Giải thích các bước giải:
a.Ta có:
$PM//AN\to \dfrac{AP}{AB}=\dfrac{NM}{NB}$
$AN//MQ\to \dfrac{AQ}{QC}=\dfrac{MN}{NC}$
Vì $N$ là trung điểm $BC\to NB=NC$
$\to \dfrac{NM}{NP}=\dfrac{MN}{NC}$
$\to \dfrac{AP}{AB}=\dfrac{AQ}{QC}$
b.Ta có:
$\dfrac{PM}{AN}+\dfrac{QM}{AN}=\dfrac{BM}{BN}+\dfrac{CM}{CN}$
$\to \dfrac{PM}{AN}+\dfrac{QM}{AN}=\dfrac{BM}{\dfrac12BC}+\dfrac{CM}{\dfrac12BC}$
$\to \dfrac{PM}{AN}+\dfrac{QM}{AN}=\dfrac{BM+CM}{\dfrac12BC}$
$\to \dfrac{PM}{AN}+\dfrac{QM}{AN}=\dfrac{BC}{\dfrac12BC}$
$\to \dfrac{PM}{AN}+\dfrac{QM}{AN}=2$
$\to PM+QN=2AN$