Question

兩條平行直線被第三條直線所截，則：                                                    

①一對同位角的角平分線互相平行；                                                       

②一對內錯角的角平分線互相平行；                                                       

③一對同旁內角的角平分線互相平行；                                                    

④一對同旁內角的角平分線互相垂直．                                                    

其中正確的結論是　　　　　　．（注：請把你認為所有正確的結論的序號都填上）   

Answer 1

　①②④　．                                                

【考點】平行線的判定．                                                                         

【分析】根據平行線的性質，結合圖形分析平分角之后得到的角之間的位置關系，運用平行線的判定判斷是否平行；若不平行，則進一步探究其特殊性．                                                              

【解答】解：①兩直線平行，同位角相等，其角平分線分得的角也相等．根據同位角相等，兩直線平行可判斷角平分線平行；                                                                                                   

②兩直線平行，內錯角相等，其角平分線分得的角也相等．根據內錯角相等，兩直線平行可判斷角平分線平行；                                              

③顯然不對；                                                                                     

④兩直線平行，同旁內角互補，其角平分線分得的不同的兩角互余，從而推出兩條角平分線相交成90°角，即互相垂直．                                                                                                          

故正確的結論是①②④．                                                                         

【點評】本題考查的是平行線的性質和判定．