Page 246 - Ganit Kaushal

9 Symmetry

9.1 INTRODUCTION Learning Outcomes

Mathematics is all around us, and so is symmetry! From By the end of this chapter, students will be able to:
the delicate patterns of a butterfly’s wings to the perfect • understand what is symmetry, and why it is
shapes of flowers and the artistic designs in rangoli, important.
symmetry adds beauty and balance to the world. • identify lines of symmetry in different shapes.

• differentiate between different types of symmetry,
such as reflectional and rotational symmetry.
• recognise how symmetry is used in everyday
life – from designing logos to creating intricate
artwork.
Butterfly Flower Rangoli

But what exactly is symmetry?
In this chapter, we will explore the fascinating concept of symmetry, which plays an important role not only
in nature, but also in art, architecture, and most importantly in mathematics.

9.2 CONCEPT AND DEFINITION

Symmetry is when one half of a shape remains the same as the other half if we flip, slide or turn it. Figures
which can be divided into two parts of identical shape and size are called symmetrical figures, and those
which cannot be divided into two halves are called non-symmetrical or asymmetrical figures.
Linear Symmetry and Line of Symmetry (LoS)
Line of Symmetry
A line that cuts a figure into two parts that exactly overlap when
folded along that line is called a line of symmetry (LoS) of the
figure, and such figures are said to have linear symmetry. We
can observe that each of the given figures can be divided by a
line into two identical parts (shown by a dotted line).
The two halves of a symmetrical figure are also called mirror
halves or mirror images of each other because if we place a mirror
on the line of symmetry, then the image of one side of the figure Girl Moustache Heart
will be exactly on the other side of the line. So, the line of symmetry is also called the ‘Mirror Line’ or the
‘Axis of Symmetry’. The line of symmetry divides the shape into two identical parts.
The line of symmetry can be vertical, horizontal, diagonal or inclined at some angle. A figure may have one
or more lines of symmetry.

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