Symmetry - Solutions
CBSE Class –VII Mathematics
NCERT Solutions
Chapter 14 Symmetry (Ex. 14.1)
Question 1. Copy the figures with punched holes and find the axes of symmetry for the following:
(a) (b)
(c)
(d) (e)
(f)
(g) (h)
(i)
(j) (k)
(l)
Answer: Sol.
S.No. | Punched holed figures | The axes of symmetry |
(a) | ![]() | ![]() |
(b) | ![]() | ![]() |
(c) | ![]() | ![]() |
(d) | ![]() | ![]() |
(e) | ![]() | ![]() |
(f) | ![]() | ![]() |
(g) | ![]() | ![]() |
(h) | ![]() | ![]() |
(i) | ![]() | ![]() |
(j) | ![]() | ![]() |
(k) | ![]() | ![]() |
(l) | ![]() | ![]() |
Question 2. Given the line(s) of symmetry, find the other hole(s):
S.No. | Line(s) of symmetry | Other holes on figures |
(a) | ![]() | |
(b) | ![]() | |
(c) | ![]() | |
(d) | ![]() | |
(e) | ![]() |
Ans.
S.No. | Line(s) of symmetry | Other holes on figures |
(a) | ![]() | ![]() |
(b) | ![]() | ![]() |
(c) | ![]() | ![]() |
(d) | ![]() | ![]() |
(e) | ![]() | ![]() |
Question 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?
Answer: Sol.
S.No. | Question figures | Complete figures | Names of the figure |
(a) | ![]() | ![]() | Square |
(b) | ![]() | ![]() | Triangle |
(c) | ![]() | ![]() | Rhombus |
(d) | ![]() | ![]() | Circle |
(e) | ![]() | ![]() | Pentagon |
(f) | ![]() | ![]() | Octagon |
Question 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:
Answer:
S.No. | Problem Figures | Lines of symmetry |
(a) | ![]() | ![]() |
(b) | ![]() | ![]() |
(c) | ![]() | ![]() |
(d) | ![]() | ![]() |
(e) | ![]() | ![]() |
(f) | ![]() | ![]() |
(g) | ![]() | ![]() |
(h) | ![]() | ![]() |
Question 5. Copy the figure given here:
Answer figures are:
Yes, there is more than one way.
Yes, this figure will be symmetric about both the diagonals.
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?Answer: Question 6. Copy the diagram and complete each shape to be symmetric about the mirror line(s):
Question 6. Copy the diagram and complete each shape to be symmetric about the mirror line (s) :
Answer:
Question 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
Answer:
S.No. | Figure’s name | Diagram with symmetry | Number of lines |
(a) | Equilateral triangle | ![]() | 3 |
(b) | Isosceles triangle | ![]() | 1 |
(c) | Scalene triangle | ![]() | 0 |
(d) | Square | ![]() | 4 |
(e) | Rectangle | ![]() | 2 |
(f) | Rhombus | ![]() | 2 |
(g) | Parallelogram | ![]() | 0 |
(h) | Quadrilateral | ![]() | 0 |
(i) | Regular Hexagon | ![]() | 6 |
(j) | Circle | ![]() | Infinite |
Question 8. What letters of the English alphabet have reflectional symmetry (i.e., symmetry related to mirror reflection) about:
1. a vertical mirror
2. a horizontal mirror
3. both horizontal and vertical mirrors
Answer: (a) Vertical mirror – A, H, I, M, O, T, U, V, W, X and Y mirror mirror
(b) Horizontal mirror – B, C, D, E, H, I, O and X
(c) Both horizontal and vertical mirror – H, I, O and X
Question 9. Give three examples of shapes with no line of symmetry.
Answer: The three examples are:
1. Quadrilateral
2. Scalene triangle
3. Parallelogram
Question 10. What other name can you give to the line of symmetry of:
1. an isosceles triangle?
2. a circle?
Answer: (a) The line of symmetry of an isosceles triangle is median or altitude.
(b) The line of symmetry of a circle is diameter.