在三角形ABC中,角C=2倍的角B,AD是角ABC的角平分线,求证AB=AC+CD
问题描述：
在三角形ABC中,角C=2倍的角B,AD是角ABC的角平分线,求证AB=AC+CD
答
在AB上截取AE,使AE = AC.连结DE∵AC = AE,AD是∠BAC的角平分线,AD =AD∴△ACD≌△AED∴CD = ED,∠C = ∠AED∵∠C = 2∠B∴∠AED = 2∠B∵∠AED = ∠B + ∠EDB∴∠B=∠EDB∴ED = EB∴CD = EB∵AB = AE + EB = AC + CD...