Statements Reasons 1. line segment AB is parallel to line segment DE 1. given 2. angle ACB and angle ECD are vert. angle s 2. definition of vertical angles 3. angle ACB is congruent to angle DCE 3. vertical angles are congruent 4. angle BDE and angle DBA are alt. int. angle s 4. definition of alternate interior angles 5. angle BDE is congruent to angle DBA 5. alternate interior angles are congruent 6. triangle ABC approximates triangle EDC 6. ? Which reason is missing in step 6?
The proof establishes two pairs of congruent angles: ∠ACB ≅ ∠DCE and ∠BDE ≅ ∠DBA. Two matching angle pairs are enough to prove triangles similar by the AA similarity theorem. So the missing reason is AA similarity theorem.
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