如图,AB∥CD,AC∥BD,AD与BC交于O,AE⊥BC于E,DF⊥BC于F,那么图中全等的三角形有(  )

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如图,AB∥CD,AC∥BD,AD与BC交于O,AE⊥BC于E,DF⊥BC于F,那么图中全等的三角形有(  ) A. 5对B. 6对C. 7对D. 8对

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缓慢的老鼠

2026-10-08 20:35:12

∵AB∥CD,AC∥BD,∴∠ABC=∠DCB,∠ACB=∠DBC.∵BC=CB,∴△CAB≌△CDB,∴AB=CD,AC=BD.∵AB∥CD,AC∥BD,∴∠BAO=∠CDO,∠OBA=∠OCD,∠OBD=∠OCA,∠OAC=∠ODB.∴△AOB≌△COD,△AOC≌△BOD.∴OA=OD,OC=OB.∵AE⊥BC,DF⊥BC,∠AOE=∠DOF,∴△AOE≌△DOF.∴OE=OF.∴CE=BF.∵AE=DF,AC=BD,∴△AEC≌△BFD.∵AE=DF,AB=CD,BE=CF,∴△AEB≌△DFC.还有△ACD≌△DBA.故选:C.

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  • 感性的狗
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    2026-10-08 20:35:12

    ∵AB∥CD,AC∥BD,∴∠ABC=∠DCB,∠ACB=∠DBC.∵BC=CB,∴△CAB≌△CDB,∴AB=CD,AC=BD.∵AB∥CD,AC∥BD,∴∠BAO=∠CDO,∠OBA=∠OCD,∠OBD=∠OCA,∠OAC=∠ODB.∴△AOB≌△COD,△AOC≌△BOD.∴OA=OD,OC=OB.∵AE⊥BC,DF⊥BC,∠AOE=∠DOF,∴△AOE≌△DOF.∴OE=OF.∴CE=BF.∵AE=DF,AC=BD,∴△AEC≌△BFD.∵AE=DF,AB=CD,BE=CF,∴△AEB≌△DFC.还有△ACD≌△DBA.故选:C.

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