https://file.aiquickdraw.com/mathbot/file/1728875650879zvok4ief.jpg

The two triangles in the image are similar because of the **Angle-Angle (AA) similarity criterion**. 

Here's why:
1. In both triangles \( \triangle XYZ \) and \( \triangle ABC \), there are two pairs of corresponding angles that are equal.
2. The angle at vertex \( Y \) in \( \triangle XYZ \) is equal to the angle at vertex \( B \) in \( \triangle ABC \), as they are marked with the same arc.
3. The angle at vertex \( Z \) in \( \triangle XYZ \) is equal to the angle at vertex \( C \) in \( \triangle ABC \), as they are both marked with a different single arc.

When two angles of one triangle are congruent to two angles of another triangle, the triangles are similar by the AA similarity criterion. Therefore, the correct answer is **Angle Angle**.

Would you like further details or have any other questions? Here are some related questions for further exploration:

1. How does the Side-Angle-Side (SAS) similarity criterion work?
2. What is the Side-Side-Side (SSS) similarity criterion, and how does it differ from AA?
3. Can two triangles be similar if they have only one pair of corresponding angles equal?
4. How can you determine similarity if the triangles are not drawn to scale?
5. What are some real-life applications of triangle similarity?

**Tip:** When solving for triangle similarity, checking for two pairs of equal angles can be the quickest way to determine similarity through the AA criterion.

Understand how two triangles are similar using the Angle-Angle (AA) similarity criterion. This problem illustrates how to compare two triangles with two pairs of corresponding angles equal, suitable for Grades 8-10.

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