Final answer:
Pairs of opposite sides in a regular hexagon are parallel because of the hexagon's symmetry. This symmetry is evident as the hexagon can be divided into equal equilateral triangles, with the sides facing each other in parallel arrangements.
Step-by-step explanation:
The interior angles of a regular hexagon are congruent, meaning they all have the same measure. In a regular hexagon, not only are the angles congruent, but the sides are also all equal in length. The reason that any pair of opposite sides is parallel is due to the symmetry of the hexagon. A regular hexagon can be divided into six equal equilateral triangles, each with angles of 60 degrees, and those triangles help maintain the overall symmetry of the shape.
When we look at opposite sides of a regular hexagon, we can conclude that they're parallel because they are continuations of each other. If you were to extend these sides, they would never intersect, which is a property of parallel lines. The symmetry inherent in the regular hexagon ensures that each side faces a corresponding parallel side, upholding the shape's uniformity and balance.