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Given: In ∆ABC, segment DE is parallel to segment AC .
Prove: BD over BA equals BE over BC
Triangles ABC and DBE where DE is parallel to AC.
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.
1. Line segment DE is parallel to line AC
Given
2. Line segment BA is a transversal that intersects two parallel lines.
Conclusion from Statement 1.
3.
3.
4. ∡BDE ≅ ∡BAC
Reflexive Property of Equality
5. ∆ABC ~ ∆DBE
Angle-Angle (AA) Similarity Postulate
6.
6.
Complete the proof by entering the correct statements and reasons.
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