Statements
Reasons

1. △STU with ST || XY

1. given

2. ∠1 and ∠2 are corresponding angles

2. def. of corresponding angles

3. ∠3 and ∠4 are corresponding angles

3. def. of corresponding angles

4. ∠1 ≅ ∠2; ∠3 ≅ ∠4

4. corresponding angles theorem

5. ♣

5. AA similarity theorem

6. $&\frac{\sf SU}{\sf XU} = \frac{\sf TU}{\sf YU}$&

6. def. of similar triangles

7. SU = SX + XU;
TU = TY + YU

7. segment addition postulate

8. $&\frac{\sf SX \, + \, XU}{\sf XU} = \frac{\sf TY \, + \, YU}{\sf YU}$&

8. substitution property

9. $&\frac{\sf SX}{\sf XU} + \frac{\sf XU}{\sf XU} = \frac{\sf TY}{\sf YU} + \frac{\sf YU}{\sf YU}$&

9. addition of fractions

10. $&\frac{\sf SX}{\sf XU} + {\sf 1} = \frac{\sf TY}{\sf YU} + {\sf 1}$&

10. simplification

11. $&\frac{\sf SX}{\sf XU}=\frac{\sf TY}{\sf YU}$&

11. ♦