1. $ABCD$ is a parallelogram.

$\overset{\rightarrow}{BD}=a$ and $\overset{\rightarrow}{AD}=b$.
$F$ is the midpoint of $BC$.
$G$ is the midpoint of $DC$.
$AE=3EB.$

Prove that $\overset{\rightarrow}{EF}$and $\overset{\rightarrow}{AG}$ are parallel.