In the image provided, you are asked to determine if $\triangle ABC \sim \triangle DEF$ and, if so, identify the similarity postulate or theorem that applies.

Key Information from the Diagram:

• Both triangles have angles marked $30^\circ$ and $85^\circ$.
• The remaining angle in both triangles must be $180^\circ - (85^\circ + 30^\circ) = 65^\circ$ since the sum of the angles in any triangle is always $180^\circ$.

Conclusion:

Since two corresponding angles in $\triangle ABC$ and $\triangle DEF$ are congruent, by the Angle-Angle (AA) Similarity Postulate, the triangles are similar.

Correct Answer:

A. Similar - AA

Would you like further details or have any questions about this? Here are some related questions for deeper understanding:

1. What is the Angle-Angle (AA) Similarity Postulate?
2. Can you explain how to verify similarity using the Side-Side-Side (SSS) theorem?
3. How does the Side-Angle-Side (SAS) theorem establish triangle similarity?
4. Why is the sum of the angles in any triangle always $180^\circ$?
5. How do you prove two triangles are congruent instead of just similar?

Tip: Always check if two triangles have at least two equal angles to quickly apply the AA similarity postulate.