Question

△ABC中,∠B=2∠C,AD⊥BC,M为BC中点,求证：DM=1/2AB

Answer 1

取AB的中点E,连接DE、EM.
因为,DE是Rt△ABD斜边上的中线,
所以,DE = BE = (1/2)AB ,
可得：∠BDE = ∠B .
因为,EM是△ABC的中位线,
所以,EM‖AC ,
可得：∠DME = ∠C .
因为,∠DEM = ∠BDE-∠DME = ∠B-∠C = ∠C = ∠DME ,
所以,DM = DE = (1/2)AB .