过点\(E\)作\(EH \bot AB\)于点\(H\)，反向延长\(EH\)交\(DC\)的延长线于点\(G\)，过点\(E\)作\(EF \bot AD\)于点\(F\)，

\(\because AB//CD\)，\(EH \bot AB\)，

\(\therefore EG \bot DC\)，

\(\because \)点\(E\)是\(BC\)的中点，

\(\therefore CE = BE\)，

在\(\Delta CGE\)与\(\Delta BHE\)中，

\(\left\{ {\begin{array}{*{20}{l}}
{\angle GCE = \angle B} \\
{CE = EB} \\
{\angle CEG = \angle BEH}
\end{array}} \right.\)，

\(\therefore \Delta CGE \cong \Delta BHE\)，

\(\therefore GE = EH\)，

\(\because DE\)平分\(\angle ADC\)，

\(\therefore GE = EF\)，

\(\therefore GE = EH\)，

\(\therefore EF = EH\)，

\(\therefore AE\)是\(\angle DAB\)的平分线．

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