In geometry, which characteristic is true for all regular polygons?

In geometry, which characteristic is true for all regular polygons?

• A. They have both congruent angles and sides.
• B. They can have angles that measure less than 90 degrees.
• C. They have a varying number of sides and angles.
• D. They always contain curved edges.

Answer: (A)

All regular polygons are defined by having both congruent angles and congruent sides. This means that each angle within the polygon has the same measure, and each side is of equal length. This uniformity is what classifies a polygon as "regular," distinguishing it from irregular polygons, which may have sides and angles of different lengths and measures. Regarding congruencess, for example, an equilateral triangle (which is a regular polygon) has three equal sides and three equal angles, each measuring 60 degrees. Similarly, a square, another type of regular polygon, features four sides of equal length and four right angles, each measuring 90 degrees. In contrast, while regular polygons can indeed include angles that measure less than 90 degrees (such as in an equilateral triangle), this statement is not universally true for all regular polygons. Additionally, the number of sides and angles in regular polygons can vary, but this property is not a characteristic specific to them because irregular polygons can have varying numbers of sides and angles as well. Finally, regular polygons are strictly made up of straight edges; they do not contain curved edges, which also helps affirm why the first statement about congruent angles and sides is the defining characteristic.

All regular polygons are defined by having both congruent angles and congruent sides. This means that each angle within the polygon has the same measure, and each side is of equal length. This uniformity is what classifies a polygon as "regular," distinguishing it from irregular polygons, which may have sides and angles of different lengths and measures.

Regarding congruencess, for example, an equilateral triangle (which is a regular polygon) has three equal sides and three equal angles, each measuring 60 degrees. Similarly, a square, another type of regular polygon, features four sides of equal length and four right angles, each measuring 90 degrees.

In contrast, while regular polygons can indeed include angles that measure less than 90 degrees (such as in an equilateral triangle), this statement is not universally true for all regular polygons. Additionally, the number of sides and angles in regular polygons can vary, but this property is not a characteristic specific to them because irregular polygons can have varying numbers of sides and angles as well. Finally, regular polygons are strictly made up of straight edges; they do not contain curved edges, which also helps affirm why the first statement about congruent angles and sides is the defining characteristic.