Question

已知：如图AE⊥BC，∠EAC=∠ACD，试说明BC垂直于DC．                       

                                                                        

Answer 1

【考点】平行线的判定与性质；垂线．                                                    

【分析】利用平行线的判定推出AE∥CD，再根据平行线的性质及垂线定义可得出．                 

【解答】解：∵AE⊥BC，                                                                       

∴∠AEB=90°，                                                                                  

∵∠EAC=∠ACD，                                                                            

∴AE∥CD，                                                                                      

∴∠DCB=∠AEB=90°，                                                                           

∴BC⊥DC．                                                                                      

【点评】本题考查了平行线的判定和性质，垂直的定义，熟练掌握平行线的判定定理是解题的关键．