a)Xét \(\Delta ABH\) và \(\Delta CBA\) có:
\(\widehat{BHA}\)=\(\widehat{BAC}\)=900
\(\widehat{B}\) chung
\(\Rightarrow\Delta ABH\sim\Delta CBA\left(g.g\right)\)
b)Áp dụng định lý Pitago,ta có:
BC2=AB2+AC2
\(\Rightarrow\)BC2=152+202
\(\Rightarrow BC^2=225+400\)
\(\Rightarrow BC^2=625\)
\(\Rightarrow BC=\sqrt{625}\)
\(\Rightarrow BC=25cm\)
c) Xét tam giác $ABH$ và $CAH$ có:
\(\widehat{AHB}=\widehat{CHA}=90^0\)
\(\widehat{BAH}=\widehat{ACH}(=90^0-\widehat{HAC})\)
\(\Rightarrow \triangle ABH\sim \triangle CAH(g.g)\Rightarrow \frac{AH}{BH}=\frac{CH}{AH}\Rightarrow AH^2=BH.CH\)
(đpcm)
