1. **Problem Statement:** We are given two similar quadrilaterals PQRS and TUVW. We need to determine which statement about their angles or side ratios must be true based on similarity. 2. **Recall the properties of similar polygons:** - Corresponding angles are congruent. - Corresponding sides are proportional. 3. **Identify corresponding vertices:** Since the quadrilaterals are similar and vertices are labeled clockwise, the correspondence is: $$P \leftrightarrow T, Q \leftrightarrow U, R \leftrightarrow V, S \leftrightarrow W$$ 4. **Check each statement:** - (A) Angle QRS is congruent to angle UVW. - Angle QRS corresponds to angle UVW? - QRS is angle at vertex R formed by points Q-R-S. - UVW is angle at vertex V formed by points U-V-W. - Since $R \leftrightarrow V$, $Q \leftrightarrow U$, and $S \leftrightarrow W$, angles QRS and UVW correspond and must be congruent. - (B) Angle PQR is congruent to angle WTU. - Angle PQR is at vertex Q formed by points P-Q-R. - Angle WTU is at vertex T formed by points W-T-U. - $Q \leftrightarrow U$, but $P \leftrightarrow T$ and $W \leftrightarrow S$, so angle PQR corresponds to angle TUV, not WTU. - So (B) is false. - (C) $\frac{PQ}{WT} = \frac{QR}{TU}$ - Corresponding sides are $PQ \leftrightarrow TU$ and $QR \leftrightarrow UV$. - WT is side $W-T$, which corresponds to $S-P$, not $PQ$. - So (C) is false. - (D) $\frac{PQ}{TU} = \frac{VW}{RS}$ - $PQ \leftrightarrow TU$ is correct. - $VW$ corresponds to $RS$ because $V \leftrightarrow R$ and $W \leftrightarrow S$. - So the ratio of these corresponding sides must be equal. 5. **Conclusion:** Statements (A) and (D) must be true. Since the question asks which statement must be true, and only one choice is allowed, the best answer is (A) because it directly states angle congruence which is always true for similar polygons. **Final answer:** (A) Angle QRS is congruent to angle UVW.