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 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
yes because of the AA Similarity Theorem

no because m∠F
and m∠R
are unknown

Answer 1

To determine if triangles \( \triangle FHG \) and \( \triangle PRQ \) are similar, we can use the Angle-Angle (AA) Similarity Theorem.

Given:
- \( \angle H = \angle P = 38^\circ \)
- \( \angle G = \angle Q = 41^\circ \)

Since both triangles share two pairs of corresponding angles that are equal, we can conclude that the triangles are similar by the AA Similarity Theorem.

Thus, the correct response is:

**yes because of the AA Similarity Theorem**