如图所示,已知AB=AC,BD=CD,DE⊥AB交AB延长线与E,DF⊥AC交AC延长线与E.求证DE=DF

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如图所示,已知AB=AC,BD=CD,DE⊥AB交AB延长线与E,DF⊥AC交AC延长线与E.求证DE=DF

如图所示,已知AB=AC,BD=CD,DE⊥AB交AB延长线与E,DF⊥AC交AC延长线与E.求证DE=DF
如图所示,已知AB=AC,BD=CD,DE⊥AB交AB延长线与E,DF⊥AC交AC延长线与E.求证DE=DF

如图所示,已知AB=AC,BD=CD,DE⊥AB交AB延长线与E,DF⊥AC交AC延长线与E.求证DE=DF
证明:连接AD
∵AB=AC,BD=CD,AD=AD
∴△ABD≌△ACD (SSS)
∴∠BAD=∠CAD
∵DE⊥AB,DF⊥AC
∴∠AED=∠AFD=90
∴△AED≌△AFD (AAS)
∴DE=DF
或:
证明:连接AD
∵AB=AC,BD=CD,AD=AD
∴△ABD≌△ACD (SSS)
∴∠BAD=∠CAD
∵DE⊥AB,DF⊥AC
∴DE=DF (角平分线性质)