Question

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. Which statement and reason accurately completes the proof?

1) Δbde ≅ Δbac; angle-angle (aa) similarity postulate
2) ∠bde ≅ ∠bac; angle-angle (aa) similarity postulate
3) ∠bde ≅ ∠bac; side-angle-side (sas) similarity postulate
4) Δbde ≅ Δbac; side-angle-side (sas) similarity postulate

Answer 1

The correct statement to complete the proof is Δbde ≅ Δbac; side-angle-side (sas) similarity postulate.

Step-by-step explanation:

The correct statement and reason that completes the proof is: 4) Δbde ≅ Δbac; side-angle-side (sas) similarity postulate. The Side-Angle-Side (SAS) similarity postulate states that if two sides of one triangle are proportional to two sides of another triangle, and the included angles are congruent, then the triangles are similar. In this case, the line parallel to one side of the triangle divides the other two sides proportionally, leading to the conclusion that the two triangles are similar.