Question

Which statements are true about the reflectional symmetry of a regular heptagon? Select two options.

It has only 1 line of reflectional symmetry.
A line of symmetry will connect 2 vertices.
A line of symmetry will connect a vertex and a midpoint of an opposite side.
It has 7-fold symmetry.
A line of symmetry will connect the midpoints of 2 opposite sides.

Answer 1

Correct choices:
- A line of symmetry will connect a vertex and a midpoint of an opposite side.
- It has 7-fold symmetry.

Reason: A regular heptagon (n = 7, odd) has 7 reflection lines; each reflection line passes through one vertex and the midpoint of the opposite side. It also has rotational symmetry of order 7 (often called 7-fold symmetry). Lines connecting two opposite vertices or midpoints of opposite sides occur only for even-sided regular polygons, and it does not have just 1 reflection line.