In ΔABC shown below, segment DE is parallel to segment AC:

Triangles ABC and DBE where DE is parallel to AC

The following 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 is parallel to line segment AC 1. Given
2. Line segment AB is a transversal that intersects two parallel lines. 2. Conclusion from Statement 1.
3. 3.
4. 4.
5. ΔABC ~ ΔDBE 5. Angle-Angle (AA) Similarity Postulate
6. BD over BA equals BE over BC 6. Converse of the Side-Side-Side Similarity Theorem

Which statement and reason accurately completes the proof?
3. ∠BDE ≅ ∠BAC; Corresponding Angles Postulate
4. ∠A ≅ ∠C; Isosceles Triangle Theorem
3. ∠BDE ≅ ∠BAC; Alternate Interior Angles Theorem
4. ∠A ≅ ∠C; Isosceles Triangle Theorem
3. ∠BDE ≅ ∠BAC; Corresponding Angles Postulate
4. ∠B ≅ ∠B; Reflexive Property of Equality
3. ∠BDE ≅ ∠BAC; Alternate Interior Angles Theorem
4. ∠B ≅ ∠B; Reflexive Property of Equality