someone please help me with with "proving that a quadrilateral is a parallelogram"

Question

anonymous · Answer

If both pairs of opposite angles of a quadrilateral are congruent, the quadrilateral is a parallelogram. If one angle is supplementary to both consecutive angles in a quadrilateral, the quadrilateral is a parallelogram. If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.

anonymous · Answer

i understand that but im asking can you help me with problems dealing with that, i need help  @kasaciara.

anonymous · Answer

oh ill try. @south843

anonymous · Answer

in the figure, the horizontal lines are parallel and AB=CD. find the measure of JM.

anonymous · Answer

@KasaCiara

anonymous · Answer

Im so sorry. Im really not sure.