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 AA AA ASA ASA SAS SAS SSS SSS

Answer 1

To determine whether the triangles ΔPRQ and ΔFGH are similar, we can analyze the angles of each triangle.

1. ΔPRQ has:

   • ∠P = 30°
   • ∠R = 127°
   • To find ∠Q: \[ \angle Q = 180° - \angle P - \angle R = 180° - 30° - 127° = 23° \]

   Therefore, the angles of ΔPRQ are: 30°, 127°, and 23°.

2. ΔFGH has:

   • ∠H = 30°
   • ∠G = 23°
   • To find ∠F: \[ \angle F = 180° - \angle H - \angle G = 180° - 30° - 23° = 127° \]

   Therefore, the angles of ΔFGH are: 30°, 23°, and 127°.

Now, we compare the angles of the two triangles:

• ΔPRQ: 30°, 127°, 23°
• ΔFGH: 30°, 23°, 127°

Since both triangles have the same angles (30°, 23°, and 127°), we can conclude that they are similar by the Angle-Angle (AA) similarity criterion.

Thus, the correct response is AA.