If H and P each equal 38 degrees and G and Q each equal 41 degrees, is FHG ~ PRQ?

Question

A) yes because of the AA similarity theorem
B) no because m F and m R are unknown
c) no because the ratio of corressponding side lengths is unknown
d) yes because of the SSS Congruence Theorem

Answer 1

To determine if triangles FHG and PRQ are similar (FHG ~ PRQ), we can apply the Angle-Angle (AA) similarity theorem, which states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

You provided the following information:

• Angle H = 38 degrees
• Angle P = 38 degrees
• Angle G = 41 degrees
• Angle Q = 41 degrees

Since:

• One angle of triangle FHG (H) is equal to one angle of triangle PRQ (P),
• Another angle of triangle FHG (G) is equal to another angle of triangle PRQ (Q),

This means that the two triangles have two pairs of corresponding angles that are equal. Therefore, by the AA similarity theorem, the triangles FHG and PRQ are similar.

The correct answer is A) yes because of the AA similarity theorem.