a:
Xét ΔMON có \(\widehat{MON}+\widehat{OMN}+\widehat{ONM}=180^0\)
=>\(\widehat{OMN}+\widehat{ONM}=180^0-\widehat{MON}\)
Xét ΔMOP có \(\widehat{MOP}+\widehat{OPM}+\widehat{OMP}=180^0\)
=>\(\widehat{OPM}+\widehat{OMP}=180^0-\widehat{MOP}\)
tia MO nằm giữa hai tia MN và MP
=>\(\widehat{NMP}=\widehat{NMO}+\widehat{PMO}\)
\(\widehat{M}+\widehat{MNO}+\widehat{MPO}\)
\(=\widehat{MNO}+\widehat{NMO}+\widehat{MPO}+\widehat{OMP}\)
\(=180^0-\widehat{MON}+180^0-\widehat{MOP}\)
\(=360^0-\left(\widehat{MON}+\widehat{MOP}\right)\)
\(=\widehat{NOP}\)
b: NO là phân giác của góc MNP
=>\(\widehat{MNO}=\dfrac{\widehat{MNP}}{2}\)
Xét ΔMNP có \(\widehat{NMP}+\widehat{MNP}+\widehat{MPN}=180^0\)
=>\(\widehat{MNP}+\widehat{MPN}=180^0-\widehat{NMP}\)
\(\widehat{MNO}+\widehat{MPO}=90^0-\dfrac{1}{2}\cdot\widehat{M}\)
\(\Leftrightarrow\widehat{MNP}\cdot\dfrac{1}{2}+\widehat{MPO}=\dfrac{180^0-\widehat{M}}{2}\)
=>\(\widehat{MNP}\cdot\dfrac{1}{2}+\widehat{MPO}=\dfrac{\widehat{MNP}+\widehat{MPN}}{2}\)
=>\(\widehat{MPO}=\dfrac{1}{2}\cdot\widehat{MPN}\)
=>PO là phân giác của góc MPN
