Yes. Regular hexagons have three sets of parallel sides.
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A hexagon (6 sides) has three sets of parallel sides.
It is possible, but not necessary. A hexagon can have 0, 2, 3, 4, 5, or 6 parallel sides. A regular hexagon has 3 parallel sides.
A regular hexagon has three pairs of parallel sides. An irregular hexagon can have two, one or none.
Of a regular hexagon, yes, since it has an even number of sides.
neither, a regular hexagon's sides hit at a 120 degree angle so they are neither parallel nor perpendicular. An irregular hexagon's can, but usually don't. In a regular hexagon (all 6 sides congruent), opposite sides are parallel.