证明：如图$,\triangle ABC$≌$\triangle {A\’}{B\’}{C\’}$，$AD$和${A\’}{D\’}$分别是两个三角形的角平分线，
求证：$AD={A\’}{D\’}$.
证明：$\because \triangle ABC$≌$\triangle {A\’}{B\’}{C\’}$，
$\because AB={A\’}{B\’}$，$\angle B=\angle {B\’}$，$\angle BAC=\angle {B\’}{A\’}{C\’}$，
$\because AD$平分$\angle BAC$，${A\’}{D\’}$平分$\angle {B\’}{A\’}{C\’}$，
$\therefore \angle BAD=\frac{1}{2}\angle BAC$，$\angle {B\’}{A\’}{D\’}=\frac{1}{2}\angle {B\’}{A\’}{C\’}$，
$\therefore \angle BAD=\angle {B\’}{A\’}{D\’}$，
在$\triangle ABD$和$\triangle {A\’}{B\’}{D\’}$中，
$\left\{\begin{array}{l}{∠B=∠B′}\\{AB=A′B′}\\{∠BAD=∠B′A′D′}\end{array}\right.$，
$\therefore \triangle ABD$≌$\triangle {A\’}{B\’}{D\’}\left(ASA\right)$，
$\therefore AD={A\’}{D\’}$，
$\therefore$全等三角形的对应角的平分线相等.

证明：如图$,\triangle ABC$≌$\triangle {A\’}{B\’}{C\’}$，$AD$和${A\’}{D\’}$分别是两个三角形的角平分线，
求证：$AD={A\’}{D\’}$.
证明：$\because \triangle ABC$≌$\triangle {A\’}{B\’}{C\’}$，
$\because AB={A\’}{B\’}$，$\angle B=\angle {B\’}$，$\angle BAC=\angle {B\’}{A\’}{C\’}$，
$\because AD$平分$\angle BAC$，${A\’}{D\’}$平分$\angle {B\’}{A\’}{C\’}$，
$\therefore \angle BAD=\frac{1}{2}\angle BAC$，$\angle {B\’}{A\’}{D\’}=\frac{1}{2}\angle {B\’}{A\’}{C\’}$，
$\therefore \angle BAD=\angle {B\’}{A\’}{D\’}$，
在$\triangle ABD$和$\triangle {A\’}{B\’}{D\’}$中，
$\left\{\begin{array}{l}{∠B=∠B′}\\{AB=A′B′}\\{∠BAD=∠B′A′D′}\end{array}\right.$，
$\therefore \triangle ABD$≌$\triangle {A\’}{B\’}{D\’}\left(ASA\right)$，
$\therefore AD={A\’}{D\’}$，
$\therefore$全等三角形的对应角的平分线相等.