Question

Given: In Triangle ABC line DE is parallel to line AC
Prove: Line BD/Line BA = Line BE/Line BC

Answer 1

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 DE is parallel to AC 1. Given
2. Line 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.


Complete the proof by entering the correct statements and reasons.

Answer 2

Statement 3

angle CAB = angle EDB ( corresponding angles in parallel lines)

Statement 6

BD/BA = BE/BC the ratio of corresponding sides in similar triangles are equal.