Tìm các dấu hiệu nhận biết hai tam giác đồng dạng :?:

a) $\Delta CHB \sim \Delta CKD (g.g)$
$=> \dfrac{CH}{CB}=\dfrac{CK}{CD}$

b) Ta có:
$\widehat{KCH}$
$=2\widehat{HCB}+\widehat{DCB}$
$=2(90^o-\widehat{CBH})+\widehat{DCB}$
$=180^o-\widehat{DCB}$
$=\widehat{ABC}$
Mà $\dfrac{CH}{CB}=\dfrac{CK}{CD}=\dfrac{CK}{AB}$
$=> \Delta HCK \sim \Delta CBA (c.g.c)$

c) Kẻ $BM \perp AC; DN \perp AC$
$=> \Delta CDN = \Delta ABM (ch-gn)$
$=> CN=AM$
Ta có: $\Delta ABM \sim \Delta ACH (g.g)$
$=> \dfrac{AB}{AC}=\dfrac{AM}{AH}$
$=> AB.AH=AM.AC$
T/tự, ta có: $AD.AK=AN.AC$
Cộng vế theo vế, ta được:
$AB.AH+AD.AK=AC(AM+AN)=AC(CN+AM)=AC^2$