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To determine if the triangles \( \triangle FGH \) and \( \triangle IJK \) are similar, we can apply the **Angle-Angle (AA) Similarity Theorem**. This theorem states that if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.

### Step 1: Identify Known Angles
- In both triangles, one angle is already labeled as \( 81^\circ \) (angle \( G \) in \( \triangle FGH \) and angle \( J \) in \( \triangle IJK \)).
- We also know that the sum of angles in any triangle is \( 180^\circ \).

#### Triangle \( FGH \):
- Angle \( G = 81^\circ \).
- We can find another angle using the law that the sum of interior angles in a triangle is \( 180^\circ \).
  
Let’s calculate angle \( F \):

\[
\text{Angle } F = 180^\circ - 81^\circ - \text{Angle } H
\]

However, the problem doesn't provide enough information about angle \( H \). Thus, we cannot immediately confirm similarity based purely on angles without additional data. Nonetheless, if angle \( H \) were congruent to another angle in triangle \( IJK \), we could confirm similarity.

Would you like to investigate any further information or try another method, such as comparing side ratios? Let me know if you'd like to explore any details further.

### Questions to Explore:
1. Can you calculate the missing angle in \( \triangle FGH \) if more data was available?
2. What does the Angle-Side-Angle (ASA) Theorem state?
3. Can the Side-Angle-Side (SAS) Theorem help in proving similarity?
4. How do the ratios of sides determine similarity of triangles?
5. What happens if two triangles share all three angles (AAA)?

**Tip:** Use angle sums and proportionality of sides to identify similar triangles when angles alone are insufficient.

Determine if triangle FGH and triangle IJK are or are not similar, and, if they are, state how you know.

Learn how to determine if triangles FGH and IJK are similar using the Angle-Angle (AA) Similarity Theorem. This problem involves checking for congruent angles and calculating missing angles based on the sum of angles in a triangle. Suitable for students in Grades 8-10.

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