Question

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. ∠BDE ≅ ∠BAC 3. Corresponding Angles Postulate 4. 4. 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? 4. ΔBDE ~ ΔBAC; Side-Angle-Side (SAS) Similarity Postulate 5. ∠B ≅ ∠B; Reflexive Property of Equality 4. ∠B ≅ ∠B; Reflexive Property of Equality 5. ΔBDE ~ ΔBAC; Angle-Angle (AA) Similarity Postulate 4. ΔBDE ~ ΔBAC; Side-Angle-Side (SAS) Similarity Postulate 5. ∠A ≅ ∠C; Isosceles Triangle Theorem 4. ∠A ≅ ∠C; Isosceles Triangle Theorem 5. ΔBDE ~ ΔBAC; Angle-Angle (AA) Similarity Postulate

Answer 1

Answer:

4.Angle B =Angle B

Reason: Reflexive property of equality

5.Triangle BDE is similar to triangle BAC

Reason: AA similarity postulate

Step-by-step explanation:

In triangle ABC

Segment DE is parallel to segment AC.

1.Segment DE is parallel to AC

Reason: Given

2.Line segment AB is a transversal line which intersects two parallel lines

Reason:Conclusion from statement 1

3.Angle BDE congruent to angle BAC

Reason: Corresponding angles postulate

4.Angle B =Angle B

Reason: Reflexive property of equality

5.Triangle BDE is similar to triangle BAC

Reason: AA similarity postulate

6.BD over BA equals BE over BC.

Reason:When two triangles are similar then the ratio of their corresponding sides are equal

Answer 2

Answer:

3. BDE is congruent to BAC; corresponding angles postulate

4. B is congruent to B; reflexive property of equality

Step-by-step explanation:

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