E在AB上,设AE=AC, AD是∠A的角平分线,∠EAD=∠CAD; AD=AD, △EAD≌△CAD,[SAS] ED=CD, ∠AED=∠C=2∠B, ∠AED=∠B+∠EDB, 所以,2∠B=∠B+∠EDA, 即∠B=∠EDA, 故EB=ED=CD, 因此AB=AE+EB=AC+CD.
