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What defines a regular polygon?

  1. All sides are equal

  2. All angles are equal

  3. Has four sides

  4. Can have different side lengths

The correct answer is: All sides are equal

A regular polygon is defined by having all sides of equal length and all interior angles of equal measure. When a polygon meets these criteria, it exhibits a high degree of symmetry, which is a fundamental characteristic of regular polygons. The equality of sides ensures that each vertex behaves consistently in relation to the others, which contributes to the shape's regularity. While the statement about all angles being equal is also true for regular polygons, simply having equal sides is often sufficient to emphasize one aspect of the polygon's regularity. The definition of a regular polygon encompasses both equal sides and equal angles, but the correct response highlights the fundamental aspect of side length that must be consistent. A polygon having four sides would be classified as a quadrilateral, but it does not necessarily mean it is regular; it could be irregular. The option stating that a polygon can have different side lengths contradicts the definition of a regular polygon, as varying side lengths are a characteristic of irregular polygons.