In ΔABC, . Complete the proof showing that is parallel to .

A triangle ABC with base BC is shown. A point D on side AB connects with a point E on point BC. Line DE is parallel to line AC.

Statement Reason
1. given
2.

3. using common denominators
4.
segment addition
5. Substitution Property of Equality
6. ∠ABC ≅ ∠DBE Reflexive Property of Congruence
7. SAS criterion for similarity
8. ∠BAC ≅ ∠BDE Corresponding angles of similar triangles are congruent.
9. If the corresponding angles formed by two lines intersected by a transversal are congruent, then the lines are parallel.