五边形ABCDE中,AB=AE,BC=ED,∠B=∠E.求证∠C=∠D.
问题描述：
五边形ABCDE中,AB=AE,BC=ED,∠B=∠E.求证∠C=∠D.
答
连接AC,AD,
AB=AE,
∠B=∠E,
BC=ED ,
△ABC≌△AED，[SAS]
∠ACB=∠ADE,
AC=AD,
∠ACD=∠ADC,
∠ACB+∠ACD=∠ADE+∠ADC,
∠BCD=∠EDC,(∠C=∠D)
答
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...