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

Question

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.

Answer 1

∠AEI ≅ ∠DEH because vertical angles are congruent; rotate ΔHED 180° around point E, then translate point D to point A to confirm ∠IAE ≅ ∠HDE.