Chapter-13 Symmetry | Class 6th | NCERT Maths Solutions | Edugrown

Ex 13.1 Class 6 Maths Question 1.
List any four symmetrical objects from your home or school.
Solution:
List of four symmetrical objects from home or school are
(i) An electric tube
(ii) A glass
(iii) An electric bulb
(iv) A fan

Ex 13.1 Class 6 Maths Question 2.
For the given figure, which one is the mirror line, l₁ or l₂

Ex 13.1 Class 6 Maths Question 3.
Identify the shapes given below. Check whether they are symmetric or not. Draw the line of symmetry as well.

Solution:
Figures (a), (b), (d), (e) and (f) are symmetrical and their line of symmetry is shown as a dotted line.

Ex 13.1 Class 6 Maths 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.

Solution:
Keeping the dotted line as the line of symmetry and completing the figure, we have

Ex 13.1 Class 6 Maths Question 5.
In the figure, l is the line of symmetry. Complete the diagram to make it symmetric.

Solution:
Complete diagram is as under:

Ex 13.1 Class 6 Maths 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.

Solution:
The image of the triangle is shown such that the complete diagram becomes symmetric.

Ex 13.2 Class 6 Maths Question 1.
Find the number of lines of symmetry for each of the following shapes.

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:

Ex 13.2 Class 6 Maths 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!)

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:

Ex 13.2 Class 6 Maths Question 3.
Complete the following table :

Solution:
Complete table with rough figures duly filled is as under:

Ex 13.2 Class 6 Maths 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.

(b) No.
(c) Yes, it is an equilateral triangle. Its rough sketch is as shown.

(d) Yes, it is a scalene triangle. Its rough sketch is as shown.

Ex 13.2 Class 6 Maths 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:

Ex 13.2 Class 6 Maths Question 6.
Trace each figure and draw the lines of symmetry, if any:

Solution:
The line(s) of symmetry of the given figures are shown as dotted lines as under:

Ex 13.2 Class 6 Maths 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.

Ex 13.2 Class 6 Maths 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.

Solution:
The rough diagram of the complete figure that would be seen when the design is cut off is as under:

Ex 13.3 Class 6 Maths Question 1.
Find the number of lines of symmetry in each of the following shapes: .
How will you check your answers?

Solution:
By drawing the line(s) of symmetry, we find that the number of line(s) possessed by them are

Ex 13.3 Class 6 Maths Question 2.
Copy the following drawing on squared paper. Complete each one of them such that the resulting figure has two dotted lines as two lines of symmetry:

How did you go about completing the picture?
Solution:
Completing the figures using the given line(s) of symmetry. The completed figures are as under:

Ex 13.3 Class 6 Maths 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?

Try for O E M N P H L T S V X
Solution:
Taking the mirror image of the letters A and B in the given line. These will look as shown.

Clearly, A after reflection looks same but B does not.
It is due to the reason that the shape is preserved but sense is not.
Out of the given letters:
O, M, H, T, V, and X look as before after reflection, whereas E, P, N, L, and S does not.