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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 AA Similarity Theorem
yes because of the AA Similarity Theorem

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
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Answer 1

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

Given:

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

We can see that if two angles in one triangle are equal to two angles in another triangle, then the triangles are similar.

Since:

• \( \angle H \) corresponds to \( \angle P \)
• \( \angle G \) corresponds to \( \angle Q \)

Thus, we have two pairs of equal angles:

• \( \angle FHG \) and \( \angle PRQ \)

By the AA Similarity Theorem, since two angles in triangle \( \triangle FHG \) are equal to two angles in triangle \( \triangle PRQ \), the triangles are similar.

So the response is:

yes because of the AA Similarity Theorem