Question

which rule explains why these triangles are similar?
q
h
53°
j
r
53°
s
i
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 congruent, the triangles are similar.
• AA (Angle - Angle) similarity: If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.

Step2: Analyze given angles

In \(\triangle RQS\) and \(\triangle IHJ\), we are given one pair of equal angles (\(\angle R=\angle I = 53^{\circ}\)). Also, the sum of angles in a triangle is \(180^{\circ}\). If two angles of one triangle are equal to two angles of another triangle (since the third angle can be found as \(180^{\circ}-\text{sum of two known angles}\) and will be equal for both triangles), we can use the AA rule.

Answer:

AA (Angle - Angle)