GSEB Class 6 Maths Solutions Chapter 13 સંમિતિ Exercise 13.3

Question 1. Find the lines of symmetry for each of the figures below. How will you verify your answer?
(a)
(b)
(c)
(d)
(e)
(f)
Answer:
(a) The given figure has a total of 4 lines of symmetry. These lines are labeled as \( I_1, I_2, I_3 \) and \( I_4 \) in the figure.
(b) The given figure has only 1 line of symmetry. It is indicated as \( I \) in the figure.
(c) The given figure has a total of 2 lines of symmetry. These lines are shown as \( I_1 \) and \( I_2 \) in the figure.
(d) The given figure has a total of 2 lines of symmetry. These lines are labeled as \( I_1 \) and \( I_2 \) in the figure.
(e) The given figure has only 1 line of symmetry. It is indicated as \( I \) in the figure.
(f) The given figure has a total of 2 lines of symmetry. These lines are shown as \( I_1 \) and \( I_2 \) in the figure.
Verification of Answer: If you accurately fold the image along the line of symmetry and one half perfectly aligns with the other half, then the line of symmetry is correct. If the two halves do not perfectly align, then the line of symmetry is incorrect, and the figure is not symmetrical along that line.
In simple words: Look for lines where you can fold the shape exactly in half, so both sides match perfectly. If you fold it and the halves fit together, the line you folded on is a symmetry line. You can check your answer by physically folding or imagining a fold.

Exam Tip: A figure can have one, many, or no lines of symmetry. Always draw the lines carefully and visualize the fold to confirm.

Question 2. Copy the following figures onto square grid paper. Complete them such that the two dashed lines shown become lines of symmetry.
(a)
(b)
(c)
(d)
(e)
(f)
How will you complete the figure?
Answer: The complete figures showing two lines of symmetry are shown below. These two lines of symmetry are indicated by dotted lines. To complete a figure with two lines of symmetry, you reflect the existing part across the first dashed line, and then reflect the entire new figure (original plus first reflection) across the second dashed line.
For example:
(a) Starting with the top-left quadrant, reflect it horizontally to complete the top half. Then reflect the entire top half vertically downwards to complete the full figure.
(b) Reflect the top-right part horizontally to form the left half. Then reflect the whole top half vertically to complete the bottom half.
(c) Reflect the top-right part horizontally. Then reflect the resulting top half vertically.
(d) Reflect the top-left part vertically to get the bottom-left part. Then reflect the entire left half horizontally to get the right half.
(e) Reflect the top-left part horizontally. Then reflect the resulting top half vertically.
(f) Reflect the top-right part horizontally. Then reflect the resulting top half vertically.
In simple words: To finish these shapes, pretend the dashed lines are mirrors. Draw what the mirror would show on the other side. Do this for the first dashed line, and then do it again for the second dashed line using the whole new shape you've drawn. This will make the complete shape perfectly balanced on both sides of each dashed line.

Exam Tip: When completing figures with multiple lines of symmetry, work step-by-step. Reflect across one line, then reflect the resulting image across the next line. This ensures all symmetry conditions are met.

Question 3. In each of the figures below, an English alphabet is drawn with a vertical dashed line. Find the reflection symmetric to this line. Which letters' reflections remain the same as the original letter and which do not? Why?
Answer: Looking at the mirror images of letter A and letter B, they appear as follows:
The letter A looks the same in its mirror image as the original. This is because A is a symmetrical letter (it has a vertical line of symmetry).
The letter B does not look the same in its mirror image. The letter B appears inverted because B is not a symmetrical letter (it does not have a vertical line of symmetry).
Similarly, try for O, E, M, N, P, H, L, T, S, V, X.
Now, looking at the mirror images of the other given letters, they appear as follows:
Original: O E M N P H L T S V X
Reflected: O 3 M И q H L T Ƨ V X
Looking at these reflections, it appears that the reflections of letters A, O, M, H, T, V, and X are the same as their original letters. All these letters are symmetrical letters.
However, letters B, E, N, P, L, and S are such that their reflections are not the same as their original letters. All these letters are not symmetrical letters.
In simple words: When you look at a letter in a mirror, some letters will look exactly the same, like A or M. These letters have a special line down the middle where both sides are a match. Other letters, like B or E, will look backward or flipped. These don't have that special matching line. If a letter has a line of symmetry, its mirror image will be identical. If it doesn't, its mirror image will be different.

Exam Tip: To determine if a letter is symmetrical, imagine folding it vertically or horizontally. If both halves perfectly match, it has that line of symmetry. This helps predict how its mirror image will appear.