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 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. ∠BDE ≅ ∠BAC 3. Corresponding Angles Postulate
4. 4.
5. ΔBDE ~ ΔBAC 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?
4. ∠A ≅ ∠A; Reflexive Property of Equality
4. ∠B ≅ ∠B; Reflexive Property of Equality
4. ∠B ≅ ∠C; Isosceles Triangle Theorem
4. ∠A ≅ ∠C; Isosceles Triangle Theorem
1 answer
1 answer