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. 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. ∠b ≅ ∠b 4. reflexive property of equality 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 ≅ ∠abc; corresponding angles postulate 3. ∠bde ≅ ∠abc; alternate interior angles theorem 3. ∠bde ≅ ∠bac; corresponding angles postulate 3. ∠bde ≅ ∠bac; alternate interior angles theorem

Which statement and reason accurately complete the proof?

a. ∠bde ≅ ∠abc; corresponding angles postulate
b. ∠bde ≅ ∠abc; alternate interior angles theorem
c. ∠bde ≅ ∠bac; corresponding angles postulate
d. ∠bde ≅ ∠bac; alternate interior angles theorem

Answer 1

The statement and reason that accurately complete the proof are: ∠bde ≅ ∠abc; corresponding angles postulate. To divide the sides proportionally, we need to show that the corresponding angles are equal. According to the corresponding angles postulate, if a transversal intersects two parallel lines, then the corresponding angles formed are congruent.

Step-by-step explanation:

The statement and reason that accurately complete the proof are:

• ∠bde ≅ ∠abc; corresponding angles postulate

To divide the sides proportionally, we need to show that the corresponding angles are equal. According to the corresponding angles postulate, if a transversal intersects two parallel lines, then the corresponding angles formed are congruent. In this case, the line segment ab is a transversal that intersects the parallel lines de and ac. Since line segment de is parallel to line segment ac, we can conclude that ∠bde ≅ ∠abc.