Given: Points C,E,B and A,E,D are collinear

Prove: AE / CE = AB / CD

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Definition
∠DAB =∠DCB
∠AEB = ∠CED
△AEB ~ △CED
AA similarity
Inscribed angle measures half its intercepted arc
∠DAB=$$\frac{1}{2}\overset{\large\frown}{DB}$$ and ∠DCB=$$\frac{1}{2} \overset{\large\frown}{DB}$$
AE / CE = AB / CD
Substitution
Vertical angles are equal