To determine whether $\triangle DEF$ is similar to $\triangle DGH$, we need to analyze the corresponding angles and sides.

Observations:

1. Angle Correspondence: The diagram shows that $\angle G$ is congruent to $\angle E$. This is marked in the image.

2. Shared Angle: $\triangle DEF$ and $\triangle DGH$ share the angle at $D$. This is another congruent angle.

   Since two pairs of corresponding angles are congruent, by the AA (Angle-Angle) Similarity Postulate, $\triangle DEF \sim \triangle DGH$.

Answer:

The correct statement is:
$\triangle DEF$ is similar to $\triangle DGH$.

Would you like a deeper explanation of similarity criteria or further examples? Here are related questions for better understanding:

1. How do the AA, SAS, and SSS criteria establish triangle similarity?
2. Can similar triangles have proportional sides but different angles? Why or why not?
3. How can similarity of triangles be applied to real-world problems?
4. How do you calculate unknown side lengths using similar triangles?
5. What are some practical uses of similar triangles in geometry?

Tip: Always look for shared angles and marked congruencies when checking for similarity in triangles.