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 ∠G in △GHI

The sum of angles in a triangle is $180^\circ$.
$\angle G = 180^\circ - 97^\circ - 51^\circ = 32^\circ$

Step2: Calculate ∠F in △FDE

The sum of angles in a triangle is $180^\circ$.
$\angle F = 180^\circ - 97^\circ - 48^\circ = 35^\circ$

Step3: Compare triangle angle sets

△GHI angles: $97^\circ, 51^\circ, 32^\circ$; △FDE angles: $97^\circ, 48^\circ, 35^\circ$. Only one pair of angles is equal, so no two pairs of matching equal angles exist. Side lengths are not provided to use SSS/SAS.

Answer:

none of the above; the triangles cannot be proven similar