Symmetry Class 6 Extra Questions Maths Chapter 9

Class 6 Maths Chapter 9 Extra Questions Symmetry

Class 6 Maths Symmetry Extra Questions

NCERT Class 6 Maths Chapter 9 Symmetry Extra Questions and Answers

Very Short Answer Type Questions

Question 1.
What is rotational symmetry?
Solution :
Rotational symmetry is the number of times a shape can ‘fit into itself’ when it is rotated 360 degrees about its centre.

Question 2.
Write a letter of English alphabet with only 1 line of symmetry.
Solution :
Symmetry Class 6 Extra Questions Maths Chapter 9 1

Question 3.
The three lines pass through the figure given below. Find the line(s) which is line of symmetry for the given figure?
Symmetry Class 6 Extra Questions Maths Chapter 9 2
Solution :
If a line divides the given figure into two identical halves, then we say that the given figure is symmetrical about that line.
Here, line l divides the given figure into two identical halves.

Symmetry Class 6 Extra Questions Maths Chapter 9 3

So the given figure is symmetrical about line l.

Question 4.
Name any 4 symmetrical objects around you.
Solution :
Four symmetrical objects are

  1. top of table.
  2. blackboard.
  3. a pair of scissors.
  4. computer disc.

Question 5.
How many digits from 0 to 9 have lines of symmetry?
Solution :
The digits from 0 to 9 which have line of symmetry are 0, 3 and 8.

Symmetry Class 6 Extra Questions Maths Chapter 9 4

Short Answer Type Questions

Question 1.
For the given figure, which one is the mirror line l1 or l2 ?
Symmetry Class 6 Extra Questions Maths Chapter 9 5
Solution :
l2 is the mirror line of the figure. When the given figure is folded about the line l2, the left part exactly covers the right part and vice versa.

Question 2.
In the figure, l is the line of symmetry. Draw the image of the triangle and complete the diagram so that it becomes symmetric.
Symmetry Class 6 Extra Questions Maths Chapter 9 6
Solution :
The required triangle can be drawn as follows to make it symmetric:
Symmetry Class 6 Extra Questions Maths Chapter 9 7

Question 3.
Find the number of lines of symmetry in each of the following shapes.
Symmetry Class 6 Extra Questions Maths Chapter 9 8
Solution :
(a) Fo the given figure, there are 4 lines of symmetry.

Symmetry Class 6 Extra Questions Maths Chapter 9 9

(b) For the given figure, there is only 1 line of symmetry.

Symmetry Class 6 Extra Questions Maths Chapter 9 10

(c) For the given figure, there are 2 lines of symmetry.

Symmetry Class 6 Extra Questions Maths Chapter 9 11

Question 4.
What is the order of the rotational symmetry of a rectangle?
Answer :
A rectangle has a rotational symmetry of order 2 shown below where one vertex is highlighted with a circle and the centre of the shape is indicated with an ‘x’. In the diagram, the shape looks identical in two orientations and so the rotational symmetry of the rectangle is 2.

Long Answer Type Questions

Question 1.
Find the number of lines of symmetry for each of the following shapes:
Symmetry Class 6 Extra Questions Maths Chapter 9 12
Solution :
(a) There are 4 lines of symmetry for the given figure.
(b) There are 4 lines of symmetry for the given figure.
(c) There are 4 lines of symmetry for the given figure.
(d) There is only 1 line of symmetry for the given figure.
(e) There are 6 lines of symmetry for the given figure.
(f) There are 6 lines of symmetry for the given figure.
(g) There is no line of symmetry for the given figure.
(h) There is no line of symmetry for the given figure.
(i) There are 3 lines of symmetry for the given figure.
The lines of symmetry in the above figures can be represented as follows.
Symmetry Class 6 Extra Questions Maths Chapter 9 13

Question 2.
On a squared paper, sketch the following:
(a) A triangle with a horizontal line of symmetry but no vertical line of symmetry
(b) A quadrilateral with both horizontal and vertical lines of symmetry
(c) A quadrilateral with a horizontal line of symmetry but no vertical line symmetry
(d) A hexagon with exactly two lines of symmetry
(e) A hexagon with six lines of symmetry
Solution :
(a) A triangle with a horizontal line of symmetry but no vertical line of symmetry can be drawn as follows:

Symmetry Class 6 Extra Questions Maths Chapter 9 14

(b) A quadrilateral with both horizontal and vertical lines of symmetry can be drawn as follows:

Symmetry Class 6 Extra Questions Maths Chapter 9 15

(c) A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry can be sketched as follows:

Symmetry Class 6 Extra Questions Maths Chapter 9 16

(d) A hexagon with exactly two lines of symmetry may be drawn as follows:

Symmetry Class 6 Extra Questions Maths Chapter 9 17

(e) A hexagon with 6 lines of symmetry may be drawn as follows:

Symmetry Class 6 Extra Questions Maths Chapter 9 18

Passage Based Questions

Passage 1: Udit made a paper fish by folding a paper. He uses a square paper, with a coloured side and a white side. He followed the steps shown below to make the fish.
Symmetry Class 6 Extra Questions Maths Chapter 9 19

Question 1.
How many lines of symmetry can be drawn on a square paper?
Solution :
A square paper sheet have 4 lines of symmetry.

Question 2.
To perform step 4, which geometrical construction was done?
(d) Dividing a line segment into two equal parts
(b) Making a perpendicular to a line segments
(c) Dividing an angle into two equal parts
(d) Joining two lines of equal length
Answer :
Option (c) is correct.

Question 3.
Udit folded the paper in step 2 and step 3 , why were the two halves after step 3 of different colours?
Solution :
Because half of the paper is folded inside and half outside

Question 4.
Shape 1 has four lines of symmetry. How many lines of symmetry will the shape will the shape have after Udit completes step 2 ?
(a) 0
(b) 1
(c) 2
(d) 4
Answer :
Option (b) is correct

Question 5.
What should be the image visible in the mirror?’
(a)
Symmetry Class 6 Extra Questions Maths Chapter 9 20
(b)
Symmetry Class 6 Extra Questions Maths Chapter 9 21
(c)
Symmetry Class 6 Extra Questions Maths Chapter 9 22
(d)
Symmetry Class 6 Extra Questions Maths Chapter 9 23
Answer :
Option (d) is correct.
Explanation:
Symmetry Class 6 Extra Questions Maths Chapter 9 24

Passage 2: Mani draws this design on a sheet of paper.
Symmetry Class 6 Extra Questions Maths Chapter 9 25

Question 1.
How many lines of symmetry are there in the design?
Solution :
There are 12 lines of symmetry.

Question 2.
Gautam modified Mani’s design by erasing all the hexagons from Mani’s design. How many lines of symmetry are there in Gautam’s design?
Solution :
Still, there are 12 lines of symmetry.

Question 3.
This is part of the design created by Mani.
Symmetry Class 6 Extra Questions Maths Chapter 9 26
Can you create the complete design by repeating this part? How?
Solution :
We can create the full design by repeating this part 5 times.

Question 4.
Mani says, ‘You can have a shape smaller than the one below to make the design.
Symmetry Class 6 Extra Questions Maths Chapter 9 27
Do you agree? Justify your response.
Solution :
Yes, we can reflect the part horizontally and then reflecting the joined parts vertically.

NCERT Exemplar Questions

Multiple Choice Questions

In the following questions, out of the four options, only one is correct. Write the correct answer.

Question 1.
In the following figures, the figure that is not symmetric with respect to any line is:
Symmetry Class 6 Extra Questions Maths Chapter 9 28
(a) (i)
(b) (ii)
(c) (iii)
(d) (iv)
Answer :
Option (b) is correct.
Explanation:
Symmetry Class 6 Extra Questions Maths Chapter 9 29

Question 2.
The number of lines of symmetry in a circle is more than 4:
(a) 0
(b) 2
(c) 4
(d) More than 4
Answer :
Option (d) is correct.
Explanation: A circle is symmetrical about each of its diameters. Thus, each diameter of a circle is an axis of symmetry.

Question 3.
Which of the following letters have both horizontal and vertical lines of symmetry?
(a) X
(b) E
(c) M
(d) K
Answer :
Option (b) is correct.
Explanation:
Symmetry Class 6 Extra Questions Maths Chapter 9 30
Above letters show that X has both horizontal and vertical line of symmetry, E and K have horizontal line of symmetry and M has vertical line of symmetry.

Question 4.
Which of the following letters does not have any line of symmetry?
(a) M
(b) S
(c) K
(d) H
Answer :
Option (d) is correct.
Explanation:
Symmetry Class 6 Extra Questions Maths Chapter 9 31

The above letters show that H and X have both vertical and horizontal line of symmetry, Z has no line of symmetry and T has only one (horizontal) line of symmetry.

Question 5.
The number of lines of symmetry in a protractor is:
(a) 0
(b) 1
(c) 2
(d) more than 2
Answer :
Option (b) is correct.
Explanation: The protractor is in the shape of letter D, which has one line of symmetry.

Fill in the Blanks

Question 1.
The distance of the image of a point (or an object) from the line of symmetry (mirror) is _____ as that of the point (object) from the line (mirror).
Answer :
same

Question 2.
The number of lines of symmetry in a picture of Taj Mahal is _____.
Answer :
one

Question 3.
If a line segment of length 5 cm is reflected in a line of symmetry (mirror), then its reflection (image) is a _____ of length _____.
Answer :
line segment, 5 cm

Question 4.
In figure, if B is the image of the point A with respect to the line 1 and p is any point lying on 1 , then the lengths of line segments PA and PB are _____.
Symmetry Class 6 Extra Questions Maths Chapter 9 32
Answer :
Equal

Question 5.
The number of digits having no line of symmetry is _____ .
Answer :
7
The digits are 1,2,4,5,6 and 7 and 9 having no line of symmetry.

True/False

Question 1.
A right triangle can have at most one line of symmetry.
Answer :
True

Question 2.
If an isosceles triangle has more than one line of symmetry, then it need not be an equilateral triangle.
Answer :
False

Question 3.
Rectangle and square have same line of symmetry.
Answer :
False

Question 4.
A circle has 16 lines of symmetry.
Answer :
False

Question 5.
A regular octagon has 10 lines of symmetry.
Answer :
False

Question 6.
Match the items of column I with that of column II:

Shape Number of lines of symmetry
(i) Isosceles triangle (a) 6
(ii) Square (b) 5
(iii) Kite (c) 4
(iv) Equilateral triangle (d) 3
(v) Rectangle (e) 2
(vi) Regular hexagon (f) 1
(vii) Scalene triangle (g) 0

Answer :

Shape Number of lines of symmetry
(i) Isosceles triangle (f) 1
(ii) Square (c) 4
(iii) Kite (f) 1
(iv) Equilateral triangle (d) 3
(v) Rectangle (e) 2
(vi) Regular hexagon (a) 6
(vii) Scalene triangle (g) 0

Very Short Answer Type Questions

Question 1.
Is there any line of symmetry in the given figure? If yes, draw all the lines of symmetry.
Symmetry Class 6 Extra Questions Maths Chapter 9 33
Solution :
Yes, the given figure has one line of symmetry.
Symmetry Class 6 Extra Questions Maths Chapter 9 34

Question 2.
Write all the capital letters of the English alphabets which have more than one lines of symmetry.
Solution :
The capital letters of English alphabets which have more than one lines of symmetry are as follows:
Symmetry Class 6 Extra Questions Maths Chapter 9 35

Question 3.
Write the letters of the word ‘MATHEMATICS’ which have no line of symmetry.
Solution :
The letter ‘S’ of the given word have no line of symmetry.

Question 4.
Write the number of lines of symmetry in each letter of the word ‘SYMMETRY’.
Solution :
S and R have no line of symmetry, whereas all the remaining letters has only one line of symmetry.
Symmetry Class 6 Extra Questions Maths Chapter 9 36

Short Answer Type Questions

Question 1.
In the given figure, PQRS is a rectangle. State the lines of symmetry of the rectangle.
Symmetry Class 6 Extra Questions Maths Chapter 9 37
Solution :
We know that a rectangle has two lines of symmetry, which are obtained by joining the midpoints of opposite sides.
∴ The given figure shows that AC and BD are the lines of symmetry.

Question 2.
Draw the images of the points A, B and C in the line m (see figure). Name them as A’, B’ and C’, respectively, and join them in pairs. Measure A B, B C, C A, A’ B’, B’ C’ and C’. Is A B = A’ B’, B C = B’ C’ and C A = C’ A’ ?
Symmetry Class 6 Extra Questions Maths Chapter 9 38
Solution :
Yes, AB = A’ B’, BC = B’ C’ and CA = CA.

Symmetry Class 6 Extra Questions Maths Chapter 9 39

Question 3.
Draw the images P’, Q’ and R’ of the points P, Q and R, respectively, in the line n (see figure). Join P’ Q’ and Q’ R’ to form an angle P’ Q’ R’. Measure ∠ PQR and ∠ P’ Q’ R’.’Are the two angles equal?
Symmetry Class 6 Extra Questions Maths Chapter 9 40
Solution :
Yes, ∠ PQR and ∠ P’ Q’ R’.
Symmetry Class 6 Extra Questions Maths Chapter 9 41

Long Answer Type Questions

Question 1.
Open your geometry box. There are some drawing tools. Observe them and complete the following table:
Symmetry Class 6 Extra Questions Maths Chapter 9 42
Solution :
(i) The ruler has 2 lines of symmetry.
(ii) The divider has 1 line of symmetry.
(iii) The compasses has no line of symmetry.
(iv) The protractor has 1 line of symmetry.
(v) Triangular pjece with two equal sides has 1 line of symmetry.
(vi) Triangular piece with unequal sides has no line of symmetry.

Question 2.
In the given figure, the point C is the image of point A in line l and line segment BC intersects the line l at P.
Symmetry Class 6 Extra Questions Maths Chapter 9 43
(a) Is the image of P in line I the point P itself?
(b) Is PA = PO
(c) Is PA + PB = PC + PB ?
(d) Is P that point on tine 1 from which the sum of the distances of points A and B is minimum?
Solution :
(a) Yes
(b) Yes
(c) Yes
Since, PA = PC
→ PA + PB = PC + PB
[by adding PB on both sides]
(d) Yes, since, PA + PB = CP + PB
Now, CP + PB will be minimum when C, P and B lie on a line

Class 6 Maths Extra Questions

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