Question

1. \\(overline{rt} parallel overline{uv}\\) 1. given\
2. 2. \
3. \\(\triangle rst sim \triangle usv\\) 3. \
4. 4. \

\\(\frac{su}{sr} = \frac{sv}{st}\\)\
\\(\angle suv \cong \angle srt\\) and \\(\angle svu \cong \angle str\\)\
\\(\angle suv \cong \angle rst\\) and \\(\angle usv \cong \angle srt\\)\
\\(\frac{su}{sr} = \frac{sv}{st}\\) and \\(\angle usv \cong \angle rst\\)

Explanation:

Step1: Identify alternate interior angles

When $\overline{RT} \parallel \overline{UV}$, the alternate interior angles formed by transversal $\overline{SR}$ are $\angle SUV \cong \angle RST$, and the alternate interior angles formed by transversal $\overline{ST}$ are $\angle USV \cong \angle SRT$. These are the angle pairs that establish similarity.

Step2: Match to similarity criterion

For $\triangle RST \sim \triangle USV$, the AA (Angle-Angle) Similarity Postulate applies: if two pairs of corresponding angles are congruent, the triangles are similar. The congruent angle pairs from Step 1 satisfy this.

Step3: Confirm the correct option

The option stating $\angle SUV \cong \angle RST$ and $\angle USV \cong \angle SRT$ matches the required angle pairs for the proof steps (as Statement 2, with Reason "Alternate Interior Angles Theorem", leading to Statement 3 by AA Similarity).

Answer:

$\boldsymbol{\angle SUV \cong \angle RST \text{ and } \angle USV \cong \angle SRT}$