Question

question 1 of 10

only regular polygons with an even number of sides are symmetrical.

a. true
b. false

Explanation:

Analyze the definition of symmetry in regular polygons

All regular polygons possess reflectional (line) symmetry and rotational symmetry, regardless of whether their number of sides is even or odd. Specifically, a regular \(n\)-gon has exactly \(n\) lines of symmetry and rotational symmetry of order \(n\).

Evaluate the statement with counterexamples

The statement claims that "Only regular polygons with an even number of sides are symmetrical."
An equilateral triangle (a regular polygon with \(3\) sides, which is odd) has \(3\) lines of symmetry and rotational symmetry of order \(3\). A regular pentagon (\(5\) sides, which is odd) has \(5\) lines of symmetry and rotational symmetry of order \(5\). Therefore, regular polygons with an odd number of sides are also symmetrical.

Determine the truth value

Since regular polygons with an odd number of sides are also symmetrical, the statement is false.

Answer:

• A. True
• B. False (Correct answer)