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:

Step1: Recall properties of regular heptagon

A regular heptagon has \(n = 7\) sides. The number of lines of symmetry of a regular \(n -\)sided polygon is \(n\). So, a regular heptagon has \(7\) lines of symmetry.

Step2: Analyze each option

• Option 1: A regular heptagon has \(7\) lines of symmetry, not \(1\). So, "It has only 1 line of reflectional symmetry" is false.
• Option 2: For a regular heptagon, a line of symmetry can connect two vertices. For example, in a regular polygon with odd number of sides (\(n = 7\)), some lines of symmetry connect vertices.
• Option 3: In a regular heptagon (odd - sided polygon), a line of symmetry connects a vertex and the mid - point of the opposite side.
• Option 4: A regular heptagon has \(7 -\)fold rotational symmetry (not just reflectional symmetry in the context of this option's mis - framing. But if we consider the number of lines of symmetry, since \(n=7\), the number of lines of symmetry is \(7\)).
• Option 5: In a regular heptagon (odd - sided polygon), we cannot connect the mid - points of two opposite sides as a line of symmetry because there is no pair of completely opposite sides (due to odd number of sides).

Answer:

A line of symmetry will connect 2 vertices and A line of symmetry will connect a vertex and a midpoint of an opposite side.