Question

CD是三角形ABC的外角---角ACE的平分线,CD与BA的延长线交于点D,比较角BAC与角B的大小,说明理由

Answer 1

∠BAC 比 ∠B大

因为

∠ACD = (1/2)∠ACE = (1/2)(∠BAC+∠B)

∠BAC = ∠D + ∠ACD = ∠D + (1/2)(∠BAC+∠B)

(1/2)(∠BAC) = ∠D + (1/2)∠B

∠BAC = 2∠D + ∠B

∠BAC - ∠B = 2∠D>0