GSEB Class 6 Maths Solutions Chapter 13 Symmetry Exercise 13.1

Gujarat Board Textbook Solutions Class 6 Maths Chapter 13 Symmetry Ex 13.1

Question 1. List any four symmetrical objects from your home or school.
Answer: Many common things in your house or school can be symmetrical. Some examples are:
(i) A pair of scissors
(ii) An electric bulb
(iii) A table fan
(iv) A blackboard
In simple words: Think about things you see every day. A pair of scissors is symmetrical because if you fold it in half, both sides match perfectly. Other items like a light bulb, a fan, and a blackboard also have matching halves.

Exam Tip: When asked for symmetrical objects, remember to pick items that can be divided into two identical halves by a line of symmetry.

Question 2. For the given figure, which one is the mirror line, l₁ or l2?

Answer: Line \( l_2 \) is the correct mirror line for the figure shown. When you reflect the figure across line \( l_2 \), both sides match exactly, creating a perfect mirror image. Line \( l_1 \) would not create a symmetric figure upon reflection.
In simple words: The line \( l_2 \) is the mirror line. If you imagine folding the picture along line \( l_2 \), both sides would look exactly the same, like a perfect match.

Exam Tip: To identify a mirror line, visually check if folding the figure along that line would make both halves perfectly overlap. It's about a flawless match.

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

Answer:
(a) The figure shown is symmetric. Its line of symmetry is displayed by the dotted line in the diagram below.

(b) The figure shown is symmetric. Its line of symmetry is displayed by the dotted line in the diagram below.

(c) The figure shown is not symmetric.

(d) The figure shown is symmetric and its line of symmetry is displayed by the dotted line in the diagram below.

(e) The figure shown is symmetric and its line of symmetry is displayed by the dotted line in the diagram below.

(f) The figure shown is symmetric and its line of symmetry is displayed by the dotted line in the diagram below.

Exam Tip: Always draw the line of symmetry precisely through the center of the object where it can be folded to make matching halves. If no such line exists, it's not symmetric.

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.

Answer: By using the dotted line as the line of symmetry, we can complete these figures as shown below, reflecting each part to create a full symmetrical shape:

Exam Tip: Use a ruler and count squares on the grid paper carefully when completing symmetrical figures. Each point must be the same distance from the line of symmetry on the opposite side.

Question 5. In the figure, l is the line of symmetry. Complete the diagram to make it symmetric.

Answer: The finished figure is shown below. We reflected the given part across the line \( l \) to create a complete and symmetric diagram.

Exam Tip: For diagonal lines of symmetry, imagine rotating the paper so the line is vertical or horizontal, then plot points at equal perpendicular distances. This helps ensure accuracy.

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.

Answer: The reflected image of the triangle is shown in the figure given below, completing the symmetric diagram.

Exam Tip: When drawing reflections across a diagonal line, ensure that each vertex of the original figure is mirrored accurately on the opposite side, maintaining both distance and angle relative to the line of symmetry.