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.

Explanation:

• A regular heptagon (7 - sided polygon) has 7 lines of symmetry. So the statement "It has only 1 line of reflectional symmetry" is false.
• For a regular heptagon, since \(n = 7\) (odd number of sides), a line of symmetry connects a vertex and the mid - point of the opposite side. When \(n\) is odd, we cannot connect two vertices (because if we connect two vertices, the two parts of the polygon on either side of the line will not be mirror images in the case of a regular odd - sided polygon) and we cannot connect the mid - points of two opposite sides (because there are no two opposite sides in a 7 - sided polygon in the sense of a regular even - sided polygon).
• The number of lines of symmetry of a regular \(n\) - sided polygon is \(n\). So for \(n = 7\), it has 7 - fold symmetry.

Answer:

C. A line of symmetry will connect a vertex and a midpoint of an opposite side.
D. It has 7 - fold symmetry.