Question

Given: In ∆ABC, segment DE is parallel to segment AC .
Prove: BD over BA equals BE over BC

Statement

Reason
1. segment DE is parallel to segment AC

1. Given
2. Line segment BA is a transversal that intersects two parallel lines

2. Conclusion from Statement 1
3.

3.
4. ∡B ≅∡B

4. Reflexive Property of Equality
5.

5.
6. BD over BA equals BE over BC

6. Converse of the Side-Side-Side Similarity Theorem