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 △TUV

Sum of angles in triangle is $180^\circ$.
$\angle V = 180^\circ - 34^\circ - 66^\circ = 80^\circ$

Step2: Find missing angle in △JHI

Sum of angles in triangle is $180^\circ$.
$\angle I = 180^\circ - 28^\circ - 66^\circ = 86^\circ$

Step3: Compare triangle angle sets

△TUV angles: $34^\circ, 66^\circ, 80^\circ$; △JHI angles: $28^\circ, 66^\circ, 86^\circ$. Only one pair of equal angles exists.

Answer:

none of the above; the triangles cannot be proven similar