Class 6 Maths NCERT Solutions for Chapter 13 Symmetry Ex – 13.2

Symmetry

Question 1.
Find the number of lines of symmetry for each of the following shapes.
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 10

Solution:
Each one of the given figures are symmetrical about the dotted line(s) drawn. The number lines of symmetry are indicated against each figure:
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 11
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 12

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 13

Solution:
(a), (b) and (d) are isosceles triangles, (c) is a right angled isosceles triangle. Their line(s) of symmetry marked with dotted line(s) in each case as under:
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 14

Question 3.
Complete the following table :

NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 15
Solution:
Complete table with rough figures duly filled is as under:
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 16
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 17

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, it is an isosceles triangle. Its rough sketch is as shown.
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 18
(b) No.
(c) Yes, it is an equilateral triangle. Its rough sketch is as shown.
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 19
(d) Yes, it is a scalene triangle. Its rough sketch is as shown.
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 20

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.

Solution:
Sketches of the required figure with their line(s) of symmetry are shown as under:
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 21

Question 6.
Trace each figure and draw the lines of symmetry, if any:
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 22

Solution:
The line(s) of symmetry of the given figures are shown as dotted lines as under:
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 23
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 24

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)

Solution:
The English alphabets A to Z having
(a) vertical lines of symmetry (like A) are
A, H, I, M, O, T, U, V, W, X and Y.
(b) horizontal lines of symmetry (like B) are
B, C, D, E, H, I, K, O and X.
(c) no lines of symmetry (like Q) are G, J, L, P, Q, R, S and 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 26
Solution:
The rough diagram of the complete figure that would be seen when the design is cut off is as under:
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry 27

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