Regular stars have n/2 lines of symmetry, where n is the number of sides. This is because each side is congruent and divides into two symmetrical halves.
Rule for the number of lines of symmetry in a regular star:
The number of lines of symmetry in a regular star is equal to the number of sides of the star divided by 2, or n / 2, where n is the number of sides.
Justification: A line of symmetry is a line that divides a shape into two congruent halves. In a regular star, each side of the star is congruent to every other side, and each angle at the vertex is congruent to every other angle at the vertex. This means that we can fold the star over any line that passes through the center of the star and the midpoint of one of the sides, and the two halves of the star will match perfectly.
Answering the question about the image:
The image shows three regular stars: a pentagon, a hexagon, and a heptagon.
The pentagon has 5 lines of symmetry, the hexagon has 3 lines of symmetry, and the heptagon has 3.5 lines of symmetry (since 7 / 2 = 3.5).
The rule for the number of lines of symmetry in a regular star is justified above.