a,
$\Delta$ ABC có MN//BC
=> $\frac{MN}{AN}= \frac{BC}{AC}$ (1)
$\Delta$ ABE có MF//BE
=> $\frac{AF}{AM}= \frac{AE}{AB}$ (2)
Lấy (1) nhân (2):
$\frac{MN}{AN}.\frac{AF}{AM}= \frac{BC}{AC}.\frac{AE}{AB}$
b,
$\Delta$ ABE có MF//BE
=> $\frac{MF}{BE}= \frac{AM}{AB}$
$\Delta$ ABC có MN//BC
=> $\frac{MN}{BC}= \frac{AM}{AB}$
=> $\frac{MF}{BE}= \frac{MN}{BC}$
<=> $\frac{MF}{MN}= \frac{BE}{BC}= \frac{1}{2}$
Vậy MF= $\frac{1}{2}$ MN => F là trung điểm MN