a, Xét \(\Delta ACD\) và \(\Delta BCE\) có :
\(\widehat{C}:chung\)
\(\widehat{ADC}=\widehat{BEC}=90^o\)
\(\Rightarrow\) \(\Delta ACD\sim\Delta BCE\left(g.g\right)\)
b, Xét \(\Delta AEH\) và \(\Delta BDH\) có :
\(\widehat{AEH}=\widehat{BDH}=90^o\)
\(\widehat{AHE}=\widehat{BHD}\) ( đđ )
\(\Rightarrow\) \(\Delta AEH\sim\Delta BDH\left(g.g\right)\)
\(\Rightarrow\) \(\frac{AE}{EH}=\frac{BD}{HD}\) \(\Rightarrow\) \(BD=\frac{AE.HD}{EH}=\frac{8.3}{6}=4\left(cm\right)\)
Ta có : \(S_{\Delta BDH}=\frac{1}{2}BD.HD=\frac{1}{2}.4.3=6\left(cm^2\right)\)