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No.
A kite
A kite has no parallel sides but it is a 4 sided quadrilateral whose 4 interior angles add up to 360 degrees
not neccessarily. it can have parallel lines, but it doesn't have to. a kite for example, has no parallel lines, but it is a quad. but it can, such as rhombuses, squares, rectangles, parallelograms, and trapezoids
Yes, plenty of delta wing 'power kites' do. each set of lines connects to a yoke to maneuver the kite.