a, Xét ΔHBA và ΔABC có :
\(\widehat{H}=\widehat{A}=90^0\)
\(\widehat{B}:chung\)
\(\Rightarrow\Delta HBA\sim\Delta ABC\left(g-g\right)\)
b,Xét ΔHBA và ΔHAC có :
\(\widehat{BHA}=\widehat{AHC}=90^0\)
\(\widehat{B}=\widehat{HAC}\left(phụ\cdot với\cdot\widehat{C}\right)\)
\(\Rightarrow\Delta HBA\sim\Delta HAC\left(g-g\right)\)
\(\Rightarrow\dfrac{AH}{HC}=\dfrac{HB}{AH}\)
\(\Rightarrow AH^2=BH.HC\)
c, Xét ΔABD và ΔHBI có :
\(\widehat{A}=\widehat{H}=90^0\)
\(\widehat{ABD}=\widehat{HBI}\left(phân\cdot giác\cdot BD\right)\)
\(\Rightarrow\Delta ABD\sim\Delta HBI\left(g-g\right)\)
\(\Rightarrow\dfrac{AB}{HB}=\dfrac{BD}{BI}\)
\(\Rightarrow AB.BI=BD.HB\)
