3. As shown in Figure 1, the side length of square $A B C D$ is 2. Take any point $G$ on line segment $C D$ to construct square $C E F G$, and connect $B D$, $B F$, and $D F$. When point $G$ moves along line segment $C D$, the area of $\triangle B D F$ ( ).
(A) is greater than 2
(B) is equal to 2
(C) is less than 2
(D) cannot be determined, and depends on the position of point $G$
3. B.

Let the side length of square $C E F G$ be $b$. Then $S_{\triangle B E F}=\frac{(2+b) b}{2}=S_{\text {trapezoid } C E F D}$.
Subtracting the common part $S_{\text {trapezoid } C E F H}$, we get $S_{\triangle B C H}=S_{\triangle D H F}$. Therefore, $S_{\triangle B D F}=S_{\triangle B D H}+S_{\triangle D H F}=S_{\triangle B D H}+S_{\triangle B C H}$ $=\frac{1}{2} S_{\text {square } A B C D}=2$.