已知:如图,AD平行BC,E是线段CD的中点,AE平分角BAD.求证BE平分角AB已知:如图,AD平行BC,E是线段CD的中点,AE平分角BAD.求证BE平分角ABC
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![已知:如图,AD平行BC,E是线段CD的中点,AE平分角BAD.求证BE平分角AB已知:如图,AD平行BC,E是线段CD的中点,AE平分角BAD.求证BE平分角ABC](/uploads/image/z/14683171-67-1.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9A%E5%A6%82%E5%9B%BE%2CAD%E5%B9%B3%E8%A1%8CBC%2CE%E6%98%AF%E7%BA%BF%E6%AE%B5CD%E7%9A%84%E4%B8%AD%E7%82%B9%2CAE%E5%B9%B3%E5%88%86%E8%A7%92BAD.%E6%B1%82%E8%AF%81BE%E5%B9%B3%E5%88%86%E8%A7%92AB%E5%B7%B2%E7%9F%A5%EF%BC%9A%E5%A6%82%E5%9B%BE%2CAD%E5%B9%B3%E8%A1%8CBC%2CE%E6%98%AF%E7%BA%BF%E6%AE%B5CD%E7%9A%84%E4%B8%AD%E7%82%B9%2CAE%E5%B9%B3%E5%88%86%E8%A7%92BAD.%E6%B1%82%E8%AF%81BE%E5%B9%B3%E5%88%86%E8%A7%92ABC)
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已知:如图,AD平行BC,E是线段CD的中点,AE平分角BAD.求证BE平分角AB已知:如图,AD平行BC,E是线段CD的中点,AE平分角BAD.求证BE平分角ABC
已知:如图,AD平行BC,E是线段CD的中点,AE平分角BAD.求证BE平分角AB
已知:如图,AD平行BC,E是线段CD的中点,AE平分角BAD.求证BE平分角ABC
已知:如图,AD平行BC,E是线段CD的中点,AE平分角BAD.求证BE平分角AB已知:如图,AD平行BC,E是线段CD的中点,AE平分角BAD.求证BE平分角ABC
过E作EF‖AD交AB于F,
∵AE是∠BAD的平分线,
∴∠DAE=∠FAE
又∠DAE=∠AEF,
∴∠FAE=∠AEF,
∴AF=EF.
又E是CD的中点,
∴F也是AB的中点,(EF是梯形的中位线)
∴EF=BF,
∴∠BEF=∠FBE,
又∠BEF=∠CBE,
∴∠FBE=∠CBE,
∴BE是∠ABC的平分线.