1. △ABC with #& \overline{\sf AB} \parallel \overleftrightarrow{\sf DE}#&
2. ∠1 and ∠3 are corresponding ∠s
2. def. of corresponding angles
3. ∠2 and ∠4 are corresponding ∠s
3. def. of corresponding angles
4. corresponding angles theorem
6. #& \frac{\sf AC}{\sf DC} = \frac{\sf BC}{\sf EC}#&
6. def. of similar triangles
7. AC = AD + DC;
BC = BE + EC
7. segment addition postulate
8. #& \frac{\sf AD + DC}{\sf DC} = \frac{\sf BE + EC}{\sf EC}#&
9. #& \frac{\sf AD}{\sf DC} + \frac{\sf DC}{\sf DC} = \frac{\sf BE}{\sf EC} + \frac{\sf EC}{\sf EC}#&
10. #& \frac{\sf AD}{\sf DC} + {\sf 1} = \frac{\sf BE}{\sf EC} + {\sf 1}#&
11. #& \frac{\sf AD}{\sf DC} = \frac{\sf BE}{\sf EC} #&