Question

两条平行直线被第三条直线所截，则：                                                    

①一对同位角的角平分线互相平行；                                                       

②一对内错角的角平分线互相平行；                                                       

③一对同旁内角的角平分线互相平行；                                                    

④一对同旁内角的角平分线互相垂直．                                                    

其中正确的结论是　　　　　　．（注：请把你认为所有正确的结论的序号都填上）   

Answer 1

　①②④　．                                                

【考点】平行线的判定．                                                                         

【分析】根据平行线的性质，结合图形分析平分角之后得到的角之间的位置关系，运用平行线的判定判断是否平行；若不平行，则进一步探究其特殊性．                                                              

【解答】解：①两直线平行，同位角相等，其角平分线分得的角也相等．根据同位角相等，两直线平行可判断角平分线平行；                                                                                                   

②两直线平行，内错角相等，其角平分线分得的角也相等．根据内错角相等，两直线平行可判断角平分线平行；                                              

③显然不对；                                                                                     

④两直线平行，同旁内角互补，其角平分线分得的不同的两角互余，从而推出两条角平分线相交成90°角，即互相垂直．                                                                                                          

故正确的结论是①②④．                                                                         

【点评】本题考查的是平行线的性质和判定．