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

Since AB is a transversal that cuts across two parallel lines DE and AC, therefore, the corresponding angles formed, ∠BDE and ∠BAC are both congruent to each other based on the corresponding angles theorem.

Also, based on the reflexive property of equality, ∠B ≅ ∠B.

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

C. 3. ∠BDE ≅∠BAC, Corresponding Angles Postulate;

4. ∠B ≅ ∠B Reflexive Property of Equality

Learn more about two-column proof on:

https://brainly.com/question/1788884