Question

將一副直角三角尺拼成如圖所示的圖形，過點C作CF平分∠DCE交DE于點F，試判斷CF與AB是否平行，并說明理由．                                                                       

                                                                   

Answer 1

【考點】平行線的判定．                                                                         

【分析】先根據直角三角板的性質得出∠BAC=45°，再由角平分線的性質得出∠1=45°，進而可得出結論．                   

【解答】解：CF∥AB．                                                                           

∵圖中是一副直角三角板，                                                                     

∴∠BAC=45°．                                                                                  

∵CF平分∠DCE，                                                                            

∴∠1=45°，                                                                                      

∴CF∥AB．                                                                                       

【點評】本題考查的是平行線的判定，熟知直角三角板各內角的度數是解答此題的關鍵．