Triangles RST and UVW are similar with a ratio of similarity 4:3, where vertex R corresponds to vertex U, vertex...

1. TRANSLATE the correspondence information

• Given information:
  • Triangles RST and UVW are similar
  • Similarity ratio is \(4:3\)
  • Vertex R corresponds to vertex U
  • Angle \(R = 45°\)

• What this tells us: Since R corresponds to U, angles R and U are corresponding angles in these similar triangles.

2. INFER the key relationship

• In similar triangles, corresponding angles are always equal
• The similarity ratio \(4:3\) only affects side lengths, not angle measures
• Since angle R and angle U are corresponding angles: \(\angle U = \angle R\)

3. Apply the angle relationship

• Angle \(R = 45°\)
• Therefore: angle \(U = 45°\)

Answer: A. 45°

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students incorrectly assume the similarity ratio affects angle measures, not just side lengths.

They might think: "If the ratio is 4:3, then angle U = \(\frac{3}{4} \times 45° = 33.75°\)" or try to apply the ratio in some other way to the angle measurement. Since 33.75° isn't among the choices, this leads to confusion and guessing.

Second Most Common Error:

Poor TRANSLATE reasoning: Students misunderstand the correspondence notation and think they need to use the given angle S (60°) somehow.

They might incorrectly assume angle U corresponds to angle S instead of angle R, leading them to select Choice B (60°).

The Bottom Line:

The key insight is recognizing that similarity ratios apply only to side lengths - corresponding angles in similar triangles are always equal regardless of how much larger or smaller one triangle is compared to the other.