求证:如果两个三角形三条内角分线分别对应相等,证明这两个三角形全等.

证明：
过C作CP//AB交AD延长线于P,过C'作C'P'//A'B'交A'D'延长线于P'
∴∠APC=∠BAP=∠CAP
∴AC=PC
同理,A'C'=P'C'
又∵AC=A'C'
∴PC=AC=A'C'=P'C'
∵CP//AB
∴△ABD∽△PCD
∴AD/PD=AB/PC
∴AD/PD=AB/AC
同理,A'D'/P'D'=A'B'/A'C'
∴AD/PD=A'B'/A'C'=AB/AC=A'D'/P'D'
又∵AD=A'D'
∴PD=P'D'
∴AP=A'P'
又∵AC=A'C',PC=P'C'
∴△ACP≌△A'C'P'
∴∠PAC=∠P'A'C'
又∵∠PAC=∠BAD,∠P'A'C'=∠B'A'D'
∴∠PAC=∠BAD=∠P'A'C'=∠B'A'D'
∴∠BAC=∠B'A'C'
又∵AB=A'B',AC=A'C'
∴△ABC≌△A'B'C'