[Toán hình 8] Chứng minh vuông góc

P

phankyanhls2000

Ta có:
$\frac{BH}{AB}=\frac{HC}{BC}=\frac{HN}{AI}$ \Rightarrow $\frac{AI}{AB}=\frac{HN}{HB}$
Xét tam giác ABI và HBN:
$\widehat{ABI}=\widehat{NHB}=90^o$
$\frac{AI}{AB}=\frac{HN}{HB}$
\Rightarrow tam giác ABI~HBN
$\widehat{ABI}=\widehat{HBN}$ \Rightarrow $\widehat{NBI}=\widehat{HBA}$
$\frac{BN}{BH}=\frac{IB}{BA}$ \Rightarrow $\frac{BN}{BI}=\frac{BM}{BA}$
\Rightarrow tam giác BNI~BHA
\Rightarrow $\widehat{BNI}=\widehat{BHA}=90^o$
\Rightarrow IN vuông góc BN
 
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