Question

which rule explains why these triangles are similar?
sss
sas
aa
none of the above; the triangles cannot be proven similar

Explanation:

Step1: Find missing angle in $\triangle RST$

Sum of angles in triangle is $180^\circ$.
$\angle S = 180^\circ - 52^\circ - 98^\circ = 30^\circ$

Step2: Find missing angle in $\triangle IGH$

Sum of angles in triangle is $180^\circ$.
$\angle I = 180^\circ - 98^\circ - 47^\circ = 35^\circ$

Step3: Compare corresponding angles

$\triangle RST$ angles: $30^\circ, 52^\circ, 98^\circ$
$\triangle IGH$ angles: $35^\circ, 47^\circ, 98^\circ$
Only one pair of angles is equal.

Answer:

none of the above; the triangles cannot be proven similar