Statements
Reasons

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

1. given

2. $&\frac {\sf AD}{\sf DC} + {\sf 1} = \frac {\sf BC}{\sf EC} + {\sf 1}$&

2. addition property

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

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 + BC

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