Ta có hình vẽ:
a/ Vì AB < AC \(\Rightarrow\widehat{ABC}>\widehat{ACB}\) (t/c cạnh đối diện....)
\(\Rightarrow\widehat{ABM}< \widehat{ACN}\)
Ta có: BM = BA (gt)
=> \(\Delta BAMcân\) tại B
\(\Rightarrow\widehat{A_1}=\widehat{AMB}=\dfrac{180^o-\widehat{ABM}}{2}\)
Lại có: CN = CA (gt)
=> \(\Delta CANcân\) tại C
=> \(\widehat{A_3}=\widehat{ANC}=\dfrac{180^o-\widehat{ACN}}{2}\)
Có: \(\widehat{ABM}< \widehat{ACN}\left(đãcm\right)\)
=> \(180^o-\widehat{ABM}>180^o-\widehat{ACN}\)
=> \(\dfrac{180^o-\widehat{ABM}}{2}>\dfrac{180^o-\widehat{ACN}}{2}\)
hay \(\widehat{AMB}>\widehat{ANC}\)
b/ Vì \(\widehat{AMB}>\widehat{ANC}\left(ýa\right)\)
=> AM < AN (cạnh đối diện......)
