The similarity theorem that proves the two given triangles are similar is: B. AA similarity theorem.
Recall:
The angle-angle similarity theorem (AA) states that if two angles in one triangle are of the same measure with two corresponding angles in another triangle, both triangles are similar to each other.
In the image given:
[tex]\angle F[/tex] in [tex]\triangle ETF[/tex] is congruent to [tex]\angle U[/tex] in [tex]\triangle VTU[/tex] ([tex]\angle F = \angle U = 78[/tex])
[tex]\angle ETF = \angle VTU[/tex] (vertical angles are equal)
This implies that two angles in [tex]\triangle ETF[/tex] are congruent to two corresponding angles in [tex]\triangle VTU[/tex].
Therefore, both triangles can be proven to be similar by the angle-angle similarity theorem (AA).
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