Symmetry Class 6 Solutions Question Answer

By using Ganita Prakash Book Class 6 Solutions and Chapter 9 Symmetry Class 6 NCERT Solutions Question Answer, students can improve their problem-solving skills.

Class 6 Maths Chapter 9 Symmetry Solutions

Symmetry Class 6 Solutions Questions and Answers

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 the picture of the cloud?



Solution:
Yes, in the pictures of the Taj Mahal and Gopuram, we could see a line of symmetry. They are identical about a line that is both sides completely overlapping each other. The picture of clouds is non-symmetrical.

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

Solution:

9.1 Line of Symmetry Figure it Out (Page no. 223 – 230)

Punching Game
The fold is a line of symmetry. Punch holes at different locations of folded square sheet of paper using a punching machine and create different symmetric patterns.

Question 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:

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

Solution:

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.

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

Solution:

Question 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 fiures in the centre satisfy both the properties of a square.
Solution:
Do it yourself

Question 6.
How many lines of symmetry do these shapes have?
(i)

Solution:

(ii) A triangle with equal sides and equal angles.

Solution:

There are 3 lines of symmetry.

(iii) A hexagon with equal sides and equal angles.

Solution:

There are 6 lines of symmetry.

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


Solution:

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

Solution:

Question 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:


No, drawing a triangle with exactly two lines of symmetry is not possible.

Question 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:

Question 11.
Copy the following on squared paper. Complete them so that the pink 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:

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

Solution:

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.

Solution:

9.2 Rotational Symmetry Figure it Out (Page 235 – 236)

Question 1.
Find the angles of symmetry for the given figures about the point marked.

Solution:
(a) The given figure comes to its original position after rotation of 90°, 180°, 270° and 360°. Thus, the angles of symmetry are 90°, 180°, 270° and 360°.

(b) The figure comes back to its original shape only after 3600 rotation. So, the angle ofsymmetry is 3600.

(c) The figure comes back to its original shape when we rotate it about 180° and 360°. Thus, the angle of symmetry are 180° and 360°.

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

Solution:

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

Solution:
Do it yourself

9.2 Rotational Symmetry Figure it Out (Page 238 – 239)

Question 1.
Colour the sectors of the circle below so that the figure has (i) 3 angles of symmetry, (ii) 4 angles of symmetry and (iii) what are the possible numbers of angles of symmetry you can obtain by colouring the sectors in different ways?

Solution:
(i) 3 angles of symmetry

(ii) Four angles of symmetry

(iii) Possible angle of symmetry are 30°, 60°, 90°, 180°, 360°. Hence, the required possible number of angles of symmetry is 5.

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

Question 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.
Solution:

(b) A triangle with only one line of symmetry but not having rotational symmetry.
Solution:

(c) A quadrilateral with rotational symmetry but no reflction symmetry.
Solution:

(d) A quadrilateral with reflction symmetry but not having rotational symmetry.
Solution:

Question 4.
In a figure, 60° is the smallest angle of symmetry. What are the other angles of symmetry of this figure?
Solution:
If 60° is the smallest angle of symmetry, then the other angles of symmetry are the multiples of 60° less than or equal to 360°, i.e., 120°, 180°, 240°, 300°, 360°.

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:
30°, 15°

Question 6.
Can we have a figure with rotational symmetry whose smallest angle of symmetry is
(a) 45°
(b) 17°
Solution:
(a) 45° is a factor of 360°, so the figure will have rotational symmetry of order more than 1 and there would be 8 rotations.
(b) 17° is not a factor of 360°, so the figure will not have rotational symmetry of order of more than 1.

Question 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 there?
(b) Does it have rotational symmetry around its center? If so, find the angles of rotational symmetry.
Solution:
(a) Yes

(b) Yes, angles of rotational symmetry are 120°, 240° and 360°.

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

Solution:

3 sided regular polygon ( equilateral triangle) has 3 lines of symmetry
4 sided regular polygon ( square) has 4 lines of symmetry
5 sided regular polygon ( regular pentagon) has 5 lines of symmetry
6 sided regular polygon ( regular hexagon) has 6 lines of symmetry We observe the following pattern:
Number of sides in a regular polygon*= number of lines of symmetry. Number sequence : 3, 4, 5, 6, 7, ……………………….

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?

Solution:
Do Yourself

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?

Solution:

There are 3 lines of symmetry and when we rotate it about 120°, 240° and 360°, we get its original shape. Thus, there are 3 angles of symmetry (120°, 240° and 360°).

In figures 2, 3 and 4, there are six lines of symmetry Also when we rotate them about 60°, 120°, 180°. 240°. 300° and 360°, we get their original shape. Thus, angle of symmetry, these figures have is 6.

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

Solution:
Do Yourself