Question

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. Which statement and reason accurately completes the proof?

1) ∠bde ≅ ∠abc; corresponding angles postulate
2) ∠bde ≅ ∠abc; alternate interior angles theorem
3) ∠bde ≅ ∠bac; corresponding angles postulate
4) ∠bde ≅ ∠bac; alternate interior angles theorem

Answer 1

Answer:4) <bde=<bac; alternate interior angles

Step-by-step explanation:

Did test got it correct.

Answer 2

The correct statement to complete the proof based on the properties of parallel lines in a triangle is that ∠BDE ≅ ∠BAC by the alternate interior angles theorem.

Step-by-step explanation:

The question deals with the properties of parallel lines and triangles. Specifically, it is related to the concept of similar triangles and the way parallel lines divide the sides of a triangle proportionally.

In ΔABC, segment DE is parallel to AC which invokes the theorem which states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally. The correct statement to complete the proof would be: ∠BDE ≅ ∠BAC; alternate interior angles theorem.

By the theorem, since DE is parallel to AC, the angles formed between these parallel lines and a transversal (line BD) are equal. Therefore, ∠BDE is congruent to ∠BAC since they are alternate interior angles formed by the parallel lines DE and AC, and the transversal BD.