Parallelograms ABCD and EFGH are similar, where A and B correspond to E and F, respectively. angle A has a...

1. TRANSLATE the problem information

• Given information:
  • Parallelograms ABCD and EFGH are similar
  • Vertex A corresponds to vertex E
  • Vertex B corresponds to vertex F
  • \(\mathrm{Angle\;A = 72°}\)
  • Need to find: angle E

2. INFER the relationship between angles A and E

• Since A corresponds to E in similar figures, angle A and angle E are corresponding angles
• Key insight: In similar figures, corresponding angles are always congruent (equal in measure)
• This means angle E must equal angle A

3. Apply the similarity property

• Since corresponding angles are congruent:
  \(\mathrm{angle\;E = angle\;A = 72°}\)

Answer: C (72°)

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about similarity: Students think that when figures are similar but different sizes, the angles must also change proportionally.

They might reason: "If the parallelograms are different sizes, then the angles should be different too." This leads them to look for answer choices that seem "scaled" from 72°, potentially selecting Choice A (18°) as \(\mathrm{72° \div 4}\) or Choice B (36°) as \(\mathrm{72° \div 2}\).

Second Most Common Error:

Weak INFER skill: Students don't connect the correspondence statement to the concept of corresponding angles.

They might focus on parallelogram properties instead of similarity properties, potentially trying to find supplementary angles and selecting Choice D (108°) since \(\mathrm{72° + 108° = 180°}\).

The Bottom Line:

This problem tests whether students truly understand that similarity preserves angle measures - only the side lengths change proportionally, never the angles. The key insight is recognizing that "corresponding" in similar figures means the angles are identical.