如图, $A B=A E, A B / / D E, \angle D A B=66^{\circ}, \angle E=36^{\circ}$.

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(1) 求 $\angle D A E$ 的度数;

(2) 若 $\angle B=30^{\circ}$, 求证: $A D=B C$.
解： (1) $\because A B / / D E$,

$\therefore \angle E=\angle E A B=36^{\circ}$,

$\because \angle D A B=\angle D A E+\angle E A B=66^{\circ}$,

$\therefore \angle D A E=\angle D A B-\angle E A B=66^{\circ}-36^{\circ}=30^{\circ}$,

$\therefore \angle D A E$ 的度数为 $30^{\circ}$.

（2）证明：由（1）可知 $\angle D A E=30^{\circ}$,

$\because A B / / D E$

$\therefore \angle E=\angle E A B$,

在 $\triangle A B C, \triangle E A D$ 中,

$\left\{\begin{array}{l}\angle D A E=\angle B=30^{\circ} \\ A E=B A \\ \angle E=\angle E A B\end{array}\right.$

$\therefore \triangle A B C \cong \triangle E A D(\mathrm{ASA})$,

$\therefore A D=B C$.