To determine the similarity of the triangles ΔPRQ and ΔFGH based on the given angle measures, we can use the AA (Angle-Angle) similarity criterion.
For ΔPRQ:
- ∠P = 30°
- ∠R = 127°
- Therefore, ∠Q = 180° - ∠P - ∠R = 180° - 30° - 127° = 23°
For ΔFGH:
- ∠H = 30°
- ∠G = 23°
- Therefore, ∠F = 180° - ∠H - ∠G = 180° - 30° - 23° = 127°
Now we can see that:
- ∠P = ∠H = 30°
- ∠R = ∠F = 127°
- ∠Q = ∠G = 23°
Since we have established that two angles of one triangle are equal to two angles of another triangle (∠P = ∠H and ∠R = ∠F), the AA criterion is satisfied.
So the correct response is:
AA
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