Question

Use the image to answer the question.

Triangles upper F upper G upper H and upper P upper Q upper R are plotted on a grid. Triangle upper P upper Q upper R is larger.

If ∠H
and ∠P
each equal 38 degrees and ∠G
and ∠Q
each equal 41 degrees, is △FHG∼△PRQ
?

(1 point)
Responses

no because m∠F
and m∠R
are unknown
no because m∠F
and m∠R
are unknown

no because the ratio of corresponding side lengths is unknown
no because the ratio of corresponding side lengths is unknown

yes because of the SSS Congruence Theorem
yes because of the SSS Congruence Theorem

yes because of the AA Similarity Theorem

Answer 1

To determine whether △FHG is similar to △PRQ, we can use the AA (Angle-Angle) Similarity Theorem.

We know:
- ∠H = ∠P = 38 degrees
- ∠G = ∠Q = 41 degrees

Since both triangles have two angles equal, by the AA Similarity Theorem, the two triangles are similar.

Therefore, the answer is:

**yes because of the AA Similarity Theorem.**