证明角平分线在三角形ABC中,D,E在边BC上,角CAD等于角CDA,DE=EC,AC=BD,求证AD平分角BAE.(在线段BC上,各点的排列顺序是B,D,E,C,)
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![证明角平分线在三角形ABC中,D,E在边BC上,角CAD等于角CDA,DE=EC,AC=BD,求证AD平分角BAE.(在线段BC上,各点的排列顺序是B,D,E,C,)](/uploads/image/z/1230320-56-0.jpg?t=%E8%AF%81%E6%98%8E%E8%A7%92%E5%B9%B3%E5%88%86%E7%BA%BF%E5%9C%A8%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%AD%2CD%2CE%E5%9C%A8%E8%BE%B9BC%E4%B8%8A%2C%E8%A7%92CAD%E7%AD%89%E4%BA%8E%E8%A7%92CDA%2CDE%3DEC%2CAC%3DBD%2C%E6%B1%82%E8%AF%81AD%E5%B9%B3%E5%88%86%E8%A7%92BAE.%EF%BC%88%E5%9C%A8%E7%BA%BF%E6%AE%B5BC%E4%B8%8A%2C%E5%90%84%E7%82%B9%E7%9A%84%E6%8E%92%E5%88%97%E9%A1%BA%E5%BA%8F%E6%98%AFB%2CD%2CE%2CC%2C%EF%BC%89)
证明角平分线在三角形ABC中,D,E在边BC上,角CAD等于角CDA,DE=EC,AC=BD,求证AD平分角BAE.(在线段BC上,各点的排列顺序是B,D,E,C,)
证明角平分线
在三角形ABC中,D,E在边BC上,角CAD等于角CDA,DE=EC,AC=BD,求证AD平分角BAE.(在线段BC上,各点的排列顺序是B,D,E,C,)
证明角平分线在三角形ABC中,D,E在边BC上,角CAD等于角CDA,DE=EC,AC=BD,求证AD平分角BAE.(在线段BC上,各点的排列顺序是B,D,E,C,)
∵∠CAD=∠CDA∴AC=DC∴BD=DC∴AC=1/2BC∵DE=EC∴CE=1/2AC∴CE/AC=AC/BC∵∠C=∠C三角形CAE相似于三角形CAB∴∠CAE=∠ABD∵∠ADB=∠DBA+∠DAB,∠CAD=∠CAE+∠EAD∴∠BAD=∠DAE∴AD平分角BAE