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Any polygon with four or more sides can have perpendicular and parallel lines.
Perpendicular lines
Oh, dude, a rectangle has like, two perpendicular lines. One going up and down, and one going side to side. It's like, the basic geometry you learn in elementary school, man. So, yeah, two perpendicular lines for a rectangle.
Yes, being that perpendicular lines are by definition intersecting lines forming four 90 degree (right) angles.
A right trapezoid has exactly one pair of perpendicular lines and is a quadrilateral.