Question

如图，D是AB上一点，DF交AC于点E，AE=EC，CF∥AB．                        

求证：AD=CF．                                                                                 

                                                                     

Answer 1

【考点】全等三角形的判定与性质；平行线的性质．                                      

【专题】证明题．                                                                              

【分析】求证边相等，要先想到利用全等三角形的性质，这是一般思路．根据ASA证明△AED≌△CEF求解．                                                

【解答】证明：∵AB∥CF，                                                                    

∴∠A=∠ECF．                                                                                 

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

∴△AED≌△CEF．                                                                           

∴AD=CF．                                                                                        

【点评】本题考查三角形全等的判定方法即平行线的性质，判定两个三角形全等的一般方法有：SSS、SAS、SSA、HL．                                                                         

注意：AAA、SSA不能判定两个三角形全等，判定两个三角形全等时，必须有边的参与，若有两边一角对应相等时，角必须是两边的夹角．