证明:作DE垂直AB于E.
AC=BC,角C=90度,则角B=45度=∠BDE,得DE=EB;
又AD平分角BAC,则CD=DE=EB;
又AD=AD,故Rt⊿ACD≌RtΔ AED(HL),得AC=AE.
所以,AC+CD=AE+EB=AB.