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 SAS SAS AA AA SSS

Answer 1

To determine if the triangles ΔPRQ and ΔFGH are similar based on the given angles, we can examine the angle measures of both triangles.

For ΔPRQ:

• ∠P = 30°
• ∠R = 127°

We can find ∠Q using the fact that the sum of the angles in a triangle is 180°: ∠Q = 180° - ∠P - ∠R ∠Q = 180° - 30° - 127° ∠Q = 23°

So, the angles of ΔPRQ are:

• ∠P = 30°
• ∠R = 127°
• ∠Q = 23°

For ΔFGH:

• ∠H = 30°
• ∠G = 23°

We can find ∠F using the same principle: ∠F = 180° - ∠H - ∠G ∠F = 180° - 30° - 23° ∠F = 127°

So, the angles of ΔFGH are:

• ∠H = 30°
• ∠G = 23°
• ∠F = 127°

Now we can compare the angles of both triangles:

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

Since all corresponding angles are equal (30°, 127°, and 23°), the criterion that has been met to prove the triangles similar is AA (Angle-Angle).

Thus, the answer is: AA