Let's analyze the given triangles to determine which, if any, are similar by AA (Angle-Angle) similarity.

Triangles:

1. Triangle ABC:

   • Angle A = 51°
   • Angle C = 89°

2. Triangle FED:

   • Angle F = 38°
   • Angle E = 51°

3. Triangle TUV:

   • Angle T = 89°
   • Angle V = 51°

Steps to Determine Similarity:

1. Triangle ABC:

   • The angles provided are 51° and 89°.
   • The third angle can be calculated as: $180° - (51° + 89°) = 40°$.

2. Triangle FED:

   • The angles provided are 38° and 51°.
   • The third angle can be calculated as: $180° - (38° + 51°) = 91°$.

3. Triangle TUV:

   • The angles provided are 89° and 51°.
   • The third angle can be calculated as: $180° - (89° + 51°) = 40°$.

Comparing the Triangles:

• Triangle ABC and Triangle TUV both have angles 51° and 89°. Since two corresponding angles are equal, these triangles are similar by AA similarity.
• Triangle FED has different angle measures (38° and 51°) and does not have any pair of corresponding angles equal to those in Triangle ABC or Triangle TUV.

Conclusion:

The triangles that are similar by AA similarity are ABC and TUV. The correct answer should be "ABC and TUV."

Would you like any further details or have any questions?

Here are some related questions:

1. What are the other criteria for proving triangle similarity besides AA similarity?
2. How can similar triangles be used in solving real-world problems?
3. What is the relationship between similar triangles and proportional sides?
4. Can two triangles be similar if they have only one pair of equal angles?
5. How do you prove that two triangles are congruent instead of just similar?

Tip: When identifying similar triangles by AA, always check if any two angles in one triangle match with two angles in another triangle. This is sufficient to confirm similarity.