Students can refer to BSE Odisha Class 6 Math Solution and Ganita Prakash Chapter 9 Symmetry Class 6 Question Answer to understand textbook questions step by step.
Class 6 Maths Chapter 9 Symmetry Solutions
Ganita Prakash Class 6 Chapter 9 Solutions
Class 6 Maths Ganita Prakash Chapter 9 Solutions Symmetry
Question 1.
For each of the following figures, identify the line(s) of symmetry if it exists.
Solution:
Question 2.
Given the line(s) of symmetry, find the other hole(s).
Solution:
Question 3.
Find the lines of symmetry for the kolam below.
Solution:
Question 4.
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:
(a)
One line of symmetry (Isosceles Triangle)
(b)
Three lines of symmetry
(Equilateral Triangle)
(c)
No line of symmetry (Scalene Triangle)
No, it is not possible to draw a triangle with exactly two lines of symmetry.
Question 5.
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:
Question 6.
Color 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 coloring the sectors in different ways?
Solution:
(i) Three angles of symmetry
(ii) Four angles of symmetry
(iii)
For 2 angles of symmetry, the angles are: 180°, 360°
For 3 angles of symmetry, the angles are: 120°, 240°, 360° 1
For 4 angles of symmetry, the angles are: 90°, 180°, 270°, 360°
For 6 angles of symmetry, the angles are: 60°, 120°, 180°, 240°, 300°, 360°
For 12 angles of symmetry, the angles are: 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°, 270°, 300°, 330°, 360°
Question 7.
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:
We know that the angles of symmetry of a figure having rotational symmetry about a point are multiples of the smallest angle of symmetry.
Let the smallest angle of symmetry be x. Then, the other angles of symmetry are 2x, 3x, 4x, 360°.
It is given that the figure has two angles of symmetry less than 60°. This means the third angle of symmetry is 60° itself.
∴ 3x = 60°
⇒ x = 20°
Hence, the smallest angle of symmetry is 20°.
Question 8.
How many lines of symmetry does the shape sequence, the Koch Snowflake sequence, have? Also, find numbers of angles of symmetry.
Solution:
The equilateral triangle has 3 lines of symmetry and 3 angles of symmetry.
In six-pointed star, lines of symmetry are 6 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.
InText Questions
Question 1.
Is there any other way to fold the square so that the two halves overlap? How many lines of symmetry does the square shape have?
Solution:
Yes, there are other ways to fold a square so that the two halves overlap exactly. This can be done along its lines of symmetry.
A square has 4 lines of symmetry:
(i) A vertical line (through the midpoints of the top and bottom sides),
(ii) A horizontal line (through the midpoints of the left Square and right sides),
(iii) A diagonal from the top-left to bottom-right corner,
(iv) A diagonal from the top-right to bottom-left corner.
So, we can fold the square along any of these 4 lines, and the two halves will perfectly overlap.
Question 2.
We saw that the diagonal of a square is also a line of symmetry. Let us take a rectangle that is not a square. Is its diagonal a line of symmetry?
Solution:
No, the diagonal of a rectangle is not a line of symmetry. Folding along the diagonal does not produce two matching parts.
So, while a square has both its diagonals as lines of symmetry (because they divide the square into two mirror-image triangles), a non-square rectangle does not have this property.
Question 3.
Consider a figure with radial arms having exactly 7 angles of symmetry. What will be its smallest angle of symmetry? Is the number of degrees a whole number in this case? If not, express it as a mixed fraction.
Solution:
When a figure has rotational symmetry with 7 angles of symmetry, it means it can be rotated around a central point and still look the same 7 times in a full 360° turn.
To find the smallest angle of symmetry, divide 360° by the number of symmetrical positions:
Smallest angle of symmetry = \(\frac{360^{\circ}}{7}\) = \(\left(51 \frac{3}{7}\right)^0\) which is not a whole number.
Mixed fraction form: \(\left(51 \frac{3}{7}\right)^0\)
Symmetry Class 6 Extra Questions
Symmetry Class 6 Very Short Question Answer
Question 1.
In the below figure, line l is the line of symmetry. Complete the figure to be symmetric about line /.
Solution:
The complete figure is as shown below.
Question 2.
For each of the following figure, identify the line(s) of symmetry if it exists.
Solution:
The line(s) of symmetry in the given figures are as follows:
Question 3.
In the following figures if the dotted lines represent the lines of symmetry, find the other hole(s).
Solution:
The other hole(s) in the given figures is(are) as follows:
Question 4.
Observe each of the following sequences of paper folding and cutting. Draw the pattern obtained after unfolding the paper.
Solution:
The pattern obtained after unfolding the paper in each case are as follows:
Question 5.
In the following figure, identify the line of symmetry.
Solution:
We know that a line that cuts a plane figure into two parts that exactly overlap when folded along that line is called a line of symmetry or axis of symmetry of the figure.
In the given figure, we can see the figure is symmetrical about the line l.
Thus, the line of symmetry of the given figure is line l.
Question 6.
In a figure, 60° is the smallest angle of symmetry. What are the other angles of symmetry of this figure?
Solution:
We know that the angles of symmetry of a figure having rotational symmetry about a point are multiples of the smallest angle of symmetry.
So, the other angles of symmetry are
2 × 60° = 120°,
3 × 60° = 180°,
4 × 60° = 240°,
5 × 60° = 300° and
6 × 60° = 360°.
Question 7.
In a given figure, 45° is the smallest angle of symmetry. What are the other angles of symmetry?
Solution:
We know that the angles of symmetry of a figure having rotational symmetry about a point are multiples of the smallest angle of symmetry,
So, the other angles of symmetry are 2 × 45° = 90°, 3 × 45° = 135°, 4 × 45° = 180°, 5 × 45° = 225°, 6 × 45° = 270°, 7 × 45° = 315° and 8 × 45° = 360°.
Symmetry Class 6 Short Question Answer
Question 1.
Copy the following on square paper. Complete them so the dotted line is a line of symmetry.
Solution:
To complete a figure so that it becomes symmetric about dotted line, let us take the mirror image of the figure with respect to the dotted line. Therefore, the completed figures are as follows:
Question 2.
Each of the following figures shows a piece of paper with punched holes. Copy these figures onto a plain sheet of paper and draw the line of symmetry such that, when the paper is folded along this line, the holes on one side match exactly with the holes on the other side.
Solution:
The line(s) of symmetry in the given figures are as follows:
Question 3.
In each letter of the English alphabet given below, find the number of line(s) of symmetry.
(i) U
(ii) E
(iii) I
(iv) V
Solution:
We know that a line of symmetry cuts a plane figure into two equal but flipped figures.
Question 4.
For each of the following figure, identify the line(s) of symmetry if it exists.
Solution:
The line(s) of symmetry in the given figures are as follows:
Question 5.
In the following figures if the dotted lines represent the lines of symmetry, find the other hole(s).
Solution:
We know that a line that cuts a plane figure into two parts that exactly overlap when folded along that line is called a line of symmetry or axis of symmetry of the figure.
Therefore, the other hole(s) in the given figures is(are) as follows:
Question 6.
In a figure, 90° is an angle of symmetry. The figure has two angles of symmetry less than 90°. What is the smallest angle of symmetry?
Solution:
We know that the angles of symmetry of a figure having rotational symmetry about a point are multiples of the smallest angle of symmetry.
Let the smallest angle of symmetry be x. Then, the other angles of symmetry are 2x, 3x, 4x, …, 360°.
It is given that the figure has two angles of symmetry less than 90°. This means the third angle of symmetry is 90° itself.
∴ 3x = 90°
⇒ x = 30°
Hence, the smallest angle of symmetry is 30°.
Question 7.
How many angles of rotational symmetry does the given figure have and what are they?
Solution:
We notice that the figure returns to its original position only after a complete turn or a 360° rotation.
Therefore, the figure does not possess rotational symmetry, as 360° is the only angle at which it maps onto itself.
Hence, it has no angle of rotational symmetry.
Question 8.
Discuss the rotational symmetry of the given figure.
Solution:
We observe that when the given figure is rotated by 180° and 360°, it coincides exactly with its original position.
Thus, the given figure has rotational symmetry of order 2.
Question 9.
Discuss the rotational symmetry of the given figure.
Solution:
We observe that when the given figure is rotated by 120°, 240° and 360°, it coincides exactly with its original position.
Thus, the given figure has rotational symmetry of order 3.
Symmetry Class 6 Long Question Answer
Question 1.
Observe each of the following sequences of paper folding and cutting. Draw the pattern obtained after unfolding the paper.
(i)
(ii)
Solution:
The pattern obtained after unfolding the paper in each case are as follows:
Question 2.
Which of the following figures have rotational symmetry? Also, find the order of rotational symmetry.
Solution:
(i) We observe that the figure fits onto itself when we give it a half turn, i.e. when it is rotated through 180° as shown in given figure.
Thus, the figure has rotational symmetry of order 4.
(ii) We observe that the given figure fits onto itself once only when it is rotated through 360°, i.e. when it takes a full turn.
Thus, the figure has rotational symmetry of order 4.
(iii) We observe that the given figure fits onto itself once only when it is rotated through 360°, i.e. when it takes a full turn.
Thus, it does not have rotational symmetry.
Question 3.
Show that each of the letters H, I and N has a rotational symmetry of order 2. Also, mark the point of rotational symmetry in each case.
Solution:
Each of the letters H, I and N fits into itself when it is rotated through 180° and 360° about the marked point. Thus, each of the letters H, I and N has a
rotational symmetry of order 2.
