Question

question 21 of 25

what kinds of polygons are symmetrical?

a. circles
b. scalene triangles
c. all regular polygons
d. none of these

Explanation:

Analyze the question requirements

The question asks: "What kinds of polygons are symmetrical?" We need to evaluate the given options based on geometric definitions of polygons and symmetry.

Evaluate Option A

Using the Geometric Definitions knowledge point, a circle is a set of all points in a plane at a given distance from a center. However, a circle is not a polygon because it does not have straight sides or vertices. Therefore, Option A is incorrect.

Evaluate Option B

Using the Polygon Symmetry knowledge point, a scalene triangle has three sides of different lengths and three different angles. It possesses no lines of symmetry and no rotational symmetry. Therefore, Option B is incorrect.

Evaluate Option C

Using the Regular Polygons and Regular Polygon Symmetry knowledge points, a regular polygon is both equilateral (all sides equal) and equiangular (all angles equal). Every regular polygon with \(n\) sides has exactly \(n\) lines of reflectional symmetry and rotational symmetry of order \(n\). Thus, all regular polygons are symmetrical. This makes Option C correct.

Evaluate Option D

Since Option C is correct, Option D ("None of these") must be incorrect.

Answer:

• A. Circles
• B. Scalene triangles
• C. All regular polygons (Correct answer)
• D. None of these