2. In $\square A B C D$, $E, F$ are the midpoints of $A B, B C$ respectively, $A F$ intersects $C E$ at $G$, $A F$ intersects $D E$ at $H$, find $A H: H G: G F$.
2. Let the extensions of $C B$ and $D E$ intersect at $P$, and also $B P = B C, \frac{F P}{P B} = \frac{3}{2}$. For $\triangle A F B$ and the transversal lines $H E P$ and $C G E$, we have $\frac{A H}{H F} \cdot \frac{F P}{P B} \cdot \frac{B E}{E A} = \frac{A H}{H F} \cdot \frac{3}{2} \cdot \frac{1}{1} = 1$, which means $\frac{A H}{H F} = \frac{2}{3} ; \frac{A G}{G F} \cdot \frac{F C}{C B} \cdot \frac{B E}{E A} = \frac{A G}{G F} \cdot \frac{1}{2} \cdot \frac{1}{1} = 1$, which means $\frac{A G}{G F} = \frac{2}{1}$. From this, we find $A H: H G: G F = 6: 4: 5$.