问题转化为证:∠CFE=∠CEF
∠CFE = ∠CAB + ∠FBA(三角形外角等于不想邻两内角和)
∠CEF = ∠DCB + ∠CBF(同上)
因为BF为平分∠ABC,故 ∠CBF = ∠FBA
又有 ∠CAB + ∠ACD = ∠ACD + ∠DCB = 90°
故 ∠CAB = ∠DCB
所以:∠CFE=∠CEF,得证
问题转化为证:∠CFE=∠CEF
∠CFE = ∠CAB + ∠FBA(三角形外角等于不想邻两内角和)
∠CEF = ∠DCB + ∠CBF(同上)
因为BF为平分∠ABC,故 ∠CBF = ∠FBA
又有 ∠CAB + ∠ACD = ∠ACD + ∠DCB = 90°
故 ∠CAB = ∠DCB
所以:∠CFE=∠CEF,得证