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Find the number of lines of symmetry for each of the following shapes:
(a) There are 4 lines of symmetry for the given figure.
(b) There are 4 lines of symmetry for the given figure.
(c) There are 4 lines of symmetry for the given figure.
(d) There is only 1 line of symmetry for the given figure.
(e) There are 6 lines of symmetry for the given figure.
(f) There are 6 lines of symmetry for the given figure.
(g) There is no line of symmetry for the given figure.
(h) There is no line of symmetry for the given figure.
(i) There are 3 lines of symmetry for the given figure.
The lines of symmetry in the above figures can be represented as follows.
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| (a) | (b) | (c) |
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| (d) | (e) | (f) |
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| (i) | ||
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!)
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| (a) | (b) |
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| (c) | (d) |
(a) It is an isosceles triangle. There will be only 1 line of symmetry.
(b) It is an isosceles triangle. There will be only 1 line of symmetry.
(c) It is a right-angled triangle. There will be only 1 line of symmetry.
(d) It is a scalene triangle. There will be no line of symmetry.
Complete the following table.
| Shape | Rough figure | Number of lines of symmetry |
| Equilateral triangle |
| 3 |
| Square | - | - |
| Rectangle | - | - |
| Isosceles triangle | - | - |
| Rhombus | - | - |
| Circle | - | - |
The given table can be completed as follows.
| Shape | Rough figure | Number of lines of symmetry |
| Equilateral triangle |
| 3 |
| Square |
| 4 |
| Rectangle |
| 2 |
| Isosceles triangle |
| 1 |
| Rhombus |
| 2 |
| Circle |
| Infinite |
In case of a circle, there are infinite lines. In the above table, only some lines of symmetry are drawn. More symmetric lines can be similarly drawn for it.
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.
(a) Yes, we can make an isosceles triangle which has 1 line of symmetry.
(b) No, we cannot draw such a triangle.
(c) Yes, we can make an equilateral triangle which has 3 lines of symmetry.
(d) Yes, we can make a scalene triangle which has no line of symmetry.
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.
(Hint: It will be helpful if you first draw the lines of symmetry and then complete the figures.)
(a) A triangle with only 1 horizontal line of symmetry and no other vertical line of symmetry can be sketched as follows.
(b) A quadrilateral with both horizontal and vertical lines of symmetry
can be drawn as follows.
(c) A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry can be drawn as follows.
(d) A hexagon with exactly two lines of symmetry can be sketched as follows.
(e) A hexagon with six lines of symmetry can be sketched as follows.
Trace each figure and draw the lines of symmetry, if any:
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| (a) | (b) | (c) |
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| (d) | (e) | (f) |
(a) The given figure is an isosceles triangle. Therefore, there will be 1 line
of symmetry.
(b) The given figure has 2 lines of symmetry.
(c) The given figure has 4 lines of symmetry.
(d) The given figure is an octagonal having 2 lines of symmetry.
(e) The given figure has only 1 line of symmetry.
(f) The given figure has 4 lines of symmetry.
Consider the letters of English alphabet, 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)
(a) A, H, I, M, O, T, U, V, W, X, Y
(b) B, C, D, E, H, I, K, O, X
(c) F, G, J, L, N, P, Q, R, S, Z
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.
The complete figures will be as follows.
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