已知:如图,AB=AC,BD=CD,DE⊥AB于E,DF⊥AC于F.求证:DE=DF.已知:如图,AB=AC,BD=CD,DE⊥AB于E,DF⊥AC于F.求证:DE=DF.

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已知:如图,AB=AC,BD=CD,DE⊥AB于E,DF⊥AC于F.求证:DE=DF.已知:如图,AB=AC,BD=CD,DE⊥AB于E,DF⊥AC于F.求证:DE=DF.
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已知:如图,AB=AC,BD=CD,DE⊥AB于E,DF⊥AC于F.求证:DE=DF.已知:如图,AB=AC,BD=CD,DE⊥AB于E,DF⊥AC于F.求证:DE=DF.
已知:如图,AB=AC,BD=CD,DE⊥AB于E,DF⊥AC于F.求证:DE=DF.
已知:如图,AB=AC,BD=CD,DE⊥AB于E,DF⊥AC于F.求证:DE=DF.

已知:如图,AB=AC,BD=CD,DE⊥AB于E,DF⊥AC于F.求证:DE=DF.已知:如图,AB=AC,BD=CD,DE⊥AB于E,DF⊥AC于F.求证:DE=DF.
有图
证明:
AB=AC,DB=DC,AD=AD,
根据SSS判定定理,得
△ADB≌△ADC,
∴∠DAB=∠DAC,
又∵∠AED=∠AFD=90°,
∴∠ADE=∠ADF,
又∵AD=AD,∠DAE=∠DAF,
∴△ADE≌△ADF,
∴DE=DF,
得证.

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