Answer
never
Work Step by Step
A parallelogram has opposite sides that are parallel; therefore, parallelograms have two sets of parallel sides. A parallelogram also has opposite angles that are congruent and opposite sides that are congruent.
A trapezoid, on the other hand, only has one set of parallel lines. None of the sides or angles have to be congruent.
Similar figures must have corresponding angles that are congruent and corresponding sides that are proportional, so we can conclude that a parallelogram and a trapezoid can never be similar.
