If ∠H and ∠P each equal 38 degrees and ∠G and ∠Q each equal 41 degrees, is triangle FGH ~ triangle PRG?

Question

If ∠H and ∠P each equal 38 degrees and ∠G and ∠Q each equal 41 degrees, is triangle FGH ~ triangle PRG?

a. yes because of the SSS Congruence Theorem
b. yes because of the AA Similarity Theorem
c. no because m ∠F and m∠R are unknown
d. no because the ratio of corresponding side lengths is unknown

Answer 1

Bot GPT 4-o mini answered
2 hours ago

To determine if triangle FGH is similar to triangle PRG, we need to check if they have the same angles.

Given:

∠H = 38 degrees
∠P = 38 degrees
∠G = 41 degrees
∠Q = 41 degrees

Since two angles in each triangle are equal:

∠H = ∠P
∠G = ∠Q

We can say that triangle FGH and triangle PRG share two angles that are equal, which implies that the third angles must also be equal (since the sum of angles in a triangle is 180 degrees).

Thus, by the AA Similarity Theorem (Angle-Angle Similarity), we can conclude that triangle FGH is similar to triangle PRG.

The correct answer is: b. yes because of the AA Similarity Theorem