如图所示,在三角形ABC中,角ABC=90°,BD垂直于AC于D,AE平分角BAC,AE交BD于点F. (1)求证:角BEF=角BFE. (2)若BC=80cm,BE:EC=3:5,AC=100cm,求S三角形AEC和S三角形ABC.
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![如图所示,在三角形ABC中,角ABC=90°,BD垂直于AC于D,AE平分角BAC,AE交BD于点F. (1)求证:角BEF=角BFE. (2)若BC=80cm,BE:EC=3:5,AC=100cm,求S三角形AEC和S三角形ABC.](/uploads/image/z/13700070-54-0.jpg?t=%E5%A6%82%E5%9B%BE%E6%89%80%E7%A4%BA%2C%E5%9C%A8%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%AD%2C%E8%A7%92ABC%EF%BC%9D90%C2%B0%2CBD%E5%9E%82%E7%9B%B4%E4%BA%8EAC%E4%BA%8ED%2CAE%E5%B9%B3%E5%88%86%E8%A7%92BAC%2CAE%E4%BA%A4BD%E4%BA%8E%E7%82%B9F.+%281%29%E6%B1%82%E8%AF%81%3A%E8%A7%92BEF%3D%E8%A7%92BFE.+%282%29%E8%8B%A5BC%3D80cm%2CBE%3AEC%3D3%3A5%2CAC%3D100cm%2C%E6%B1%82S%E4%B8%89%E8%A7%92%E5%BD%A2AEC%E5%92%8CS%E4%B8%89%E8%A7%92%E5%BD%A2ABC.)
如图所示,在三角形ABC中,角ABC=90°,BD垂直于AC于D,AE平分角BAC,AE交BD于点F. (1)求证:角BEF=角BFE. (2)若BC=80cm,BE:EC=3:5,AC=100cm,求S三角形AEC和S三角形ABC.
如图所示,在三角形ABC中,角ABC=90°,BD垂直于AC于D,AE平分角BAC,AE交BD于点F. (1)求证:角BEF=角BFE. (2)若BC=80cm,BE:EC=3:5,AC=100cm,求S三角形AEC和S三角形ABC.
如图所示,在三角形ABC中,角ABC=90°,BD垂直于AC于D,AE平分角BAC,AE交BD于点F. (1)求证:角BEF=角BFE. (2)若BC=80cm,BE:EC=3:5,AC=100cm,求S三角形AEC和S三角形ABC.
作EG⊥AC交AC于G,EG的长度即E点到AC的距离
因为 AE平分 ∠BAC,∠ABE=∠AGE=90度
所以三角形ABE和三角形AGE全等
所以EG=BE = 3×BC/(3+5) = 30(厘米)