Question

which rule explains why these triangles are similar?
j
83°
r
83°
q
k
s
i
sss
sas
aa
none of the above; the triangles cannot be proven similar

Explanation:

1. First, identify the given angles: Both triangles have an \(83^\circ\) angle, and the marked angles (at \(K\) and \(Q\)) are equal (indicated by the red arcs).
2. In triangle similarity, the AA (Angle - Angle) criterion states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. Here, we have two pairs of equal angles (the \(83^\circ\) angle and the marked equal angle), so by AA similarity criterion, the triangles are similar. SSS requires all three sides to be in proportion, and SAS requires two sides in proportion with the included angle equal, which we don't have information for. So the correct rule is AA.

Answer:

AA