如图,已知AE⊥AD,AF⊥AB,AB//CD,AE=CD,AE=AD,AF=CD,求证AC=EF

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如图,已知AE⊥AD,AF⊥AB,AB//CD,AE=CD,AE=AD,AF=CD,求证AC=EF
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如图,已知AE⊥AD,AF⊥AB,AB//CD,AE=CD,AE=AD,AF=CD,求证AC=EF
如图,已知AE⊥AD,AF⊥AB,AB//CD,AE=CD,AE=AD,AF=CD,求证AC=EF

如图,已知AE⊥AD,AF⊥AB,AB//CD,AE=CD,AE=AD,AF=CD,求证AC=EF
思路:通过证明△DAC≌△AEF得到AC=EF
1) 由AB//CD可知∠ADC+∠DAB=180°
2) 又∠DAB+∠BAF+∠EAF+∠DAE=360°,将∠BAF=∠DAE=90°代入可知∠DAB+∠EAF=180°
3) 比较1)、2)的结论可知∠ADC=∠EAF,结合DA=AE,DC=AF可知△DAC≌△AEF(SAS),于是AC=EF
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