$AB$与$AD$相等.

$\because \angle ABC+\angle 1=180^{\circ}$，$\angle ADC+\angle 2=180^{\circ}$，

而$\angle 1=\angle 2$，

$\therefore \angle ABC=\angle ADC$，

$\because AC$平分$\angle BAD$，

$\therefore \angle BAC=\angle DAC$，

在$\triangle ABC$和$\triangle ADC$中

$\left\{\begin{array}{l}\angle ABC=\angle ADC\\\angle BAC=\angle DAC\\AC=AC\end{array}\right.$，

$\therefore \triangle ABC$≌$\triangle ADC\left(AAS\right)$，

$\therefore AB=AD$.

$AB$与$AD$相等.

$\because \angle ABC+\angle 1=180^{\circ}$，$\angle ADC+\angle 2=180^{\circ}$，

而$\angle 1=\angle 2$，

$\therefore \angle ABC=\angle ADC$，

$\because AC$平分$\angle BAD$，

$\therefore \angle BAC=\angle DAC$，

在$\triangle ABC$和$\triangle ADC$中

$\left\{\begin{array}{l}\angle ABC=\angle ADC\\\angle BAC=\angle DAC\\AC=AC\end{array}\right.$，

$\therefore \triangle ABC$≌$\triangle ADC\left(AAS\right)$，

$\therefore AB=AD$.