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 angle cap f and m angle cap r are 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 the ratio of corresponding side lengths is unknown

Answer 1

Yes — because ∠H = ∠P and ∠G = ∠Q, the triangles have two equal angles, so △FHG ∼ △PRQ by the AA (angle-angle) Similarity Theorem.