如图,在平行四边形ABCD中,过点A作AE⊥BC,垂足为E,连接DE,F为线段DE上一点,且∠AFE=∠B.若AB=4,AD=33,AE=3,则AF的长为_.

问题描述:

如图,在平行四边形ABCD中,过点A作AE⊥BC,垂足为E,连接DE,F为线段DE上一点,且∠AFE=∠B.若AB=4,AD=3

3
,AE=3,则AF的长为______.

∵四边形ABCD是平行四边形,∴AD∥BC,AB∥CD,又∵AE⊥BC,∴AE⊥AD,∵AD=33,AE=3,在Rt△ADE中,DE=AD2+AE2=6;∵AD∥BC,AB∥CD,∴∠ADF=∠CED,∠B+∠C=180°,∵∠AFE+∠AFD=180,∠AFE=∠B,∴∠AFD=∠C,...