Question

If triangle PRG has ∠P = 30 and ∠R = 127 and triangle FGH has ∠H = 30 and ∠G = 23, what criterion has been met to prove the triangles similar?

a. SAS
b. ASA
c. SSS
d. AA

Answer 1

To determine if the triangles PRG and FGH are similar, we can look at their angles.

In triangle PRG:
- ∠P = 30°
- ∠R = 127°

To find ∠G, we can calculate it as follows:
∠G = 180° - ∠P - ∠R = 180° - 30° - 127° = 23°.

In triangle FGH:
- ∠H = 30°
- ∠G = 23°

Now we can check the angles:
- ∠P (30°) is equal to ∠H (30°).
- ∠R (127°) is equal to the third angle in triangle FGH which we just calculated as 127°.

So the third angle in triangle FGH can also be derived as follows:
∠F = 180° - ∠H - ∠G = 180° - 30° - 23° = 127°.

Both triangles share two angles:
- ∠P = ∠H (30°)
- ∠R = ∠F (127°)

Since both triangles have two corresponding angles that are equal, we can use the Angle-Angle (AA) similarity criterion.

Thus, the answer is:

**d. AA**