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The problem asks if triangles \( \triangle PQR \) and \( \triangle XYZ \) are similar and which similarity postulate or theorem applies.

Given:
- \( \triangle PQR \) has a right angle at \( R \), with side \( PR = 10 \).
- \( \triangle XYZ \) has a right angle at \( Z \), with side \( XZ = 5 \).

### Observations:
1. Both triangles are right-angled triangles.
2. The ratio of the corresponding legs: 
   - \( PR \) and \( XZ \) (the legs adjacent to the right angle) is \( 10:5 = 2:1 \).
   - The angles opposite the legs \( PQ \) and \( XY \) are right angles.

Since the triangles have two corresponding angles equal (one from the right angle, and one due to proportional sides), the **AA Similarity Postulate** applies. 

Thus, the correct answer is:
- **A. Similar - AA**

Would you like further clarification or details on the reasoning?

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Here are 5 related questions to expand your understanding:
1. What are the conditions for two triangles to be similar by the AA postulate?
2. How does the SSS similarity theorem differ from the AA postulate?
3. Can two triangles be congruent if they are similar? If so, under what conditions?
4. How can you determine similarity using the SAS theorem?
5. What real-life applications rely on triangle similarity?

**Tip:** Always check for angle similarity first when triangles share a common angle or are right-angled!

Is △PQR ~ △XYZ? If so, name which similarity postulate or theorem applies.

Understand how to determine if triangles △PQR and △XYZ are similar using the AA similarity postulate. Explore key concepts in triangle similarity, proportionality, and right triangles. Suitable for students in Grades 8-10.

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