菱形ABCD中,E在BC上,AE交BD于M,AB等于AE,角BAE等于二分之一角EAD.求证菱形ABCD中,E在BC上,AE交BD于M,AB等于AE,角BAE等于二分之一角EAD.求证 BE=BM
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![菱形ABCD中,E在BC上,AE交BD于M,AB等于AE,角BAE等于二分之一角EAD.求证菱形ABCD中,E在BC上,AE交BD于M,AB等于AE,角BAE等于二分之一角EAD.求证 BE=BM](/uploads/image/z/9304229-29-9.jpg?t=%E8%8F%B1%E5%BD%A2ABCD%E4%B8%AD%2CE%E5%9C%A8BC%E4%B8%8A%2CAE%E4%BA%A4BD%E4%BA%8EM%2CAB%E7%AD%89%E4%BA%8EAE%2C%E8%A7%92BAE%E7%AD%89%E4%BA%8E%E4%BA%8C%E5%88%86%E4%B9%8B%E4%B8%80%E8%A7%92EAD.%E6%B1%82%E8%AF%81%E8%8F%B1%E5%BD%A2ABCD%E4%B8%AD%2CE%E5%9C%A8BC%E4%B8%8A%2CAE%E4%BA%A4BD%E4%BA%8EM%2CAB%E7%AD%89%E4%BA%8EAE%2C%E8%A7%92BAE%E7%AD%89%E4%BA%8E%E4%BA%8C%E5%88%86%E4%B9%8B%E4%B8%80%E8%A7%92EAD.%E6%B1%82%E8%AF%81+++BE%3DBM)
菱形ABCD中,E在BC上,AE交BD于M,AB等于AE,角BAE等于二分之一角EAD.求证菱形ABCD中,E在BC上,AE交BD于M,AB等于AE,角BAE等于二分之一角EAD.求证 BE=BM
菱形ABCD中,E在BC上,AE交BD于M,AB等于AE,角BAE等于二分之一角EAD.求证
菱形ABCD中,E在BC上,AE交BD于M,AB等于AE,角BAE等于二分之一角EAD.
求证 BE=BM
菱形ABCD中,E在BC上,AE交BD于M,AB等于AE,角BAE等于二分之一角EAD.求证菱形ABCD中,E在BC上,AE交BD于M,AB等于AE,角BAE等于二分之一角EAD.求证 BE=BM
证明:∵ABCD是菱形
∴∠ABD=∠CBD
AD∥BC
∴∠AEB=∠EAD
∵2∠BAE=∠EAD
∴2∠BAE=∠AEB
∵AB=AE
∴∠ABE=∠AEB
∵∠ABE+∠AEB+∠BAE=180°
∴∠BAE=36°
∠ABE=∠AEB=72°
∴∠ABD=∠CBD=36°
∵∠BME=∠BAE+∠ABD=72°
∴∠ABM=∠BAM=36°
∴AM=BM
∠BEM=∠BME=72°
∴BE=BM