連接AD
AB=AE -> △ADE繞A點(diǎn)旋轉(zhuǎn),使E點(diǎn)與B點(diǎn)重合,D點(diǎn)轉(zhuǎn)至D'
-> AD=AD',BD'=DE,∠D'BA=∠AED,∠BD'A=∠ADE
∠ABC+∠AED=180°
-> ∠ABC+∠D'BA=∠ABC+∠AED=180°
-> D',B,C三點(diǎn)在同一直線上
BC+DE=CD,BD'=DE
-> CD'=BC+BD'=BC+DE=CD
連接DD',CD'=CD
-> ∠CD'D=∠CDD'
AD=AD'
-> ∠AD'D=∠ADD'
∠BD'A=∠CD'D+∠AD'D
∠ADC=∠CDD'+∠ADD'
-> ∠BD'A=∠ADC
∠BD'A=∠ADE
-> ∠ADC=∠ADE
-> AD平分角CDE