Mình làm cho bạn bài 1, bạn làm bài 2 tương tự nhé.
Bạn nên tự vẽ hình nhé.
\[\begin{array}{l}
a)\,\,\,Xet\,\,\Delta AHD\,\,va\,\,\Delta ABH\,\,ta\,\,\,co:\\
\angle D = \angle H = {90^0}\\
\angle A\,\,chung\\
\Rightarrow \Delta AHD \sim \Delta ABH\,\,\left( {g - g} \right)\\
\Rightarrow \frac{{AH}}{{AB}} = \frac{{AD}}{{AH}}\\
\Rightarrow A{H^2} = AB.AD\,\,\,\left( 1 \right)\\
Xet\,\,\Delta AHE\,\,va\,\,\Delta ACH\,\,ta\,\,\,co:\\
\angle E = \angle H = {90^0}\\
\angle A\,\,chung\\
\Rightarrow \Delta AHE \sim \Delta ACH\,\,\left( {g - g} \right)\\
\Rightarrow \frac{{AH}}{{AC}} = \frac{{AE}}{{AH}}\\
\Rightarrow A{H^2} = AE.AC\,\,\,\left( 2 \right)\\
Tu\,\,\,\left( 1 \right)\,\,va\,\,\,\left( 2 \right) \Rightarrow AD.AB = AE.AC\,\,\left( { = A{H^2}} \right).\\
\Rightarrow \frac{{AD}}{{AC}} = \frac{{AE}}{{AB}}\\
Xet\,\,\,\Delta ABC\,\,\,va\,\,\,\Delta AED\,\,\,co:\\
\angle A\,\,\,chung\\
\frac{{AD}}{{AC}} = \frac{{AE}}{{AB}}\\
\Rightarrow \Delta ABC\,\, \sim \,\,\,\Delta AED\,\,\left( {c - g - c} \right).\\
b)\,\,Em\,\,\,xem\,\,lai\,\,\,de\,\,bai\,\,con\,\,\,thieu\,\,gi\,\,k\,\,nhe.\\
Ta\,\,co:\,\,\Delta ABC\,\, \sim \,\,\,\Delta AED\,\,\left( {cmt} \right)\\
\Rightarrow \frac{{AD}}{{AC}} = \frac{{AE}}{{AB}} = \frac{{ED}}{{BC}}
\end{array}\]