Question

question 25 of 25

which of the following are true statements about any regular polygon? check all that apply.

a. its sides are congruent line segments.
b. all of its angles have equal measures.
c. all of its angles measure \\(90^\circ\\).
d. it is a closed figure.
e. it is a quadrilateral.
f. it is a hexagon.

Explanation:

Define a regular polygon

A regular polygon is a closed geometric figure that is both equilateral (all sides are congruent) and equiangular (all angles are congruent).

Evaluate each statement

• A: True. By definition, all sides of a regular polygon are congruent.
• B: True. By definition, all interior angles of a regular polygon are equal in measure.
• C: False. The angle measure depends on the number of sides \(n\) via \(\frac{(n-2) \times 180^\circ}{n}\) (e.g., \(60^\circ\) for an equilateral triangle).
• D: True. Any polygon, by definition, is a closed plane figure.
• E: False. A regular polygon can have any number of sides \(n \ge 3\), not just 4.
• F: False. A regular polygon can have any number of sides \(n \ge 3\), not just 6.

Answer:

• A. Its sides are congruent line segments. (Correct answer)
• B. All of its angles have equal measures. (Correct answer)
• C. All of its angles measure 90°.
• D. It is a closed figure. (Correct answer)
• E. It is a quadrilateral.
• F. It is a hexagon.