a, Xét $\Delta ABD$ và $\Delta ACE$
Ta có: $\begin{cases}\widehat{A}:\ \rm{góc\ chung}\\\widehat{ADB}=\widehat{AEC}\ \big(=90^o\big)\end{cases}$
$\Rightarrow \Delta ABD \sim \Delta ACE\ (g-g)$
$\Rightarrow \dfrac{AB}{AC}=\dfrac{AD}{AE}$
$\Rightarrow AB.AE=AC.AD$ (đpcm)
b, Ta có: $\Delta ABD \sim \Delta ACE$ (câu a)
$\Rightarrow \dfrac{AB}{AC}=\dfrac{AD}{AE}$
Xét $\Delta ADE$ và $\Delta ABC$
Ta có: $\begin{cases}\widehat{A}:\ \rm{góc\ chung}\\\dfrac{AB}{AC}=\dfrac{AD}{AE}\ \rm{(cmt)}\end{cases}$
$\Rightarrow \Delta ADE \sim \Delta ABC\ (c-g-c)$
