What defines a regular polygon?

What defines a regular polygon?

• A. It has at least one curved side.
• B. All sides are congruent and all angles are equal.
• C. It has unequal sides and angles.
• D. It must contain at least 10 sides.

Answer: (B)

A regular polygon is defined as a polygon where all sides are of equal length and all interior angles are of equal measure. This property of uniformity ensures that the shape is symmetrical, making it both visually appealing and mathematically interesting. In essence, the congruence of sides means that each side of the polygon is exactly the same length, while the equality of angles means that each angle measures the same degree. This allows regular polygons to be classified into various types, such as equilateral triangles, squares, and regular pentagons, all of which exhibit these characteristics. The other options suggest different, incorrect attributes of polygons. For example, having at least one curved side would imply a shape that is not a polygon, as polygons are defined by straight sides. Unequal sides and angles describe irregular polygons, which do not meet the criteria of being regular. Finally, stating that a regular polygon must contain at least 10 sides limits the definition unnecessarily, as there are regular polygons with fewer sides, such as the triangle or square, which are also regular polygons.

A regular polygon is defined as a polygon where all sides are of equal length and all interior angles are of equal measure. This property of uniformity ensures that the shape is symmetrical, making it both visually appealing and mathematically interesting.

In essence, the congruence of sides means that each side of the polygon is exactly the same length, while the equality of angles means that each angle measures the same degree. This allows regular polygons to be classified into various types, such as equilateral triangles, squares, and regular pentagons, all of which exhibit these characteristics.

The other options suggest different, incorrect attributes of polygons. For example, having at least one curved side would imply a shape that is not a polygon, as polygons are defined by straight sides. Unequal sides and angles describe irregular polygons, which do not meet the criteria of being regular. Finally, stating that a regular polygon must contain at least 10 sides limits the definition unnecessarily, as there are regular polygons with fewer sides, such as the triangle or square, which are also regular polygons.