Question

How many lines of symmetry are there in a regular octagon?

Answer 1

Hint: Find the line that will divide the shape in two equal and symmetric parts. The two parts are a mirror image of each other.

Complete step by step solution:
In the question, we have to find all the lines of symmetry in a regular octagon.
Now, it is known that the line of symmetry will divide the octagon in two equal parts in such a way that if we fold the figure with reference to this line of symmetry then the figure will overlap.
Now the regular octagon will have eight sides and hence one line of symmetry will be as shown below.

Here the line AE is dividing the octagon in two equal and overlapping parts. Hence, AE is one of the lines of symmetry.
Other possible line of symmetry can be shown as follows:

Similarly, other lines of symmetry can be shown as follows;

So, there are 8 lines of symmetry of the regular octagon.

Note: There is a difference between line of symmetry and the point of symmetry, as they both are not the same thing. Another thing that we have to keep in mind is that the line of symmetry from A to E is the same as the line of symmetry from E to A, and hence they are the same line and not two different lines.