic Symmetry.
