1.
a,
$\Delta$ HAC và $\Delta$ ABC có:
$\widehat{AHC}=\widehat{BAC}=90^o$
$\widehat{C}$ chung
$\Rightarrow \Delta$ HAC $\backsim$ $\Delta$ ABC (g.g) (*)
b,
$\Delta$ ADH và $\Delta$ AHB có:
$\widehat{ADH}=\widehat{AHB}=90^o$
$\widehat{BAH}$ chung
$\Rightarrow \Delta$ ADH $\backsim$ $\Delta$ AHB (g.g)
$\Rightarrow \frac{AD}{AH}=\frac{AH}{AB}$
$\Leftrightarrow AB^2=AD.AH$ (1)
c,
Tương tự câu b, ta có $\Delta$ AEH $\backsim$ $\Delta$ AHC (g.g)
$\Rightarrow \frac{AE}{AH}=\frac{AH}{AC}$
$\Leftrightarrow AH^2= AE.AC$ (2)
(1)(2) $\Rightarrow AD.AH=AE.AC$
d,
AEHD là hình chữ nhật (3 góc vuông) nên $\Delta$ ADE= $\Delta$ EHA (c.c.c)
$\Delta$ EHA $\backsim$ $\Delta$ CHA, $\Delta$ CHA $\backsim$ $\Delta$ CAB
$\Rightarrow $$\Delta$ ADE $\backsim$ $\Delta$ ACB
(*) $\Rightarrow \frac{AH}{AC}=\frac{AB}{BC}$
$BC=\sqrt{AB^2+AC^2}=20cm$
$\Rightarrow$ AH= 9,6cm
$\frac{S_{ADE}}{S_{ABC}}= k^2=(\frac{9,6}{20})^2=\frac{144}{625}$
2. (Kết quả đúng)
