Statements
Reasons

1. $&\frac{\sf AD}{\sf DC}=\frac{\sf BE}{\sf EC}$&

1. given

2. $&\frac{\sf AD}{\sf DC} + {\sf1} = \frac{\sf BE}{\sf EC} + {\sf1}$&

2. addition property

3. $&\frac{\sf AD}{\sf DC} + \frac{\sf DC}{\sf DC} = \frac{\sf BE}{\sf EC} + \frac{\sf EC}{\sf EC}$&

3. property of proportion

4. $&\frac{\sf AD \, + \, DC}{\sf DC} = \frac{\sf BE \, + \, EC}{\sf EC}$&

4. addition of fractions

5. AC = AD + DC;
BC = BE + EC

5. segment addition postulate

6. $&\frac{\sf AC}{\sf DC}=\frac{\sf BC}{\sf EC}$&

6. substitution property

7. ∠3 ≅ ∠3

7. reflexive property

8. △ABC ~ △DEC

8. ♣

9. ∠1 ≅ ∠2

9. ♦

10. AB || $&\overleftrightarrow{\sf DE}$&

10. corresponding angles theorem