已知如图,菱形ABCD中,E是BC上一点,AE,BD交于M,若AB=AE,∠EAD=2∠BAE.求证:AM=BE.

问题描述:

已知如图,菱形ABCD中,E是BC上一点,AE,BD交于M,若AB=AE,∠EAD=2∠BAE.求证:AM=BE.

证明:∵AB=AE∴∠ABE=∠AEB∴四边形ABCD是菱形∴∠ABE=2∠ABM(菱形对角线平分对角)     BC//AD∴∠EAD=∠AEB=∠ABE∵∠EAD=2∠BAE∴∠ABM=∠BAE∴AM=BM∵∠BME=∠ABM+∠BAE=2∠BAE=∠AEB∴BM=BE∴...