What shapes can never have parallel lines? Asked by Ryan Ford Triangles are shapes that have no parallel sides. All triangles will have three sides and it is impossible for any of them to be parallel. If two lines out of three were parallel, it would be impossible to draw the shape. Arthur Nash, BA Contributor 4.9/533 ratings Rate this answer Leave your comment You may be interested inHow many parallel lines does a pentagon have? A pentagon has five sides and also has no sets of parallel lines.What polygons have parallel lines? Some shapes that have parallel sides include the parallelogram, the rectangle, the square, the trapezoid, the hexagon, and the octagon.Does a pentagon have parallel lines? A regular pentagon has no parallel or perpendicular sides, but a non-regular pentagon might have parallel and perpendicular sides. It all depends on the polygon.