Triangle ABC is reflected across a line to form triangle A'B'C'. Angles A, B, and C correspond to angles A',...

1. TRANSLATE the problem information

• Given information:
  • Triangle ABC is reflected across a line to create triangle A'B'C'
  • Angle A corresponds to angle A', angle B to B', angle C to C'
  • \(\angle\mathrm{A} = 38°\) and \(\angle\mathrm{B} = 71°\)
  • We need to find \(\angle\mathrm{A}'\)

2. INFER the key geometric principle

• Since reflection is a rigid transformation (also called an isometry), it preserves all distances, shapes, and angle measures
• This means when we reflect a figure, every angle in the original figure equals its corresponding angle in the reflected figure

3. Apply the correspondence relationship

• Since angle A corresponds to angle A', and reflections preserve angle measures:
• \(\angle\mathrm{A}' = \angle\mathrm{A} = 38°\)

Answer: (A) 38°

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't recognize that reflections preserve angle measures

Some students treat reflections like they somehow change angle sizes, perhaps thinking the reflection process alters the triangle's internal angles. They might attempt to use the given angle measures in complex calculations or look for relationships between angles A and B, not realizing the direct correspondence principle.

This leads to confusion and guessing among the available choices.

Second Most Common Error:

Poor TRANSLATE reasoning: Students misunderstand the correspondence relationship

Students might confuse which angle corresponds to which, perhaps thinking angle A corresponds to angle B' or some other incorrect pairing. With \(\angle\mathrm{A} = 38°\) and \(\angle\mathrm{B} = 71°\), they might incorrectly conclude that \(\angle\mathrm{A}' = 71°\).

This may lead them to select Choice (B) (71°).

The Bottom Line:

The key insight is recognizing that reflections are rigid transformations that preserve all geometric properties, including angle measures. Once you understand this fundamental property, the problem becomes straightforward - corresponding angles in the original and reflected figures are always equal.