Question

如图所示,DE平行BC,EF平行DC,求证：AD:AB=AF:AD

Answer 1

∵DE平行BC,∴∠ADE=∠ABC,∠AED=∠ACB,∴△ADE∽△ABC,∴AD:AB=AE:AC,

EF平行DC,∴∠AFE=∠ADC,∠AEF=∠ACD,∴△AFE∽△ADC,∴AF:AD=AE:AC,

∴AD:AB=AF:AD

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