如图,AB=AD,AC=AE,∠BAD=∠CAE=90°,AH⊥BC鱼H,HA的延长线交DE与H,求证:GD=GE

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如图,AB=AD,AC=AE,∠BAD=∠CAE=90°,AH⊥BC鱼H,HA的延长线交DE与H,求证:GD=GE如图,AB=AD,AC=AE,∠BAD=∠CAE=90°,AH⊥BC鱼H,HA的延长线

如图,AB=AD,AC=AE,∠BAD=∠CAE=90°,AH⊥BC鱼H,HA的延长线交DE与H,求证:GD=GE
如图,AB=AD,AC=AE,∠BAD=∠CAE=90°,AH⊥BC鱼H,HA的延长线交DE与H,求证:GD=GE

如图,AB=AD,AC=AE,∠BAD=∠CAE=90°,AH⊥BC鱼H,HA的延长线交DE与H,求证:GD=GE
在BC上截取BG'=AG
∵∠BAD=∠CAE=∠AHB=∠AHC=90°
∴∠BAH+∠ABC=∠BAH+∠DAG=∠CAH+∠BCA=∠CAH+∠EAG=90°
∴∠CBA=∠DAG,∠BCA=∠EAG
又∵AB=AD,AG=BG'
∴△ABG'≌△ADG(SAS)
∴DG=AG',∠DGA=∠BG'A
∴∠EGA=∠CG'A
又∵∠BCA=∠EAG,AC=AE
∴△ACG'≌△AEG(AAS)
∴GE=AG'=GD

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