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? (5 points)

Answer 1

Answer: see #7 below

Step-by-step explanation:

$\begin{array}{lcl}\underline{\quad \text{ Statement}\quad }&&\underline{\quad \text{Reason}\quad}\\1.\ DE||AC&&1.\ Given\\2.\ AB\ is\ a\ transversal&&2.\ Conclusion\ from\ Statement\ 1\\3.\ &&3.\ \\4.\ \angle B=\angle B&&4.\ Reflexive\ Property\ of\ Equality\\5.\ &&5.\ \\6.\ \dfrac{BD}{BA}=\dfrac{BE}{BC}&&6.\ Converse\ of\ SSS\ Similarity\ Thm\\\end{array}$

7. ΔABC ≅ ΔDBC               7. SAS Similarity Theorem

A much easier way to prove these triangles are similar is to add either #3 or #5:

   Statement           Reason

3. ∠A ≡ ∠D              3. Corresponding Angles Postulate

                      or

5.  ∠C ≡ ∠E              5. Corresponding Angles Postulate

                    to prove

7. ΔABC ≅ ΔDBC    7. AA Similarity Theorem