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 ASA ASA AA AA SAS SAS SSS

Answer 1

To determine if triangles ΔPRQ and ΔFGH are similar, we look at the angles given:

1. In ΔPRQ:

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

2. In ΔFGH:

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

Now we have:

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

Both triangles have the same set of angles:

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

Since both triangles have two pairs of equal angles, we can use the Angle-Angle (AA) criterion for triangle similarity.

Thus, the criterion that has been met to prove the triangles similar is AA.