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

yes because of the SSS Congruence Theorem
yes because of the SSS Congruence 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 AA Similarity Theorem
yes because of the AA Similarity Theorem
Skip to navigation

Answer 1

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

From the given information:

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

The angles \( \angle H \) and \( \angle G \) correspond to \( \angle P \) and \( \angle Q \) respectively. Since two pairs of corresponding angles are equal, we can conclude by the AA Similarity Theorem that the triangles are indeed similar.

Thus, the answer is:

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