Question

a regular octagon has what type of symmetry?
a. line symmetry only
b. point symmetry only
c. both point and line symmetry
d. neither point nor line symmetry

Explanation:

Step1: Recall regular polygon symmetry

A regular octagon has 8 equal sides and angles. Line symmetry: A regular \(n\)-gon has \(n\) lines of symmetry. For \(n = 8\), there are 8 lines (e.g., through opposite vertices, midpoints of opposite sides). Point symmetry: A regular polygon with an even number of sides has point symmetry (180° rotational symmetry about the center).

Step2: Evaluate options

• A: Incorrect, as it has point symmetry too.
• B: Incorrect, as it has line symmetry too.
• C: Correct, as regular octagon (even - sided regular polygon) has both line and point symmetry.
• D: Incorrect, as it has both symmetries.

Answer:

C. both point and line symmetry