AB=AC,AF=AG,AF⊥BD,交BD延长线于F,AG⊥CE交CE延长线于G求证AD=AE

AB=AC,AF=AG,AF⊥BD,交BD延长线于F,AG⊥CE交CE延长线于G求证AD=AE
AB=AC,AF=AG,AF⊥BD,交BD延长线于F,AG⊥CE交CE延长线于G求证AD=AE

AB=AC,AF=AG,AF⊥BD,交BD延长线于F,AG⊥CE交CE延长线于G求证AD=AE
证明：
因为：AB=AC,AF=AG,又∠AGC=∠AFB=90度,
则 ∠GAC=∠BAF
所以 ∠GAE=∠FAD
又因为 AG=AF ∠AGC=∠AFB=90度
所以 AD=AE

先证△AGC与△AFB全等
得到∠B=∠C
BF=CA
再证△ABD和△ACE全等
就能得出AD=AE