Question

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Explanation:

Step1: Identify corresponding angles

∠1 ≅ ∠3 and ∠2 ≅ ∠4 (corresponding angles, since $\overline{ST} \parallel \overline{XY}$)

Step2: Apply AA similarity

$\triangle UXY \sim \triangle UST$ (AA similarity: two pairs of corresponding angles congruent)

Step3: Subtract 1 from both sides

From $\frac{SX}{XU} + 1 = \frac{TY}{YU} + 1$, subtract 1 from both sides (subtraction property of equality)

Answer:

Step 5: $\triangle UXY \sim \triangle UST$
Step 11: Subtraction property of equality