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Let $ABCD$ be a convex quadrilateral, and let $M$ and $N$ be the midpoints of sides $\overline{AD}$ and $\overline{BC}$, respectively. Prove that $MN \le (AB + CD)/2$. When does equality occur?
Hint(s):
Let $P$ be the midpoint of diagonal $\overline{BD}$. What does the triangle inequality tell you about triangle $MNP$?