Tu $H$ ke $HG//DE (G\in AB)$Ta co:$\frac{BG}{BD}=\frac{BH}{BE}=\frac{1}{4}$
mat khac :$\frac{AD}{AB}=\frac{1}{5}\Rightarrow \frac{AD}{BD}=\frac{1}{4}$
$\Rightarrow \frac{BG}{BD}=\frac{AD}{BD}\Rightarrow BG=AD\Rightarrow \frac{AD}{AG}=\frac{1}{4}$
$D,I,E$ thang hang$\Rightarrow DI//HG\Rightarrow \frac{AI}{AH}=\frac{AD}{AG}=\frac{1}{4}$
Vay $\overrightarrow{AI}=\frac{1}{4}\overrightarrow{AH}\Rightarrow m=4$