如图,在△ABC中,AB=AC,AD⊥BD,AE⊥CE,垂足分别为D,E,且AD=AE,BD与CE交于点O,请说明OB=OC的理由.

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/26 05:14:30
如图,在△ABC中,AB=AC,AD⊥BD,AE⊥CE,垂足分别为D,E,且AD=AE,BD与CE交于点O,请说明OB=OC的理由.如图,在△ABC中,AB=AC,AD⊥BD,AE⊥CE,垂足分别为D

如图,在△ABC中,AB=AC,AD⊥BD,AE⊥CE,垂足分别为D,E,且AD=AE,BD与CE交于点O,请说明OB=OC的理由.
如图,在△ABC中,AB=AC,AD⊥BD,AE⊥CE,垂足分别为D,E,且AD=AE,BD与CE交于点O,请说明OB=OC的理由.

如图,在△ABC中,AB=AC,AD⊥BD,AE⊥CE,垂足分别为D,E,且AD=AE,BD与CE交于点O,请说明OB=OC的理由.
证明:
∵AB=AC,∠E=∠D=90°,AD=AE
∴△AEC≌△ADB
∴∠ACE=∠ABD
∵AB=AC
∴∠ABC=∠ACB
∴∠ABC-∠ABD=∠ACB-∠ACE
∴∠OBC=∠OCB
∴OB=OC

∵AB = AC,AG = AF,∠AGB = ∠AFC = 90°
∴Rt△ABG≌Rt△ACF
∴∠ABG = ∠ACF
且∠BAG = ∠CAF
∴∠BAF = ∠CAG
∵AB = AC
∴∠ABC = ∠ACB
∴∠AEF = ∠ADB
∵AF = AG
∴△AEF≌△ADG
希望改下数据
∴AE = AD