There can be no convex polygon with three parallel sides. There are concave polygons with 6 or more sides that have three parallel lines.
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The parallel sides of a polygon are sides that are segments of parallel lines. A polygon need not have any parallel lines. A triangle, for example, is a polygon that cannot have parallel lines.
Triangles never have parallel lines
Any polygon with four or more sides can have perpendicular and parallel lines.
Lines that never touch and are equal distance from each other.
No. it is the only polygon that can not have parallel lines all though any regular polygon with an odd number of lines will have no parallel lines If three points were in a straight line it could be argued that these formed a triangle with parallel sides, though really it would be just a line; or if we had a triangle with infinite height the sides would be parallel. In any other case, no.