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 △FGH

Sum of angles in a triangle is $180^\circ$.
$\angle H = 180^\circ - 101^\circ - 47^\circ = 32^\circ$

Step2: Find missing angle in △WVU

Sum of angles in a triangle is $180^\circ$.
$\angle W = 180^\circ - 96^\circ - 47^\circ = 37^\circ$

Step3: Compare triangle angle sets

△FGH angles: $101^\circ, 47^\circ, 32^\circ$; △WVU angles: $96^\circ, 47^\circ, 37^\circ$. Only one pair of angles is equal, so no two pairs of matching equal angles exist.

Answer:

none of the above; the triangles cannot be proven similar