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 the properties of a regular polygon's reflectional symmetry

A regular \(n -\)sided polygon has \(n\) lines of reflectional symmetry. For a regular heptagon (\(n = 7\)), it has \(7\) lines of reflectional symmetry.

Step2: Analyze each option

• Option 1: A regular heptagon has \(7\) lines of reflectional symmetry, not \(1\). So, "It has only 1 line of reflectional symmetry" is false.
• Option 2: For a regular heptagon (odd - numbered \(n\)), a line of symmetry connects a vertex and the mid - point of the opposite side. It does not connect two vertices. So, "A line of symmetry will connect 2 vertices" is false.
• Option 3: For a regular heptagon (since \(n=7\) is odd), a line of symmetry connects a vertex and the mid - point of the opposite side. This is true.
• Option 4: A regular heptagon has \(7\) lines of reflectional symmetry, which means it has \(7 -\)fold symmetry. This is true.
• Option 5: For a regular heptagon (odd \(n\)), a line of symmetry does not connect the mid - points of two opposite sides. For a regular polygon with even \(n\), a line of symmetry can connect mid - points of opposite sides. So, "A line of symmetry will connect the midpoints of 2 opposite sides" is false.

Answer:

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