Definition

∠DAB =∠DCB

Substitution

AA similarity

Inscribed angle measures half its intercepted arc

∠AEB = ∠CED

△AEB ~ △CED

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

AE / CE = AB / CD

Vertical angles are equal