Question

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

Explanation:

Step1: Calculate third angle of △HIJ

Sum of angles in triangle is $180^\circ$.
$\angle J = 180^\circ - 96^\circ - 32^\circ = 52^\circ$

Step2: Calculate third angle of △DEF

Sum of angles in triangle is $180^\circ$.
$\angle D = 180^\circ - 96^\circ - 32^\circ = 52^\circ$

Step3: Match corresponding equal angles

$\angle I = \angle E = 96^\circ$, $\angle H = \angle F = 32^\circ$

Step4: Apply similarity rule

Two pairs of equal angles satisfy AA (Angle-Angle) similarity criterion.

Answer:

AA