如图所示,已知∠BAC=∠DAE,∠ABD=∠ACE,BD=CE.求证:AB=AC,AD=AE

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如图所示,已知∠BAC=∠DAE,∠ABD=∠ACE,BD=CE.求证:AB=AC,AD=AE
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如图所示,已知∠BAC=∠DAE,∠ABD=∠ACE,BD=CE.求证:AB=AC,AD=AE
如图所示,已知∠BAC=∠DAE,∠ABD=∠ACE,BD=CE.求证:AB=AC,AD=AE

如图所示,已知∠BAC=∠DAE,∠ABD=∠ACE,BD=CE.求证:AB=AC,AD=AE

∵∠BAC=∠DAE 
   ∠BAD=∠BAC-∠DAC,∠CAE=∠DAE-∠DAC
∴∠BAD=∠CAE
又∵∠ABD=∠ACE ,BD=CE 
∴△BAD≌△CAE(AAS)
∴AB=AC,AD=AE

∵∠BAC=∠DAE 
   ∠BAD=∠BAC-∠DAC,∠CAE=∠DAE-∠DAC
∴∠BAD=∠CAE
又∵∠ABD=∠ACE ,BD=CE 
∴△BAD≌△CAE(AAS)
∴AB=AC,AD=AE