Question

将一副直角三角尺拼成如图所示的图形，过点C作CF平分∠DCE交DE于点F，试判断CF与AB是否平行，并说明理由．                                                                       

                                                                   

Answer 1

【考点】平行线的判定．                                                                         

【分析】先根据直角三角板的性质得出∠BAC=45°，再由角平分线的性质得出∠1=45°，进而可得出结论．                   

【解答】解：CF∥AB．                                                                           

∵图中是一副直角三角板，                                                                     

∴∠BAC=45°．                                                                                  

∵CF平分∠DCE，                                                                            

∴∠1=45°，                                                                                      

∴CF∥AB．                                                                                       

【点评】本题考查的是平行线的判定，熟知直角三角板各内角的度数是解答此题的关键．