Chapter 12.CR, Problem 22CR

ABCD is a trapezoid with $\overline{BC}\Vert \overline{AD}$. Points M and N are midpoints of the diagonals. Line $\stackrel{\leftrightarrow }{CN}$ intersects $\overline{AD}$ at E.

a. Prove that $\Delta BCN\cong \Delta DEN$.

b. Prove that $\overline{MN}$ is a midsegment of $\Delta ACE$.

c. If $AD=a$, $BC=b$, express $MN$ in terms of a and b. justify your answer.