Question

如图,在△ABC中,∠B=2∠C,AD⊥BC于D,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 .