Question

which rule explains why these triangles are similar?
q
h
53°
j
r
53°
i
s
sss
sas
aa
none of the above; the triangles cannot be proven similar
write a similarity statement.
△ ~ △

Explanation:

Step1: Recall triangle similarity criteria

The AA (Angle - Angle) similarity criterion states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Step2: Identify congruent angles

In \(\triangle RQS\) and \(\triangle HIJ\), we are given one pair of congruent angles (\(53^{\circ}\) angles). Also, the marked angles (the angles at \(R\) and \(J\)) are congruent. So, two pairs of angles are congruent.

Answer:

\(\triangle RQS\sim\triangle HIJ\)