如图,已知AB=DC,AE=DF,CE=BF,求证AF=DE
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如图,已知AB=DC,AE=DF,CE=BF,求证AF=DE
如图,已知AB=DC,AE=DF,CE=BF,求证AF=DE
如图,已知AB=DC,AE=DF,CE=BF,求证AF=DE
证明:
∵CE=BF,
∴BF+EF=EF+CE,
即BE=CF,
在△ABE与△DCF中,
┌ AB=DC,
┤ AE=DF,
└ BE=CF,
∴△ABE≌△DCF (SSS),
∴∠B=∠C,
在△ABF与△DCE中,
┌ AB=DC,
┤ ∠B=∠C,
└ BF=CE,
∴△ABF≌△DCE (SAS),
∴AF=DE.
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