Question

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

Answer 1

因为AE⊥AD,AF⊥AB,则∠EAF+∠DAB=180°

CD//AB,则∠DAB+∠ADC=180°.

即∠EAF=∠ADC.

△EAF和△ADC中,AE=AD,∠EAF=∠ADC,AF=DC,

则△EAF≌△ADC(边角边)

则AC=EF.