a) Có \(\widehat{ABC}+\widehat{ABM}=180^o;\widehat{ACB}+\widehat{ACN}=180^o\)
mà \(\widehat{ABC}=\widehat{ACB}\) do tam giác ABC cân tại A\
=> \(\widehat{ABM}=\widehat{ACN}\)
Xét \(\Delta AMB\) và \(\Delta ANC\) có :
\(AB=AC;MB=NC;\widehat{ABM}=\widehat{ACN}\)
=> \(\Delta AMB\) = \(\Delta ANC\)
=> \(\widehat{MAB}=\widehat{NAC}\) ; AM = AN ; \(\widehat{AMB}=\widehat{ANC}\)
b) Xét \(\Delta AMH\) và \(\Delta ANI\) có :
\(\widehat{MAB}=\widehat{NAC}\) ;AM = AN ; \(\widehat{AHM}=\widehat{AIN}=90^o\)
=> MH = NI ; \(\widehat{AMH}=\widehat{ANI}\)
c) Có : \(\widehat{AMB}+\widehat{HMB}=\widehat{AMH};\widehat{ANC}+\widehat{INC}=\widehat{ANI}\)
mà \(\widehat{AMH}=\widehat{ANI}\); \(\widehat{AMB}=\widehat{ANC}\)
=> \(\widehat{HMB}=\widehat{INC}\Rightarrow\Delta MON\)cân tại O