Answer:
The given two column proof is completed as follows;
Statements [tex]{}[/tex] Reasons
1. [tex]\overline{BE}[/tex] ║ [tex]\overline {CD}[/tex] [tex]{}[/tex] 1. Given
2. ∠1 ≅ ∠2, ∠3 ≅ ∠4 [tex]{}[/tex] 2. Corresponding ∠s Post.
3. ΔABE ~ ΔACD [tex]{}[/tex] 3. AA similarity Postulate
4. [tex]\dfrac{AC}{AB} = \dfrac{AD}{AE}[/tex] [tex]{}[/tex] 4. Def. of ~ Δs
5. AC = AB + BC; AD = AE + ED [tex]{}[/tex] 5. Segment Add. Post
6. [tex]\dfrac{AB + BC}{AB} = \dfrac{AE + ED}{AE}[/tex] [tex]{}[/tex] 6. SAS Similarity Theorem
7. [tex]\dfrac{AB}{AB} + \dfrac{BC}{AB} = \dfrac{AE }{AE} + \dfrac{AE}{AE}[/tex] [tex]{}[/tex] 7. Distributive property of equality
8. [tex]1 + \dfrac{BC}{AB} = 1 + \dfrac{AE}{AE}[/tex] [tex]{}[/tex] [tex]{}[/tex] 8. [tex]Simplify \left(\dfrac{AB}{AB} =1; \dfrac{AE }{AE} =1\right)[/tex]
9. [tex]\dfrac{BC}{AB} =\dfrac{AE}{AE}[/tex] [tex]{}[/tex] [tex]{}[/tex] 9. Subtraction prop. of =
Step-by-step explanation:
The given two column proof is completed as follows;
Statements [tex]{}[/tex] Reasons
1. [tex]\overline{BE}[/tex] ║ [tex]\overline {CD}[/tex] [tex]{}[/tex] 1. Given
2. Corresponding angles are congruent (postulate)
3. Angle Angle, AA similarity Postulate
4. Def. of ~ Δs Definition of similar triangles
5. Segment Addition Postulate
6. Side-Angle-Side SAS Similarity Theorem
7. Distributive property of equality
8. [tex]1 + \dfrac{BC}{AB} = 1 + \dfrac{AE}{AE}[/tex] [tex]{}[/tex] [tex]{}[/tex] 8. [tex]Simplify \left(\dfrac{AB}{AB} =1; \dfrac{AE }{AE} =1\right)[/tex]
9. Subtraction property of equality, by subtracting 1 from both sides
