Question

过等腰直角三角形直角顶点A作直线AM平行于斜边BC,在AM上取点D,

Answer 1

过A作AF⊥BC于F,过D作DG⊥BC于G,则DG=AF=1/2BC=1/2BD,

在Rt△BDG中,DG=1/2BD =>∠DBC=30° =>∠BDC=∠BCD=1/2(180°-30°)=75°,即∠EDC=75°

∠DEC=∠DBC+∠BCA=30°+45°=75° ∴∠EDC=∠DEC =>CD=CE