Ta có: $\widehat{NMQ} = $180^{0} - $\widehat{PMQ}$
$\widehat{PMQ}$ = $180^{0} - $$\widehat{NQM}$
Mà $\widehat{PMQ} = $$\widehat{NQM}$
=> $\widehat{PQM} = $$\widehat{NMQ}$
Xét $\Delta MNP và \Delta MPQ$ có:
$\widehat{PMQ} = $\widehat{NQM}$
$\widehat{PQM} = $\widehat{NMQ}$
MQ chung
=> $\Delta MNP = \Delta MPQ$
=> MN=QP; MP=QN