Chứng minh vtAB+vtDC=2vtMN biết M, N là trung điểm AD,BC

a) ta có : \(\overrightarrow{AB}+\overrightarrow{DC}=\overrightarrow{AM}+\overrightarrow{MN}+\overrightarrow{NB}+\overrightarrow{DM}+\overrightarrow{MN}+\overrightarrow{NC}\)

\(=2\overrightarrow{MN}+\left(\overrightarrow{AM}+\overrightarrow{DM}\right)+\left(\overrightarrow{NB}+\overrightarrow{NC}\right)=2\overrightarrow{MN}\left(đpcm\right)\)

b) ta có : \(\overrightarrow{AB}+\overrightarrow{CD}=\overrightarrow{AI}+\overrightarrow{IJ}+\overrightarrow{JB}+\overrightarrow{CI}+\overrightarrow{IJ}+\overrightarrow{JD}\)

\(=2\overrightarrow{IJ}+\left(\overrightarrow{AI}+\overrightarrow{CI}\right)+\left(\overrightarrow{JB}+\overrightarrow{JD}\right)=2\overrightarrow{IJ}\left(đpcm\right)\)

bn dùng định lí ta lét chứng minh được \(\overrightarrow{MJ}=\overrightarrow{IN}=\dfrac{1}{2}\overrightarrow{AB}\)

C) ta có : \(\overrightarrow{MN}+\overrightarrow{IJ}=\overrightarrow{MA}+\overrightarrow{AB}+\overrightarrow{BN}+\overrightarrow{IA}+\overrightarrow{AB}+\overrightarrow{BJ}\)

\(=2\overrightarrow{AB}+\left(\overrightarrow{MA}+\overrightarrow{BJ}\right)+\left(\overrightarrow{BN}+\overrightarrow{IA}\right)\)

d) ta có : \(\overrightarrow{IM}+\overrightarrow{IN}=\overrightarrow{IJ}+\overrightarrow{JM}+\overrightarrow{IN}=\overrightarrow{IJ}\left(đpcm\right)\)