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NCERT Solutions for class 6 Maths chapter 13 – Symmetry


Back Exercise

Exercise 13.1

Question 1.
List any four symmetrical objects from your home or school.
Solution :
The blackboard, the table top, a pair of scissors, the computer disc.

Question 2.
For the given figure, which one is the mirror line, l1 or l2?
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 1
Solution :
I2 is the mirror line.

Question 3.
Identify the shapes given below. Check whether they are symmetric or not. Draw the line of symmetry as well.
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 2
Solution :
(a) Symmetric
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 3
(b) Symmetric
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 4
(c) Not symmetric
(d) Symmetric
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 5
(e) Symmetric
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 6
(f) Symmetric
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 7

Question 4.
Copy the following on a squared paper. A square paper is what you would have used in your arithmetic notebook in earlier classes. Then complete them such that the dotted line is the line of symmetry.
tiwari academy class 6 maths Chapter 13 Symmetry 8
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 9
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 10
Solution :
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 11
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 12
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 13

Question 5.
In the figure, l is the line of symmetry. Complete the diagram to make it symmetric.
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 14
Solution :
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 15
Question 6.
In the figure, l is the line of symmetry. Draw the image of the triangle and complete the diagram so that it becomes symmetric.
tiwari academy class 6 maths Chapter 13 Symmetry 16
Solution :
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 17

Exercise 13.2

Question 1.
Find the number of lines of symmetry for each of the following shapes :
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 18
Solution :
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 19
Question 2.
Copy the triangle in each of the following figures, on squared paper. In each case, draw the line(s) of symmetry if any and identify the type of triangle. (Some of you may like to trace the figures and try paper-folding first!)
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 20
Solution :
tiwari academy class 6 maths Chapter 13 Symmetry 21
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 22

Question 3.
Complete the following table :
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 23
Solution :
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 24
Question 4.
Can you draw a triangle which has
(a) exactly one line of symmetry?
(b) exactly two lines of symmetry?
(c) exactly three lines of symmetry?
(d) no lines of symmetry?
Sketch a rough figure in each case.
Solution :
(a) Yes; an isosceles triangle
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 25
(b) No
(c) Yes; an equilateral triangle
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 26
(d) Yes, an equilateral triangle
tiwari academy class 6 maths Chapter 13 Symmetry 27

Question 5.
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 of symmetry.
(d) A hexagon with exactly two lines of symmetry.
(e) A hexagon with six lines of symmetry.
(Hint: It will be helpful if you first draw the lines of symmetry and then complete the figures.)
Solution :
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 28
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 29
Question 6.
Trace each figure and draw the lines of symmetry, if any :
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 30
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 31
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 32
Solution :
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 33
no line symmetry
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 34
tiwari academy class 6 maths Chapter 13 Symmetry 35
Question 7.
Consider the letters of English alphabets A to Z. List among them the letters which have
(a) vertical lines of symmetry (like A)
(b) horizontal lines of symmetry (like B)
(c) no lines of symmetry (like Q)
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 36
Solution :
(a) A, H, I, M, O, T, U, V, W, X, Y
(b) B, C, D, E, H, I, K, O, X
(c) F, G, J, L, N, P, Q, R, S, Z

Question 8.
Given here are figures of a few folded sheets and designs drawn about the fold. In each case, draw a rough diagram of the complete figure that would be seen when the design is cut off.
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 37
Solution :
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 38

Exercise 13.3

Question 1.
Find the number of lines of symmetry in each of the following shapes. How will you check your answers?
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 39
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 40
Solution :
(a)
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 41

Number of lines of symmetry = 4
(b)
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 42
Number of lines of symmetry = 1
(c)
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 43
Number of lines of symmetry = 2
(d)
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 44
Number of lines of symmetry = 2
(e)
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 45
Number of lines of symmetry = 1
(f)
tiwari academy class 6 maths Chapter 13 Symmetry 46
Number of lines of symmetry = 2

Question 2.
Copy the following drawing on squared paper. Complete each one of them such that the resulting figure has the two dotted lines as two lines of symmetry :
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 47
How did you go about completing the picture?
Solution :
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 48
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 49
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 50
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 51
Using the given lines of symmetry, we go about completing the picture.

Question 3.
In each figure alongside, a letter of the alphabet is shown along with a vertical line. Take the mirror image of the letter in the given line. Find which letters look the same after reflection (i.e., which letters look the same in the image) and which do not. Can you guess why?
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 52
Solution :
The letter A looks the same after reflection but not the letter B. The reason is that in reflection, the sense of direction changes. In the given letters, the letters O, M, N, H, T, V, and X look the same after reflections because these letters have a vertical line of symmetry.

In-Text Questions