题目

（8分）如图，在△ABC中，D是BC的中点，DE⊥AB,DF⊥AC,垂足分别是E,F，BE=CF.求证：AD是△ABC的角平分线。                                                                                                                                                                                                                                                                                               答案： 如图，在△ABC中，D是BC的中点，DE⊥AB,DF⊥AC,垂足分别是E,F，BE=CF.求证：AD是△ABC的角平分线。解：∵DE⊥AB,DF⊥AC∴△BDE和Rt△DCF是直角三角形。∵BD=DC,  BE=CF∴△BDE≌Rt△DCF(HL)     ∴DE=DF∵DE⊥AB,DF⊥AC∴AD是角平线  解析:略 

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