I rewrote my proof as:
AB and CD are parallel and M and N are the midpoints of AD and BC (given hypothesis).
Draw a perpendicular line from point B to line DC.
Draw a perpendicular line from point A to line DC.
Label them points O and P.
Since AO and BP are both perpendicular lines between the same two parallel lines AO = BP
Mark the midpoint of AO and BP, label them Q and R
Both points Q and R fall on line MN
Therefore, MN is parallel to AB and CD