Question

 Draw the lines of symmetry for the following figure. Identify which of them has a point of symmetry. Is there any implication between lines of symmetry and point of symmetry?

Answer 1

Hint: Divide each figure with the lines such that the line divide the polygon in two equal parts. Then, write the number of lines of symmetry each figure has. Then, identify the figures which have the same distance from the central part, that is, the figures which have the point of symmetry.

Complete step-by-step answer:
First of all, we will draw the lines of symmetry for each of the given figures.
1)

Rectangle has 2 lines of symmetry.



2)

For the equilateral triangle, there are 3 lines of symmetry.
3)

For square, there are 4 lines of symmetry.
4)

Similarly, the regular pentagon has five lines of symmetry.

5)

Similarly, a regular hexagon has six lines of symmetry.
6)

Heptagon has 7 lines of symmetry
7)

A regular octagon has 8 lines of symmetry.
As we can see, there is an implication between lines of symmetry and point of symmetry
Now, identify the figures which have the same distance from the central part, that is, the figures which have the point of symmetry.
The figures with an even number of lines of symmetry have a point of symmetry.
Therefore, the figures with the point of symmetry are:

Note: The regular polygons are the polygons with all sides of the same length and each angle is also equal. If the regular polygon has $n$ equal sides, then there are $n$ lines of symmetry.