Question

the triangles in each pair are similar. state which \similarity theorem\ best identifies these triangles.
sss~
sas~
aa~

Explanation:

Step1: Analyze the given angles

We are given that \(\angle T = 61^{\circ}\) and \(\angle G=61^{\circ}\). Also, \(\angle SHT\) and \(\angle FHG\) are vertical angles. By the vertical - angles theorem, \(\angle SHT=\angle FHG\) (vertical angles are equal).

Step2: Apply the AA (Angle - Angle) similarity criterion

The AA (Angle - Angle) similarity theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. In \(\triangle SHT\) and \(\triangle FHG\), we have two pairs of congruent angles (\(\angle T\cong\angle G\) and \(\angle SHT\cong\angle FHG\)).

Answer:

AA~