Triangle Proportionality Theorem

Since DE and AB are parallel, by the Corresponding Angles Theorem, ∠ CDE and ∠ CAB are congruent. Similarly, ∠ CED and ∠ CBA are congruent.

Therefore, by the Angle-Angle Similarity Theorem, △ ABC and △ DEC are similar. Consequently, their corresponding sides are proportional. △ ABC ~ △ DEC ⇓ AC/DC=BC/EC Applying the Segment Addition Postulate, both numerators can be rewritten. AC &= AD+DC BC &= BE+EC Substituting these expressions into the equation above, the required proportion will be obtained.