a,
\(\Delta ABC\) có \(AB=AC\)
\(\Leftrightarrow\Delta ABC\) cân tại A
\(\Leftrightarrow\widehat{B1}=\widehat{C1}\)
Lại có :
\(\widehat{B1}+\widehat{B2}=180^0\)
\(\widehat{C1}+\widehat{C2}=180^0\)
\(\Leftrightarrow\widehat{B2}=\widehat{C2}\)
Xét \(\Delta AMB;\Delta ANC\) có :
\(\left\{{}\begin{matrix}AB=AC\\\widehat{B2}=\widehat{C2}\\BM=CN\end{matrix}\right.\)
\(\Leftrightarrow\Delta AMB=\Delta ANC\left(c-g-c\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}AM=AN\\\widehat{M}=\widehat{N}\end{matrix}\right.\)
b, \(\Delta AMB=\Delta ANC\left(cmt\right)\)
\(\Leftrightarrow\widehat{A1}=\widehat{A2}\)
\(\Leftrightarrow\widehat{A1}+\widehat{A3}=\widehat{A2}+\widehat{A3}\)
\(\Leftrightarrow\widehat{MAC}=\widehat{BAN}\)
Xét\(\Delta AMC;\Delta ANB\) có :
\(\left\{{}\begin{matrix}AM=AN\\\widehat{MAC}=\widehat{BAN}\\AB=AC\end{matrix}\right.\)
\(\Leftrightarrow\Delta AMC=\Delta ANB\left(c-g-c\right)\)
\(\Leftrightarrow MC=NB\left(đpcm\right)\)
