`a.` Xét \(\Delta ABC\) và \(\Delta HBA\) có:
\(\widehat{A}=\widehat{H}=90^o\left(gt\right)\)
\(\widehat{B}\) chung
\(\Rightarrow\Delta ABC\sim\Delta HBA\left(g-g\right)\)
\(\Rightarrow\widehat{C}=\widehat{A}\) (2 góc tương ứng)
`b.` Xét \(\Delta ABC\): Theo định lí Pytago:
\(\Rightarrow BC=\sqrt{AB^2+AC^2}=\sqrt{3^2+4^2}=5\left(cm\right)\)
\(\Rightarrow\Delta ABC\sim\Delta HBA\left(cmt\right)\)\(\Rightarrow\frac{AC}{AH}=\frac{BC}{AB}\left(t/c\right)\)
\(\Leftrightarrow AH=\frac{AC.AB}{BC}=\frac{3.4}{5}=2,4\left(cm\right)\)
`c.` Xét \(\Delta HBA\) và \(\Delta HAC\) có:
\(\widehat{H_1}=\widehat{H_2}=90^o\left(gt\right)\)
\(\widehat{A}=\widehat{C}\left(cmt\right)\)
\(\Rightarrow\Delta HBA\sim\Delta HAC\left(g-g\right)\)
\(\Rightarrow\frac{AH}{CH}=\frac{BH}{AH}\left(t/c\right)\Leftrightarrow AH^2=CH.BH\)