Triangle ABC is similar to triangle XYZ, such that A, B, and C correspond to X, Y, and Z respectively....

1. TRANSLATE the problem information

• Given information:
  • Triangle ABC is similar to triangle XYZ
  • A, B, C correspond to X, Y, Z respectively
  • Each side of triangle XYZ is 2 times the corresponding side in triangle ABC
  • Side \(\mathrm{AB = 16}\)
  • Need to find: side XY

2. TRANSLATE the correspondence relationship

• Since A corresponds to X and B corresponds to Y:
  • Side AB (connecting A to B) corresponds to side XY (connecting X to Y)

3. INFER how to apply the scaling factor

• The problem states "each side of triangle XYZ is 2 times the corresponding side in triangle ABC"
• Since XY is a side of triangle XYZ and AB is its corresponding side in triangle ABC:
  \(\mathrm{XY = 2 × AB}\)

4. Calculate the answer

• \(\mathrm{XY = 2 × 16 = 32}\)

Answer: D. 32

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students don't properly understand what "correspondence" means in similar triangles. They might think the problem is asking about the same side (AB) in both triangles, leading them to believe the answer is just 16.

This may lead them to select Choice B (16).

Second Most Common Error:

Incomplete TRANSLATE reasoning: Students correctly identify that AB corresponds to XY but get confused about which triangle is larger. They might think triangle ABC is larger than triangle XYZ and incorrectly calculate \(\mathrm{XY = AB ÷ 2 = 16 ÷ 2 = 8}\), or make other calculation errors.

This leads to confusion and guessing among the remaining choices.

The Bottom Line:

Success on this problem depends entirely on correctly translating the correspondence language and the scaling relationship. The mathematical computation is straightforward once you understand which sides match up and in which direction the scaling factor applies.