Which of the following explains how ΔAEI could be proven similar to ΔDEH using the AA similarity postulate?

Quadrilateral ABDC, in which point F is between points A and C, point G is between points B and D, point I is between points A and B, and point H is between points C and D. A segment connects points A and D, a segment connects points B and C, a segment connects points I and H, and a segment connects points F and G. Segments AD, BC, FG, and IH all intersect at point E.

∠AEI ≅ ∠DEH because vertical angles are congruent; reflect ΔHED across segment FG, then translate point D to point A to confirm ∠IAE ≅ ∠HDE.
∠AEI ≅ ∠DEH because vertical angles are congruent; rotate ΔHED 180° around point E, then translate point D to point A to confirm ∠IAE ≅ ∠HDE.
∠AEI ≅ ∠DEH because vertical angles are congruent; rotate ΔHED 180° around point E, then dilate ΔHED to confirm segment ED ≅ segment EA.
∠AEI ≅ ∠DEH because vertical angles are congruent; reflect ΔHED across segment FG, then dilate ΔHED to confirm segment ED ≅ segment EI.

Two triangles are said to be similar by AA if two angles of both triangles are equal. The explanation that proves the similarity of [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex] by AA is option (a)

Given that: [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex]

To prove that [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex] are similar by AA, it means that two corresponding angles of both triangles must be congruent. So, the following must be true:

The angle at point E in both triangles must be equal. i.e. [tex]\angle AEI \cong \angle DEH[/tex]. This is so because the angle at E is a vertical angle to both triangles, and vertical angles are congruent.
The angle at A and D of both triangles must be equal, i.e. [tex]\angle IAE \cong HDE[/tex]. This is so because a 180 degrees rotation of [tex]\triangle DEH[/tex] around the center E will give a similar (but larger) triangle to [tex]\triangle AEI[/tex]. Point D can then be shifted to A.

Hence, (a) is true