2. Given tetrahedron $ABCD$ with volume $V, E$ is a point on edge $AD$, extend $AB$ to $F$ such that $BF=AB$, let the plane through points $C, E, F$ intersect $BD$ at $G$. Then the volume of tetrahedron $CDGE$ is $\qquad$ .
2. $\frac{1}{3} V$.

In $\triangle A F D$, $E$ is the midpoint of $A D$, and $B$ is the midpoint of $A F$.
$$
\begin{array}{l}
\therefore D G=\frac{2}{3} B D . \\
\therefore S_{Z_{2} E D G}=-\frac{1}{3} S_{\triangle A D B} .
\end{array}
$$
$\because$ The pyramids $C-E D G$ and $C-A D B$ have the same height,
$$
\therefore V_{C-E D G}=\frac{1}{3} V_{C-A D B}=\frac{1}{3} V .
$$