GSEB Class 6 Maths Solutions Chapter 13 Symmetry Exercise 13.2

Shape	Rough figure	Number of line of symmetry
Equilateral triangle		3
Square		4
Rectangle		2
Isosceles triangle		1
Rhombus		2
Circle		Infinite

Exam Tip: Remember the specific number of lines of symmetry for basic shapes (square, rectangle, equilateral triangle, circle, rhombus) as these are frequently tested. For a circle, it's always infinite.

Question 4. Can you draw a triangle that has Sketch a rough figure in each case?
(a) exactly one line of symmetry?
(b) exactly two lines of symmetry?
(c) exactly three lines of symmetry?
(d) no lines of symmetry?
Answer:
(a) Yes, an isosceles triangle has exactly one line of symmetry, as illustrated in the following figure.
(b) No, it is not possible to draw a triangle that possesses exactly two lines of symmetry.
(c) Yes, an equilateral triangle has exactly three lines of symmetry, as shown below.
(d) Yes, a scalene triangle contains no lines of symmetry.
In simple words: We're checking if we can draw triangles with a specific number of fold lines that make them perfectly balanced. We can draw triangles with one, three, or no such lines. But we cannot draw one with exactly two.

Exam Tip: Always remember the fundamental properties: isosceles triangles have one line of symmetry, equilateral triangles have three, and scalene triangles have none. A triangle with exactly two lines of symmetry is geometrically impossible.

Question 5. On a squared paper, sketch the following: Hint: It will be helpful if you first draw the lines of symmetry and then complete the figures.
(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.
Answer:
(a) An isosceles triangle with only a horizontal line of symmetry is displayed in the figure below.
(b) The quadrilateral (rectangle) that possesses both horizontal and vertical lines of symmetry is shown in the following figure.
(c) A quadrilateral having only a horizontal line of symmetry is presented in the following figure.
(d) A hexagon that has exactly two lines of symmetry is shown in the figure below.
(e) A hexagon with six lines of symmetry is displayed in the figure below.
In simple words: We are asked to draw different shapes on graph paper. First, we draw the lines where the shape would fold perfectly in half. Then, we complete the shape around these lines. This helps us ensure the shapes have the correct number and type of symmetry.

Exam Tip: When drawing symmetrical figures on squared paper, start by drawing the line(s) of symmetry first. This provides a clear guide for mirroring parts of the figure to achieve the desired symmetry. Use the grid lines to ensure accurate placement and shape.

Question 6. Trace each figure and draw the lines of symmetry, if any:
(a)
(b)
(c)
(d)
(e)
(f)
Answer:
(a) The presented figure is not symmetrical; consequently, it has no line of symmetry.
(b) The given figure displays two lines of symmetry, as illustrated by the dotted lines l and m.
(c) The given figure has four lines of symmetry, shown by the dotted lines p, q, r, and s.
(d) The given figure shows two lines of symmetry, as indicated by the dotted lines l and m.
(e) The given figure contains one line of symmetry, as depicted by the dotted line 'l'.
(f) The given figure displays two lines of symmetry, as shown in the figure by the dotted lines 'p' and 'q'.
In simple words: For each shape, we need to draw all the possible lines where the shape could be folded in half and match perfectly. If no such line exists, we state that.

Exam Tip: Practice tracing figures and drawing lines of symmetry. Pay close attention to shapes that might appear symmetrical but are not due to slight imperfections or specific orientations. Always check for both horizontal, vertical, and diagonal symmetry.

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)
Answer:
(a) The following letters possess vertical lines of symmetry: A, H, I, M, O, T, U, V, W, X, and Y.
(b) The following letters have horizontal lines of symmetry: B, C, D, E, H, I, K, O, and X.
(c) The following letters have no lines of symmetry: F, G, J, L, N, P, Q, R, S, and Z.
In simple words: We are looking at each letter of the alphabet to see how it can be folded. Some letters can be folded top-to-bottom, some side-to-side, and some can't be folded perfectly at all. We list the letters for each type of fold.

Exam Tip: To easily determine symmetry for letters, visualize them in a standard, capital block font. Practice drawing lines through them to confirm if they fold perfectly. Some letters like H, I, O, X have both vertical and horizontal symmetry.

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
Answer: The complete figure will appear as shown below, when unfolded from the fold. In each instance, the design on the folded sheet is mirrored across the fold line, resulting in a symmetrical complete figure once cut.
In simple words: Imagine you fold a paper, cut a design into it, and then open it up. The task is to draw what the full, unfolded design will look like. The cut design on one side of the fold will be perfectly copied onto the other side, making a balanced shape.

Exam Tip: This question tests understanding of reflectional symmetry. Visualize the fold as a line of symmetry. Any cut made on one side of the fold will be mirrored on the other side. Always consider how the design would appear if reflected perfectly across that fold line.