Quads 
 trapezoid 
 rectangle 
 square 
 parallelogram 
 quadrilateral 
 rhombus 
 all sides are equal
 never
 sometimes
 always
 sometimes
 sometimes
 always
 all angles are equal
 never
 always
 always
 sometimes
 sometimes
 sometimes
 exactly two angles are equal
 sometimes
 never
 never
 never
 sometimes
 never
 exactly one set of parallel sides
 always
 never
 never
 never
 sometimes
 never
 two sets of parallel sides
 never
 always
 always
 always
 sometimes
 always