Question 4(multiple choice worth 2 points)

(03.06 mc)

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 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. 4.
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 ≅ ∠bac; corresponding angles postulate
4. ∠a ≅ ∠c; isosceles triangle theorem
3. ∠bde ≅ ∠bac; alternate interior angles theorem
4. ∠a ≅ ∠c; isosceles triangle theorem
3. ∠bde ≅ ∠bac; corresponding angles postulate
4. ∠b ≅ ∠b; reflexive property of equality
3. ∠bde ≅ ∠bac; alternate interior angles theorem
4. ∠b ≅ ∠b; reflexive property of equality