To solve this, we need to use the property of similar triangles. When two triangles are similar, their corresponding sides are proportional.

Let's analyze the given options:

• In triangles ABC and DEF, let's assume:
  • $AB$ corresponds to $DE$,
  • $AC$ corresponds to $DF$,
  • $BC$ corresponds to $EF$.

We are looking for a proportion that includes the length of $DE$ (side of triangle DEF) in relation to the corresponding side in triangle ABC.

Given that the correct sides need to be in proportion, we are looking for a ratio where the sides of triangle ABC and triangle DEF match up correctly.

Option B: $\frac{5}{15} = \frac{DE}{4}$ is the correct proportion because the side lengths of the triangles are in the same order. This matches the corresponding sides of both triangles in a valid proportion for similar triangles.

Would you like further details or have any other questions?

Here are some questions to expand your understanding:

1. What does it mean for two triangles to be similar?
2. How do we determine corresponding sides in similar triangles?
3. What are some other ways to solve for missing side lengths in similar triangles?
4. Can we use the Pythagorean theorem when triangles are similar?
5. How can we check if two triangles are similar based on their angles?

Tip: Always ensure that corresponding sides are in the same ratio when dealing with similar triangles.