Answer
The proof is in the following form:
Column 1 of proof; Column 2 of proof.
Thus, we have:
1. Trapezoid ABCD with MN as the median; Given.
2. $CD \parallel AB \parallel MN$ ; definition of median
3. $MN = MX + NX$; Segment addition
4. The midpoint of BD is X; Whenever a line parallel to a side of a triangle passes through a midpoint of one side, it will pass through the other side's midpoint.
5. Using (2) and (4), we obtain: MN = 1/2 AB + 1/2 CD; substitution
6. $MN = 1/2(AB +CD)$; Reverse distributive property
