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. ∠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?
3. ∠BDE ≅ ∠BAC; Corresponding Angles Postulate
5. ΔBDE ~ ΔBAC; Angle-Angle (AA) Similarity Postulate
3. ΔBDE ~ ΔBAC; Corresponding Angles Postulate
5. ∠BDE ~ ∠BAC; Angle-Angle (AA) Similarity Postulate
3. ∠BDE ≅ ∠BAC; Congruent Angles Postulate
5. ΔBDE ~ ΔBAC; Angle-Angle (AA) Similarity Postulate
3. ∠BDE ≅ ∠BAC; Congruent Angles Postulate
5. ΔBDE ~ ΔBAC; Side-Angle-Side (SAS) Similarity Postulate
Question 5(Multiple Choice Worth 2 points)
(03.06 MC)

triangle ABC with segment BD where point D is between points C and A, BC equals x, BD equals y, CD equals w, DA equals z, and BA equals v

What expression represents the value of y?

y equals the square root of quantity x times v end quantity
y equals the square root of quantity w times z end quantity
y equals the square root of quantity w times the sum of w plus z end quantity
y equals the square root of quantity z times the sum of w plus z end quantity