Question

If $a$ is the number of lines of symmetry and $b$ is the order of rotational symmetry in a regular polygon of $n$ sides, then what is the relation between them?

• A. $a=b=n$
• B. $a=2b=n$
• C. $a=b=2n$
• D. $2a=b=n$

Answer 1

The correct option is A $a=b=n$

Let us understand this with an example.
Let us take a regular heptagon (n = 7) as shown below. A regular heptagon has equal sides and equal angles.
There are seven lines of symmetry (a = 7) in a regular heptagon and its order of rotational symmetry is 7 (b = 7).

So, by generalizing this, it can be concluded that
a = b = n for a regular polygon.