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To determine the similarity criterion that has been met for triangles ΔPRQ and ΔFGH, we can analyze the given angles.
1. For triangle ΔPRQ:
- ∠P = 30°
- ∠R = 127°
- Since the sum of angles in a triangle is 180°, we can find ∠Q:
- ∠Q = 180° - ∠P - ∠R = 180° - 30° - 127° = 23°.
2. For triangle ΔFGH:
- ∠H = 30°
- ∠G = 23°.
- Similar to above, we can find ∠F:
- ∠F = 180° - ∠H - ∠G = 180° - 30° - 23° = 127°.
Now we can compare the angles of both triangles:
- ΔPRQ: ∠P = 30°, ∠R = 127°, ∠Q = 23°.
- ΔFGH: ∠H = 30°, ∠G = 23°, ∠F = 127°.
We can see that:
- ∠P = ∠H = 30°,
- ∠R = ∠F = 127°,
- ∠Q = ∠G = 23°.
Since all corresponding angles are equal, we can conclude that the triangles are similar by the **AA (Angle-Angle) similarity criterion**.
So the correct response is **AA**.