Point, point $E, F$ are the centroids of $\triangle A B D$ and $\triangle A C D$ respectively, connecting $E, F$ intersects $A D$ at point $G$. What is the value of $\frac{D G}{G A}$? (1991-1992 Guangzhou, Luoyang, Fuzhou, Wuhan, Chongqing Junior High School League)
Connect $B E, C F$, and extend them to intersect at $M$. According to property $5^{\circ}$, $M$ is the midpoint of $A D$.
$\because E, F$ are the centroids of
$\triangle A B D$ and $\triangle A C D$,
$$
\therefore \frac{M E}{M B}=\frac{M F}{M C}=\frac{1}{3} \text {. }
$$

Thus, $E F / / B C, E G / / B D$.
Therefore, $\frac{M G}{D M}=\frac{M E}{M B}=\frac{1}{3}, \frac{D G}{D M}=\frac{B E}{B M}=\frac{2}{3}$.
$$
\begin{aligned}
& M G=\frac{1}{3} D M, D G=\frac{2}{3} D M, \\
A G= & A M+M G \\
= & D M+\frac{1}{3} D M=\frac{4}{3} D M .
\end{aligned}
$$

Hence $\frac{D G}{G A}=\frac{\frac{2}{3} D M}{\frac{4}{3} D M}=\frac{1}{2}$