Question

如图，有以下四个条件：①∠B+∠BCD=180°，②∠1=∠2，③∠3=∠4，④∠B=5，其中能判定AB∥CD的条件的个数有（　　）                                                                                            

                                                             

A．1                            B．2                            C．3                            D．4

Answer 1

C【考点】平行线的判定．                                                                      

【分析】根据平行线的判定定理求解，即可求得答案．                                  

【解答】解：①∵∠B+∠BDC=180°，                                                     

∴AB∥CD；                                                                                      

②∵∠1=∠2，                                                                                   

∴AD∥BC；                                                                                      

③∵∠3=∠4，                                                                                   

∴AB∥CD；                                                                                      

④∵∠B=∠5，                                                                                  

∴AB∥CD；                                                                                      

∴能得到AB∥CD的条件是①③④．                                                       

故选C．                                                                                            

【点评】此题考查了平行线的判定．此题难度不大，注意掌握数形结合思想的应用，弄清截线与被截线．