NCERT Solutions Class 7 Mathematics
Chapter – 14 (Symmetry)
The NCERT Solutions in English Language for Class 7 Mathematics Chapter – 14 Symmetry Exercise 14.1 has been provided here to help the students in solving the questions from this exercise.
Chapter : 14 Symmetry
Exercise – 14.1
1. Copy the figures with punched holes and find the axes of symmetry for the following:
Solution –
2. Given the line(s) of symmetry, find the other hole(s):
Solution –
3. In the following figures, the mirror line (i.e., the line of symmetry) is given as a dotted line. Complete each figure performing reflection in the dotted (mirror) line. (You might perhaps place a mirror along the dotted line and look into the mirror for the image). Are you able to recall the name of the figure you complete?
Solution –
4. The following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry.
Identify multiple lines of symmetry, if any, in each of the following figures:
Solution –
(a) Figure given has 3 lines of symmetry. So, it has multiple lines of symmetry.
(b) Figure given has 2 lines of symmetry. So, it has multiple lines of symmetry.
(c) Figure given has 3 lines of symmetry. So, it has multiple lines of symmetry.
(d) Figure given has 2 lines of symmetry. So, it has multiple lines of symmetry.
(e) Figure given has 4 lines of symmetry. So, it has multiple lines of symmetry.
(f) Figure given has only 1 line of symmetry.
(g) Figure given has 4 lines of symmetry. So, it has multiple lines of symmetry.
(h) Figure given has 6 lines of symmetry. So, it has multiple lines of symmetry.
5. Copy the figure given here.
Take any one diagonal as a line of symmetry and shade a few more squares to make the figure symmetric about a diagonal. Is there more than one way to do that? Will the figure be symmetric about both the diagonals?
Solution –
(i) Let us take a diagonal as the axis of symmetry and shade the square as shown in the figure.
(ii) Yes, the figure is symmetric about both the diagonals.
(iii) Yes, there are more than the line of symmetry.
6. Copy the diagram and complete each shape to be symmetric about the mirror line(s):
Solution –
7. State the number of lines of symmetry for the following figures:
(a) An equilateral triangle
(b) An isosceles triangle
(c) A scalene triangle
(d) A square
(e) A rectangle
(f) A rhombus
(g) A parallelogram
(h) A quadrilateral
(i) A regular hexagon
(j) A circle
Solution –
| Figure | Number of lines of symmetry |
| (a) An equilateral triangle | 3 |
| (6) An isosceles triangle | 1 |
| (c) A scalene triangle | 0 |
| (d) A square | 4 |
| (e) A rectangle | 2 |
| (f) A rhombus | 2 |
| (g) A parallelogram | 0 |
| (h) A quadrilateral | 0 |
| (i) A regular hexagon | 6 |
| (j) A circle | Infinite |
8. What letters of the English alphabet have reflectional symmetry (i.e., symmetry related to mirror reflection) about.
(a) a vertical mirror
(b) a horizontal mirror
(c) both horizontal and vertical mirrors
Solution –
(a) a vertical mirror.
The English alphabet have reflection symmetry about a vertical mirror are, A, H, I, M, O, T, U, V, W, X, Y
(b) a horizontal mirror
The English alphabet have reflection symmetry about a horizontal mirror are, B, C, D, E, H, I, K, O, X
(c) both horizontal and vertical mirrors
The English alphabet have reflection symmetry about both horizontal and vertical mirrors are, H, I, O, X
9. Give three examples of shapes with no line of symmetry.
Solution –
Example 1: Scalene triangle has no line of symmetry.
Example 2: Quadrilateral has no line of symmetry.
Example 3: Alphabet R has no line of symmetry.
10. What other name can you give to the line of symmetry of
(a) an isosceles triangle?
(b) a circle?
Solution –
(a) Median of an isosceles triangle is its line of symmetry.
(b) Diameter of a circle is its line of symmetry.
