Question

A heptagon has all equal side lengths.
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

The true statements are:
- A line of symmetry will connect a vertex and a midpoint of an opposite side.
- It has 7-fold symmetry.

Explanation: a regular heptagon has dihedral symmetry D7 — 7 rotations (including the identity) and 7 reflection axes. For odd n (n=7) each reflection axis passes through a vertex and the midpoint of the opposite side, so there are 7 such axes. The other options are false.