Vì N là trung điểm của CD nên ta có: $\overrightarrow{NC}+\overrightarrow{ND}=\overrightarrow{0}$
=> $\overrightarrow{MC}-\overrightarrow{MN}+\overrightarrow{MD}-\overrightarrow{MN}=\overrightarrow{0}$
=> $2\overrightarrow{MN}=\overrightarrow{MC}+\overrightarrow{MD}$
- $2\overrightarrow{MN}=\overrightarrow{MC}+\overrightarrow{MD}$
=> $2\overrightarrow{MN}=\overrightarrow{MB}+\overrightarrow{BC}+\overrightarrow{MA}+\overrightarrow{AD}$
=$\overrightarrow{BC}+\overrightarrow{AD}$
- $\overrightarrow{BC}+\overrightarrow{AD}$= $\overrightarrow{AC}-\overrightarrow{AB}+\overrightarrow{AB}+\overrightarrow{BD}$
= $\overrightarrow{AC}+\overrightarrow{BD}$
Vậy $\overrightarrow{BC}+\overrightarrow{AD}=2\overrightarrow{MN}=\overrightarrow{AC}+\overrightarrow{BD}$