五边形ABCDE中,AB=AE,BC=ED,∠B=∠E.求证∠C=∠D.

连接AC、AD.因为,在△ABC和△AED中,AB = AE ,∠ABC = ∠AED ,BC = ED ,所以,△ABC ≌ △AED ,可得：AC = AD ,∠ACB = ∠ADE ；因为,△ACD是等腰三角形,所以,∠ACD = ∠ADC ,可得：∠BCD = ∠ACB+∠ACD = ∠ADE+∠ADC...