1: \(\overrightarrow{AE}+\overrightarrow{BF}+\overrightarrow{DC}=\overrightarrow{DF}+\overrightarrow{BE}+\overrightarrow{AC}\)
=>\(\overrightarrow{AE}+\overrightarrow{BF}+\overrightarrow{DC}-\overrightarrow{DF}-\overrightarrow{BE}-\overrightarrow{AC}=\overrightarrow{0}\)
=>\(\left(\overrightarrow{AE}-\overrightarrow{AC}\right)+\left(\overrightarrow{BF}-\overrightarrow{BE}\right)+\left(\overrightarrow{DC}-\overrightarrow{DF}\right)=\overrightarrow{0}\)
=>\(\overrightarrow{CE}+\overrightarrow{EF}+\overrightarrow{FC}=\overrightarrow{0}\)
=>\(\overrightarrow{CF}+\overrightarrow{FC}=\overrightarrow{0}\)
=>\(\overrightarrow{CC}=\overrightarrow{0}\)(luôn đúng)
2: \(\overrightarrow{AC}+\overrightarrow{BD}+\overrightarrow{EF}=\overrightarrow{AD}+\overrightarrow{BF}+\overrightarrow{EC}\)
=>\(\overrightarrow{AC}+\overrightarrow{BD}+\overrightarrow{EF}-\overrightarrow{AD}-\overrightarrow{BF}-\overrightarrow{EC}=\overrightarrow{0}\)
=>\(\left(\overrightarrow{AC}-\overrightarrow{AD}\right)+\left(\overrightarrow{BD}-\overrightarrow{BF}\right)+\left(\overrightarrow{EF}-\overrightarrow{EC}\right)=\overrightarrow{0}\)
=>\(\overrightarrow{DC}+\overrightarrow{FD}+\overrightarrow{CF}=\overrightarrow{0}\)
=>\(\overrightarrow{DF}+\overrightarrow{FD}=\overrightarrow{0}\)
=>\(\overrightarrow{DD}=\overrightarrow{0}\)(luôn đúng)
