If ΔPRQ has ∠P=30 and ∠R=127 and ΔFGH has ∠H=30 and ∠G=23 , what criterion has been met to prove the triangles similar?(1 point) Responses SAS SAS AA AA ASA ASA SSS

Answer 1

To determine whether the triangles ΔPRQ and ΔFGH are similar, we analyze the given angles:

1. For ΔPRQ:

   • ∠P = 30°
   • ∠R = 127°

   To find ∠Q: \[ ∠Q = 180° - (∠P + ∠R) = 180° - (30° + 127°) = 180° - 157° = 23° \]

2. For ΔFGH:

   • ∠H = 30°
   • ∠G = 23°

   To find ∠F: \[ ∠F = 180° - (∠H + ∠G) = 180° - (30° + 23°) = 180° - 53° = 127° \]

Now we have the angles for both triangles:

• For ΔPRQ: ∠P = 30°, ∠R = 127°, ∠Q = 23°
• For ΔFGH: ∠F = 127°, ∠G = 23°, ∠H = 30°

We can see that:

• ∠P = ∠H = 30°
• ∠Q = ∠G = 23°
• ∠R = ∠F = 127°

Since all three angles in ΔPRQ correspond to the angles in ΔFGH, the criterion satisfied here is AA (Angle-Angle) similarity.

Thus, the answer is AA.