Question

which of the following are true statements about any regular polygon? check all that apply. a. it is concave. b. all of its sides are congruent. c. all of its angles are congruent. d. it has exactly 6 sides. e. it is convex. f. it is a closed figure.

Explanation:

Step1: Recall regular polygon definition

A regular polygon has all - sides congruent and all - angles congruent. It is a closed figure. Also, regular polygons are convex.

Step2: Analyze option A

Regular polygons are convex, not concave. So option A is false.

Step3: Analyze option B

By definition, all sides of a regular polygon are congruent. So option B is true.

Step4: Analyze option C

By definition, all angles of a regular polygon are congruent. So option C is true.

Step5: Analyze option D

A regular polygon can have 3 (equilateral triangle), 4 (square), 5 (regular pentagon) etc. sides, not just 6. So option D is false.

Step6: Analyze option E

Regular polygons are convex. So option E is true.

Step7: Analyze option F

A polygon is a closed - figure, and a regular polygon is a type of polygon. So option F is true.

Answer:

B. All of its sides are congruent, C. All of its angles are congruent, E. It is convex, F. It is a closed figure