Question

which rule explains why these triangles are similar?ssssasaanone of the above; the triangles cannot be proven similar

Explanation:

Step1: Find missing angle in $\triangle JKI$

Sum of angles in a triangle is $180^\circ$.
$\angle I = 180^\circ - 82^\circ - 57^\circ = 41^\circ$

Step2: Find missing angle in $\triangle QRS$

Sum of angles in a triangle is $180^\circ$.
$\angle S = 180^\circ - 57^\circ - 91^\circ = 32^\circ$

Step3: Compare all corresponding angles

$\triangle JKI$ angles: $82^\circ, 57^\circ, 41^\circ$
$\triangle QRS$ angles: $91^\circ, 57^\circ, 32^\circ$
Only one pair of angles is equal.

Answer:

none of the above; the triangles cannot be proven similar