https://file.aiquickdraw.com/mathbot/file/1728073581572gj3e975a.jpg

The image shows a right triangle \( \triangle WZX \) with a red altitude drawn from vertex \( Z \) to side \( XY \), forming two smaller right triangles. The question asks for a similarity statement comparing these triangles, which means determining how these triangles are geometrically similar by angle-angle (AA) similarity.

### Understanding the figure:

- The large triangle is \( \triangle WZX \).
- The two smaller triangles are formed by the altitude: 
  - \( \triangle ZXY \)
  - \( \triangle WXY \)

Each triangle shares angles with the others:
- All three triangles have a right angle.
- Each triangle also shares an acute angle with the others (by the angle they share with \( WZX \)).

Thus, by AA similarity, the triangles are similar.

The correct similarity statement is:
\[
\triangle WZX \sim \triangle ZXY \sim \triangle WXY
\]

This corresponds to the fourth option: 
- \( \triangle WZX \sim \triangle XZY \sim \triangle WXY \).

Would you like further details on triangle similarity or angle relationships? 

Here are 5 questions related to this topic:
1. How can you use the Pythagorean theorem to confirm triangle similarity?
2. What is AA similarity, and why does it work in this case?
3. How do the proportions of sides between similar triangles relate?
4. Can you explain how to calculate the altitude in such a triangle setup?
5. How does triangle congruence differ from triangle similarity?

**Tip:** In right triangles, the altitude from the right angle creates two smaller right triangles, both similar to the original triangle.

Which of the following is the similarity statement comparing the triangles in the figure?

Explore how to determine the similarity statement between right triangles using the AA (Angle-Angle) similarity criterion. This problem involves triangle similarity, the concept of proportional sides, and angle relationships, suitable for students in Grades 8-10.

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