Question

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**.