Question

3.已知在△ABC中,∠B=2∠C,AD⊥BC于D,M为BC的中点.试说明DM=0.5AB.

Answer 1

取AB中点N,连接DN、MN.

因为,MN是△ABC的中位线,

所以,MN‖AC,

可得：∠DMN = ∠C .

因为,DN是Rt△ABD斜边上的中线,

所以,DN = BN = (1/2)AB ,

可得：∠BDN = ∠B .

因为,∠DNM = ∠BDN-∠DMN = ∠B-∠C = ∠C = ∠DMN ,

所以,DM = DN = (1/2)AB ,即：DM = 0.5AB .