Question

which rule explains why these triangles are similar?

(images of two triangles: one with vertices e, f, g and angles 34° at e, 95° at f; the other with vertices j, i, k and angles 34° at j, 95° at i)

options:
sss
sas
aa
none of the above; the triangles cannot be proven similar

write a similarity statement.
δ __ ~ δ __

Explanation:

To determine the similarity of triangles, we use the AA (Angle - Angle) criterion. If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. In the given triangles, two angles ($34^{\circ}$ and $95^{\circ}$) are equal in both triangles.
For the similarity statement, we match the corresponding angles. $\angle E = \angle J = 34^{\circ}$ and $\angle F=\angle I = 95^{\circ}$, so the triangles are $\triangle EFG\sim\triangle JIK$.

Answer:

AA (Angle - Angle) rule explains the similarity. The similarity statement is $\triangle EFG\sim\triangle JIK$.