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Mathematics, 13.11.2020 19:10 chrisraptorofficial
N 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
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N ΔABC shown below, segment DE is parallel to segment AC:
Triangles ABC and DBE where DE is paralle...
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