Question

which rule explains why these triangles are similar?
u
f
g
s
39°
39°
t
h
sss
sas
aa
none of the above; the triangles cannot be proven similar

Explanation:

Step1: Recall triangle similarity rules

• SSS (Side - Side - Side) similarity: If the ratios of the corresponding sides of two triangles are equal, the triangles are similar.
• SAS (Side - Angle - Side) similarity: If the ratio of two pairs of corresponding sides is equal and the included angles are equal, the triangles are similar.
• AA (Angle - Angle) similarity: If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Step2: Analyze the given triangles

In \(\triangle SUT\) and \(\triangle GFH\), we are given one pair of equal angles (\(\angle U\) and \(\angle F\) as marked) and another pair of equal angles (\(\angle T=\angle H = 39^{\circ}\)).

Answer:

AA