Question

Please answer 2,3, and 6

Answer 1

Answer:

The given two column proof is completed as follows;

Statements    ${}$                                               Reasons

1. $\overline{BE}$ ║ $\overline {CD}$    ${}$                                               1. Given

2. ∠1 ≅ ∠2, ∠3 ≅ ∠4 ${}$                                    2. Corresponding ∠s Post.

3. ΔABE ~ ΔACD ${}$                                          3. AA similarity Postulate

4. $\dfrac{AC}{AB} = \dfrac{AD}{AE}$    ${}$                                              4. Def. of ~ Δs

5. AC = AB + BC; AD = AE + ED   ${}$                5. Segment Add. Post

6. $\dfrac{AB + BC}{AB} = \dfrac{AE + ED}{AE}$   ${}$                           6. SAS Similarity Theorem

7. $\dfrac{AB}{AB} + \dfrac{BC}{AB} = \dfrac{AE }{AE} + \dfrac{AE}{AE}$   ${}$                          7. Distributive property of equality

8. $1 + \dfrac{BC}{AB} = 1 + \dfrac{AE}{AE}$  ${}$    ${}$                               8. $Simplify \left(\dfrac{AB}{AB} =1; \dfrac{AE }{AE} =1\right)$

9. $\dfrac{BC}{AB} =\dfrac{AE}{AE}$          ${}$    ${}$                                    9. Subtraction prop. of =

Step-by-step explanation:

The given two column proof is completed as follows;

Statements    ${}$                                               Reasons

1. $\overline{BE}$ ║ $\overline {CD}$    ${}$                                               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. $1 + \dfrac{BC}{AB} = 1 + \dfrac{AE}{AE}$  ${}$    ${}$                               8. $Simplify \left(\dfrac{AB}{AB} =1; \dfrac{AE }{AE} =1\right)$

9. Subtraction property of equality, by subtracting 1 from both sides