The question asks for a proportion that must be true between two similar triangles, DEF and ABC. Let's analyze the image:

• Triangle DEF has angles of 44°, 102°, and 34°, with side lengths DE = 12, DF = 15, and EF = 21.
• Since triangle DEF and ABC are similar, their corresponding sides are proportional.

Let's establish the proportions between the corresponding sides of DEF and ABC:

1. Side $DE$ corresponds to a side in triangle ABC, and $DF$ corresponds to another. The question asks us to find which proportion holds for these sides. By the properties of similar triangles, the ratios of corresponding sides must be equal. So, for example: $\frac{x}{14} = \frac{15}{12}$ This is option A.

So, the correct proportion is: $\boxed{A}$ This means that the ratio of the side $x$ from triangle ABC to the corresponding side in DEF must be $\frac{15}{12}$.

Would you like further explanation or have any questions?

Here are five related questions to think about:

1. How do you determine corresponding sides in similar triangles?
2. Why must the angles in similar triangles be congruent?
3. How can you verify that two triangles are similar?
4. How would the proportions change if the side lengths of triangle DEF were different?
5. Can you use the law of sines to find unknown sides in similar triangles?

Tip: When working with similar triangles, always match corresponding angles first to avoid mistakes when setting up side ratios.