Question

如圖，D是AB上一點，DF交AC于點E，AE=EC，CF∥AB．                        

求證：AD=CF．                                                                                 

                                                                     

Answer 1

【考點】全等三角形的判定與性質；平行線的性質．                                      

【專題】證明題．                                                                              

【分析】求證邊相等，要先想到利用全等三角形的性質，這是一般思路．根據ASA證明△AED≌△CEF求解．                                                

【解答】證明：∵AB∥CF，                                                                    

∴∠A=∠ECF．                                                                                 

又∵∠AED=∠CEF，AE=CE，                                                                 

∴△AED≌△CEF．                                                                           

∴AD=CF．                                                                                        

【點評】本題考查三角形全等的判定方法即平行線的性質，判定兩個三角形全等的一般方法有：SSS、SAS、SSA、HL．                                                                         

注意：AAA、SSA不能判定兩個三角形全等，判定兩個三角形全等時，必須有邊的參與，若有兩邊一角對應相等時，角必須是兩邊的夾角．