Triangles EFG and JKL are congruent, where E, F, and G correspond to J, K, and L, respectively. The measure...

1. TRANSLATE the problem information

• Given information:
  • Triangles EFG and JKL are congruent
  • E corresponds to J, F corresponds to K, G corresponds to L
  • Angle E = \(45°\)
  • Angle F = \(20°\)
  • Need to find: angle J

2. INFER the key relationship

• Since the triangles are congruent, corresponding angles must be equal
• The problem tells us that E corresponds to J
• Therefore: \(\text{angle E} = \text{angle J}\)

3. Apply the relationship

• Since angle E = \(45°\)
• And \(\text{angle E} = \text{angle J}\)
• Therefore: angle J = \(45°\)

Answer: B. 45°

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students may confuse which angles correspond to which other angles.

Since the problem gives both angle E = \(45°\) and angle F = \(20°\), students might think that angle J equals angle F instead of angle E. They might not carefully track that E corresponds to J specifically.

This may lead them to select Choice A (20°).

Second Most Common Error:

Poor TRANSLATE reasoning: Students might try to perform unnecessary calculations with the given angle measures.

Instead of recognizing this is purely about correspondence, they might try to add angles (\(45° + 20° = 65°\)), find the third angle (\(180° - 45° - 20° = 115°\)), or perform other operations that aren't relevant to the question.

This leads to confusion and guessing among the remaining choices.

The Bottom Line:

This problem tests whether students understand the fundamental property of congruent triangles: corresponding parts are equal. The key insight is recognizing that no calculations are needed - just direct application of the correspondence relationship.