如图,已知AB=AC,AD=AE,BD=CE.试说明:∠BAC=∠DAE

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如图,已知AB=AC,AD=AE,BD=CE.试说明:∠BAC=∠DAE

如图,已知AB=AC,AD=AE,BD=CE.试说明:∠BAC=∠DAE
如图,已知AB=AC,AD=AE,BD=CE.试说明:∠BAC=∠DAE

如图,已知AB=AC,AD=AE,BD=CE.试说明:∠BAC=∠DAE
证明
∵AB=AC,AD=AE,BD=CE
∴ΔBAD≌ΔCAD(三组对边分别相等的三角形全等)
∴∠BAD=∠CAD
∠BAC=∠BAD+∠DAC
=∠CAD+∠DAC
=∠DAE
证毕!

∵AB=AC,BD=CE,AD=AE
∴△ABD≌△ACE
∴∠BAD=∠CAE
又∵∠BAC=∠BAD+∠CAD,∠DAE=∠CAE+∠CAD
∴∠BAD=∠DAE

∵AB=AC

AD=AE

BD=CE

∴△ABD≌△ACE(SSS)

∴∠BAD=∠CAE

∴∠BAD+∠DAC=∠DAC+∠ACE

即∠BAC=∠DAE

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