Question

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. ∠b ≅ ∠b 4. reflexive property of equality 5. ______ 5. 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?

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

Answer 1

In order to complete the two-column proof, we need to include the missing statements and reasons. The missing statements are ∠b ≅ ∠b and bd over ba equals be over bc. The missing reason is the converse of the side-side-side similarity theorem.

Step-by-step explanation:

The missing statements and reasons in the two-column proof are:

3. ∠b ≅ ∠b; reflexive property of equality

5. bd over ba equals be over bc; converse of the side-side-side similarity theorem

The missing statement and reason that accurately completes the proof is:

2) Δbde ≅ Δbac; angle-angle (aa) similarity postulate