Question

五边形ABCDE中,AB=AE,BC=ED,∠B=∠E.求证∠C=∠D.

Answer 1

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 = ∠CDE ,

即有：∠C = ∠D .