14. As shown in Figure 4, in: parallelogram

$ABCD$, points $E$ and

$F$ are on: $AD$ and $CD$ respectively.

$AF$ and $CE$ intersect at point $O$.

The following statements are given:

(1) If $S_{\triangle ABF}=S_{\triangle HEC}$, then $AF=CE$;

(2) If $AF=CE$, then $S_{\triangle ARF}=S_{\triangle BEC}$;

(3) If $AF=CE$, then $\angle AOB=\angle BOC$;

(4) If $\angle AOB=\angle BOC$, then $AF=CE$. 

Among these, the correct statement numbers are $\qquad$ (please fill in all the correct conclusion numbers:)
14.(2)(3)(4) . Let the distances from point $B$ to $A F$ and $C E$ be $h_{1}$ and $h_{2}$, respectively. From the above identity, we know that $A F \cdot h_{1}=C E \cdot h_{2}$. Therefore, $A F=C E \Leftrightarrow h_{1}=h_{2} \Leftrightarrow \angle A O B=\angle B O C$. The correct conclusions are (2), (3), (4).