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12. Regular Pentagon A regular pentagon has 5 lines of symmetry.
They start from a vertex and bisect the
opposite sides perpendicularly.

13. Regular Hexagon A regular hexagon has 6 lines of symmetry
in which 3 lines of symmetry are the
perpendicular bisectors of opposite sides and
other 3 lines symmetry are passes through
the opposite vertices.

• A scalene triangle has no line of symmetry because all the three sides are of different length.
Note: • Each regular polygon has as many lines of symmetry as it has sides. This means a regular pentagon
has 5 lines of symmetry, a regular hexagon has 6 lines of symmetry, and a regular octagon has 8
lines of symmetry, etc.

Example 2: Find the number of lines of symmetry in each of the following figures:

(a) (b) (c)

Solution: (a) (b) (c)

It has two lines of It has three lines of It has three lines of
symmetry. symmetry. symmetry.

Reflection Symmetry

The concept of line symmetry is closely related to mirror reflection. A shape has a
line of symmetry when one half of it is the mirror image of the other half. A mirror
line, thus, helps to visualise a line of symmetry.

Let us draw a line in the middle of an object as the position of either side of the line
are identical, and then we place a mirror along the line in the middle of the object
(see adjacent fig.).
What do we observe? In this situation, we can see that the other half of the object
reflected through the mirror, creating the remaining identical other half of the
object. It is called the mirror line symmetry or mirror image symmetry.
Similarly, when you look into a mirror, the image that we see behind the mirror
is our image that we see after reflection in the mirror, which is an exact copy of
our face. We call it the reflection symmetry.

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