Given: In ∆ABC, DE is parallel to AC
Prove: BD over BA is equal to 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. DE is parallel to AC 1. Given
2.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. ∆ABC ~ ∆DBE 5. Angle-Angle (AA) Similarity Postulate
6. 6.

Question

Given: In ∆ABC,  DE is parallel to AC
Prove:  BD over BA is equal to 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.  DE is parallel to AC 1. Given 
2.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. ∆ABC ~ ∆DBE 5. Angle-Angle (AA) Similarity Postulate 
6.  6.

anonymous · Answer

complete the proof with the correct statements and reasons for 3 and 6.