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

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