Answer
1. Given ( Defintion of congruent segments)
2. Definition of midpoint
3. Division Property of Equality
4. Substitution
5. Definition of congruent segments
Work Step by Step
1. $AB\cong DC$ ($AB=DC$)
2. $AM=MB=\frac{AB}{2}$ and $DN=NC=\frac{DC}{2}$ As both $M$ and $N$ are midpoints.
3. $\frac{AB}{2}=\frac{DC}{2}$ (Dividing both sides of the equation in statement (1.)
4. $AM=MB=DN=NC$
5. $AM\cong MB\cong DN\cong NC$
(two segments are congruent if they have the same length)
