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 ΔTSU

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

Step2: Find missing angle in ΔIJH

Sum of angles in triangle is $180^\circ$.
$\angle J = 180^\circ - 76^\circ - 66^\circ = 38^\circ$

Step3: Compare corresponding angles

ΔTSU angles: $34^\circ, 66^\circ, 80^\circ$; ΔIJH angles: $38^\circ, 66^\circ, 76^\circ$. Only one pair of angles is equal, so no two corresponding angle pairs match.

Answer:

none of the above; the triangles cannot be proven similar