Page 247 - Ganit Kaushal

Look at the following figures; the dotted lines are the lines of symmetry:

(i) (ii) (iii) (iv)
Figure (i) has one inclined line of symmetry, figure (ii) has one vertical line of symmetry, figure (iii) has one
horizontal line of symmetry, and figure (iv) has two lines of symmetry (vertical and horizontal).
Wherever there is symmetry, there is beauty. Enjoy the beauty of some of the most beautiful structures given
below.

Identify the line(s) of symmetry in these structures.

Taj Mahal Lotus Temple Eiffel Tower Parliament of India Gopuram Clouds
Well, you may find some kind of symmetry in the first 5 pictures and the line of symmetry as well. But what
about the last one, the clouds?
Do you find any kind of symmetry there, or any line of symmetry? ̶ No.
Aren’t they beautiful? ̶ Yes, they are.
So, on a lighter note, we conclude that beauty is not dependent on symmetry.
Asymmetrical things can also be beautiful, and that’s the magic of nature!

9.3 REFLECTION SYMMETRY

So far, we have discussed how folding a figure along its line of symmetry, allows the two parts to overlap
completely. This could also be understood as if the figure on one side of the line of symmetry is reflected by
the line to the other side; similarly, the part of the figure on the other side of the line of symmetry is reflected
to the first side.
Let us understand this by labelling some points on the figure. Consider a square with its P Q
corners labelled P, Q, R, and S. Let us consider the vertical line of symmetry (dotted line).
If we place a mirror on this line, the points Q and R on the right side get reflected to the left
side and occupy the positions occupied earlier by P and S. Similarly, P and S occupy the
positions occupied by Q and R, respectively. This is known as reflection symmetry. Thus, a S R
figure that has a line, or lines of symmetry, is also said to have reflection symmetry.

Till now, we have considered the cases where the
line of symmetry (mirror line) passes through the
figure. Let us now consider the cases when the
line of symmetry is alongside the figure; then the
exact shape of the figure gets reflected on the other

Symmetry 245