AB = AE-& gt； △ADE rotates around point A, so that point E coincides with point B, and point D turns to D'

-& gt； AD=AD '，BD'=DE，∠D'BA=∠AED，∠BD'A=∠ADE

∠ABC+∠AED= 180

-& gt； ∠ABC+∠ Daba =∠ABC+∠AED= 180

-& gt； D', b and c are on the same straight line.

BC+DE=CD，BD'=DE

-& gt； CD'=BC+BD'=BC+DE=CD

Connection DD', CD'=CD

-& gt； ∠CD'D=∠CDD

AD=AD '

-& gt； ∠AD'D=∠ADD '

BD'A=∠CD'D+∠AD'D

∠ADC =∠CDD '+∠ addition'

-& gt； ∠BD'A=∠ADC

∠BD'A=∠ADE

-& gt； ∠ADC=∠ADE

-& gt； AD bisection angle CDE