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. 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. ∡BDE ≅ ∡BAC

4. Reflexive Property of Equality
5. ∆ABC ~ ∆DBE
5. Angle-Angle (AA) Similarity Postulate
6.

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. 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. ∡BDE ≅ ∡BAC
	
4. Reflexive Property of Equality
5. ∆ABC ~ ∆DBE	
5. Angle-Angle (AA) Similarity Postulate
6.