GSEB Class 6 Maths Solutions Chapter 13 Symmetry Exercise 13.3

 

Question 1. Find the number of lines of symmetry in each of the following shapes. How will you check your answers?

Answer: By carefully drawing the lines of symmetry, we discover the following:
(a) There are four lines of symmetry.
(b) There is one line of symmetry.
(c) There are two lines of symmetry.
(d) There are two lines of symmetry.
(e) There is one line of symmetry.
(f) There are two lines of symmetry.In simple words: To find the lines of symmetry, imagine folding the shape so that both halves match perfectly. The fold line is a line of symmetry. Some shapes have many such lines, while others have only one or two.

Exam Tip: Use a transparent paper or draw the shapes and try folding them to physically identify the lines of symmetry. This hands-on method helps visualize the concept.

 

Question 2. Copy the following drawings 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?

Answer: We complete the given figures by reflecting each part across the two dotted lines of symmetry, effectively mirroring the initial drawing into all four quadrants. This process ensures the resulting figure is symmetrical along both axes.

The completed figures are:
(a)
(b)
(c)
(d)
(e)
(f)In simple words: To complete these figures, you reflect the given part over the vertical dotted line, then reflect both the original and the first reflection over the horizontal dotted line. This way, the picture becomes symmetrical in all directions around the center.

Exam Tip: When dealing with multiple lines of symmetry, it is best to reflect step-by-step. First, mirror the figure across one line, then reflect the entire new figure (original + first reflection) across the second line.

 

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 OEM N P H LTS V X

Answer: Taking the mirror image of 'A', we get:This shows that the letter 'A' looks the same after reflection.

However, the mirror image of 'B' is:
This shows that 'B' does not look the same.

Similarly, the mirror images of other given letters are as follows:
O O (looks the same)
E Ǝ (does not look the same)
M M (looks the same)
N И (does not look the same)
P q (does not look the same)
H H (looks the same)
L J (does not look the same)
T T (looks the same)
S Ƨ (does not look the same)
V V (looks the same)
X X (looks the same)

The letters A, O, M, H, T, V, and X appear identical after reflection because all these letters are symmetrical along their vertical axis. On the other hand, letters B, E, N, P, L, and S do not look the same after reflection because they lack this vertical symmetry.In simple words: Some letters, like A, O, M, H, T, V, and X, stay exactly the same when you see them in a mirror because they are perfectly balanced from left to right. Other letters, like B, E, N, P, L, and S, change how they look because they are not balanced in the same way.

Exam Tip: A letter appears the same after reflection if it has vertical line symmetry. Always draw the mirror line and imagine folding the paper along it to check. This rule applies to both uppercase and some lowercase letters.