Đáp án:
$\begin{array}{l}
DM//EN//BC\\
Theo\,Talet:\\
\Rightarrow \dfrac{{AD}}{{AB}} = \dfrac{{DM}}{{BC}}\\
\dfrac{{AE}}{{AB}} = \dfrac{{EN}}{{BC}}\\
\Rightarrow \dfrac{{AD}}{{AB}} + \dfrac{{AE}}{{AB}} = \dfrac{{DM}}{{BC}} + \dfrac{{EN}}{{BC}}\\
\Rightarrow \dfrac{{AD + AE}}{{AB}} = \dfrac{{DM + EN}}{{BC}}\\
\Rightarrow \dfrac{{AD + AD + ED}}{{AB}} = \dfrac{{DM + EN}}{{BC}}\\
\Rightarrow \dfrac{{AD + EB + ED}}{{AB}} = \dfrac{{DM + EN}}{{BC}}\\
\left( {Do:AD = EB} \right)\\
\Rightarrow \dfrac{{AB}}{{AB}} = 1 = \dfrac{{DM + EN}}{{BC}}\\
\Rightarrow DM + EN = BC
\end{array}$
