Question

Given: In ∆ABC, segment DE is parallel to segment AC .
Prove: BD over BA equals BE over BC
The two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally.

Statement

Reason
1. Line segment DE parallel Line 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. Line segment BD over line segment BA is