AD=BC,BE⊥AC于E,DF⊥AC于F,BE=DF.请判断△ABE≡△CDF和AB平行CD都成立吗?
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![AD=BC,BE⊥AC于E,DF⊥AC于F,BE=DF.请判断△ABE≡△CDF和AB平行CD都成立吗?](/uploads/image/z/13311663-15-3.jpg?t=AD%3DBC%2CBE%E2%8A%A5AC%E4%BA%8EE%2CDF%E2%8A%A5AC%E4%BA%8EF%2CBE%3DDF.%E8%AF%B7%E5%88%A4%E6%96%AD%E2%96%B3ABE%E2%89%A1%E2%96%B3CDF%E5%92%8CAB%E5%B9%B3%E8%A1%8CCD%E9%83%BD%E6%88%90%E7%AB%8B%E5%90%97%3F)
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AD=BC,BE⊥AC于E,DF⊥AC于F,BE=DF.请判断△ABE≡△CDF和AB平行CD都成立吗?
AD=BC,BE⊥AC于E,DF⊥AC于F,BE=DF.请判断△ABE≡△CDF和AB平行CD都成立吗?
AD=BC,BE⊥AC于E,DF⊥AC于F,BE=DF.请判断△ABE≡△CDF和AB平行CD都成立吗?
能成立
证明:
∵BE⊥AC,DF⊥AC,AD=BC,BE=DF
∴△ADF全等于△CBE
∴AD=BC,∠CAD=∠ACB
∴BC∥AD
∴平行四边形ABCD(BC∥AD,BC=AD)
∴AB∥CD,AB=CD
∵BE⊥AC,DF⊥AC,BE=DF
∴△ABE全等于△CDF
证明:
∵BE⊥AC,DF⊥AC,AD=BC,BE=DF
∴△ADF全等于△CBE
∴AD=BC,∠CAD=∠ACB
∴BC∥AD
∴平行四边形ABCD(BC∥AD,BC=AD)
∴AB∥CD,AB=CD
∵BE⊥AC,DF⊥AC, BE=DF
∴△ABE全等于△CDF
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