a/ Xét \(\Delta AMC\) có :
\(CA=CM\left(gt\right)\)
\(\Leftrightarrow\widehat{AMC}=\widehat{CAM}=\dfrac{180^0-C}{2}\)
\(\Leftrightarrow\widehat{AMC}=\widehat{CAM}\left(đpcm\right)\)
b/ Xét \(\Delta AHM\perp\) tại H
\(\Leftrightarrow\widehat{AMH}+\widehat{MAH}=90^0\)
Mà \(\widehat{CAM}+\widehat{MAN}=90^0\)
Mà \(\widehat{AMH}=\widehat{CAM}\left(cmt\right)\)
\(\Leftrightarrow\widehat{MAH}=\widehat{MAN}\)
Mà \(AM\) nằm giữa \(AB;AH\)
\(\Leftrightarrowđpcm\)
c/ Xét \(\Delta ANM;\Delta AHM\) có :
\(\left\{{}\begin{matrix}AN=AM\left(gt\right)\\\widehat{NAM}=\widehat{MAH}\left(cmt\right)\\AHchung\end{matrix}\right.\) \(\Leftrightarrow\Delta ANM=\Delta AMH\left(c.g.c\right)\)
\(\Leftrightarrow\widehat{AHM}=\widehat{AMN}\)
Mà \(\widehat{AHM}=90^0\)
\(\Leftrightarrow\widehat{AMN}=90^0\)
\(\Leftrightarrow MN\perp AB\)
