R

Question

G
-
H
P
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

yes because of the AA Similarity Theorem
yes because of the AA Similarity Theorem

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

Answer 1

To determine if triangles \( \triangle FHG \) and \( \triangle PRQ \) are similar, we can use the AA (Angle-Angle) Similarity Theorem, which states that if two angles in one triangle are equal to two angles in another triangle, the triangles are similar.

You provided the following angle measures:

• \( m\angle H = 38^\circ \)
• \( m\angle P = 38^\circ \)
• \( m\angle G = 41^\circ \)
• \( m\angle Q = 41^\circ \)

We see that:

• \( \angle H \) corresponds to \( \angle P \) (both are \( 38^\circ \)).
• \( \angle G \) corresponds to \( \angle Q \) (both are \( 41^\circ \)).

Since we have two pairs of corresponding angles that are equal, we conclude that \( \triangle FHG \sim \triangle PRQ \) by the AA Similarity Theorem.

Thus, the correct response is:

yes because of the AA Similarity Theorem.