Ta có: $\overrightarrow{MN}=\overrightarrow{MA}+ \overrightarrow{AC}+\overrightarrow{CN}$
$\overrightarrow{MN}=\overrightarrow{MB}+ \overrightarrow{BD}+\overrightarrow{DN}$
Mặt khác: $\overrightarrow{MA}=-\overrightarrow{MB}$
$\overrightarrow{DN}=-\overrightarrow{CN}$
=> $2\overrightarrow{MN}=\overrightarrow{MA}+ \overrightarrow{AC}+\overrightarrow{CN}+\overrightarrow{MB}+\overrightarrow{BD}+\overrightarrow{DN}$
=> $2\overrightarrow{MN}=\overrightarrow{AC}+ \overrightarrow{BD}$
$2\overrightarrow{MN}=\overrightarrow{BC}+ \overrightarrow{AD}$
=> $2\overrightarrow{MN}=\overrightarrow{AC}+ \overrightarrow{BD}=\overrightarrow{BC}+ \overrightarrow{AD}$ (đpcm)