如图,AB//CD,AB=CD,BF=DE.试说明:AE//CF.急

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如图,AB//CD,AB=CD,BF=DE.试说明:AE//CF.急
如图,AB//CD,AB=CD,BF=DE.试说明:AE//CF.


如图,AB//CD,AB=CD,BF=DE.试说明:AE//CF.急
∵BF=DE,∴BF+FE=DE+FE,即BE=DF.
  ∵AB//CD,∴∠B=∠D(两直线平行,内错角相等).
  在△ABE和△CDF中,∵AB=CD,∠B=∠D,BE=DF,∴△ABE≌△CDF(SAS);
  ∴∠AEB=∠CFD,
  因此AE//CF得证.

BF=DE,则BF FE=DE FE,即BE=DF,AB//CD,∠B=∠D,AB=CD,则△ABE≌△CDF(边角边),所以∠AEB=∠CFD,所以AE//CF