Question

已知：如圖，∠EAC是⊿ABC的外角，AD平分∠EAC，且AD∥BC，

求證：AB=AC

 

Answer 1

見(jiàn)解析

解析:證明：∵AD∥BC                         

∴∠EAD =∠B，∠DAC =∠C               

∵AD平分∠EAC                    

∴∠EAD=∠DAC，                       

∴∠B=∠C                        

∴AB=AC

先根據(jù)平行線性質(zhì)得到∠EAD=∠B，∠DAC=∠C，再根據(jù)角平分線的性質(zhì)得到∠EAD=∠DAC，從而推出∠B=∠C，等角對(duì)等邊所以AB=AC．