Answer:
The correct answer is;
ΔUXY ≅ Δ UST
Step-by-step explanation:
The given steps are;
1. ΔSTU with [tex]\overline{ST}\left | \right |\overline{XY}[/tex], 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. ΔUXY ≅ΔUST, 5, AA similarity theorem
6. [tex]\dfrac{SU}{XU} = \dfrac{TU}{YU}[/tex], 6. Def of similar triangles
7. SU = SX + XU, 7. Segment addition postulate
TU = TY + YU,
8. [tex]\dfrac{SX + XU}{XU} = \dfrac{TY + YU}{YU}[/tex], 8. Substitution property
9. [tex]\dfrac{SX }{XU} + 1= \dfrac{TY }{YU}+ 1[/tex], 8. Algebra simplification
By subtracting 1 from both sides of the equation, we get;
[tex]\dfrac{SX }{XU} = \dfrac{TY }{YU}[/tex]
