$解:已知:如圖,∠C=∠C'=90°,AC=A'C',$
$AD平分∠BAC,A'D'平分 ∠B'A'C',AD=A'D'$
$求證:△ABC≌△A'B'C'$
$證明:在Rt△ACD和Rt△A'C'D'中$
$\begin{cases}AC=A'C'\\AD=A'D'\end{cases}$
$∴Rt△ACD≌Rt△A'C'D'(\mathrm {HL})$
$∴∠CAD=∠C'A'D'$
$∵AD平分∠BAC,A'D'平分∠B'A'C'$
$∴∠CAB=2∠CAD,∠C'A'B'=2∠C'A'D'$
$∴∠CAB=∠C'A'B'$
$在△ABC和△A'B'C'中$
$\begin{cases}∠CAB=∠C'A'B'\\AC=A'C'\\∠C=∠C'\end{cases}$
$∴△ABC≌△A'B'C'(\mathrm {ASA})$