Question

Read the proof.

Given: AB ∥ DE

Prove: △ABC ~ △EDC

Triangles A B C and E D C connect at point C. Sides A B and D E are parallel.
Statement Reason
1. AB ∥ DE 1. given
2. ∠ACB and ∠ECD are vert. ∠s 2. definition of vertical angles
3. ∠ACB ≅ ∠DCE 3. vertical angles are congruent
4. ∠BDE and ∠DBA are alt. int. ∠s 4. definition of alternate interior angles
5. ∠BDE ≅ ∠DBA 5. alternate interior angles are congruent
6. △ABC ~ △EDC 6. ?
AA similarity theorem
ASA similarity theorem
AAS similarity theorem
SAS similarity theorem

Answer 1

6. △ABC ~ △EDC — by AA similarity (from steps 3 and 5, two pairs of corresponding angles are congruent)