菱形abcd中,E在BC上,AE交BD与M,AB=AE,∠BAE=1/2∠EAD,求证:BE=BM
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 06:41:29
![菱形abcd中,E在BC上,AE交BD与M,AB=AE,∠BAE=1/2∠EAD,求证:BE=BM](/uploads/image/z/4339531-19-1.jpg?t=%E8%8F%B1%E5%BD%A2abcd%E4%B8%AD%2CE%E5%9C%A8BC%E4%B8%8A%2CAE%E4%BA%A4BD%E4%B8%8EM%2CAB%3DAE%2C%E2%88%A0BAE%3D1%2F2%E2%88%A0EAD%2C%E6%B1%82%E8%AF%81%3ABE%3DBM)
菱形abcd中,E在BC上,AE交BD与M,AB=AE,∠BAE=1/2∠EAD,求证:BE=BM
菱形abcd中,E在BC上,AE交BD与M,AB=AE,∠BAE=1/2∠EAD,求证:BE=BM
菱形abcd中,E在BC上,AE交BD与M,AB=AE,∠BAE=1/2∠EAD,求证:BE=BM
看成AM =BM了,抱歉,只需要最最后面改下
∵ABCD是菱形
∴BC//AD
∴∠AEB=∠EAD
∵AB=AE
∴∠ABE=∠AEB=∠EAD
∵∠BAE=1/2∠EAD
∴∠EAD=2∠BAE
△ABE中
5∠BAE=180°
∴∠BAE=36°
∴∠ABE=∠AEB=∠EAD=72°
∵ABCD是菱形
∴∠ABD=∠DBC=72°/2=36°
∴∠BME=∠ABD+∠BAE=72°
∴BEM=180°-36°-72°=72°
∴ ∠BEM=∠BME
∴BE=BM