Substitution

△AEB ~ △CED

AE / CE = AB / CD

∠DAB =∠DCB

∠DAB=$$\frac{1}{2}\overset{\large\frown}{DB}$$ and ∠DCB=$$\frac{1}{2} \overset{\large\frown}{DB}$$

Definition

∠AEB = ∠CED

AA similarity

Inscribed angle measures half its intercepted arc

Vertical angles are equal