在平行四边形ABCD中,过点B作BE⊥CD,垂足为E,连结AE,F为AE上一点,且∠BFE=∠C.(1)求证:△ABF∽△EAD;(2)若AB=4,∠BAC=30°,求AE的长;(3)在(1),(2)条件下,若AD=3,求BF的长.
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![在平行四边形ABCD中,过点B作BE⊥CD,垂足为E,连结AE,F为AE上一点,且∠BFE=∠C.(1)求证:△ABF∽△EAD;(2)若AB=4,∠BAC=30°,求AE的长;(3)在(1),(2)条件下,若AD=3,求BF的长.](/uploads/image/z/3188683-19-3.jpg?t=%E5%9C%A8%E5%B9%B3%E8%A1%8C%E5%9B%9B%E8%BE%B9%E5%BD%A2ABCD%E4%B8%AD%2C%E8%BF%87%E7%82%B9B%E4%BD%9CBE%E2%8A%A5CD%2C%E5%9E%82%E8%B6%B3%E4%B8%BAE%2C%E8%BF%9E%E7%BB%93AE%2CF%E4%B8%BAAE%E4%B8%8A%E4%B8%80%E7%82%B9%2C%E4%B8%94%E2%88%A0BFE%3D%E2%88%A0C%EF%BC%8E%EF%BC%881%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9A%E2%96%B3ABF%E2%88%BD%E2%96%B3EAD%EF%BC%9B%EF%BC%882%EF%BC%89%E8%8B%A5AB%3D4%2C%E2%88%A0BAC%3D30%C2%B0%2C%E6%B1%82AE%E7%9A%84%E9%95%BF%EF%BC%9B%EF%BC%883%EF%BC%89%E5%9C%A8%EF%BC%881%EF%BC%89%2C%EF%BC%882%EF%BC%89%E6%9D%A1%E4%BB%B6%E4%B8%8B%2C%E8%8B%A5AD%3D3%2C%E6%B1%82BF%E7%9A%84%E9%95%BF%EF%BC%8E)
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