1. Problem: Identify a transformation that can be used to prove $\triangle ABC \sim \triangle ADE$ by the AA similarity postulate given that $\angle A$ is congruent to itself by the Reflexive Property.\n2. Formula and rule: The AA similarity postulate says that if two angles of one triangle are congruent to two angles of another triangle then the triangles are similar, so $\triangle XYZ \sim \triangle X'Y'Z'$.\n3. Important facts: By the Reflexive Property we have $\angle A \cong \angle A$.\nBoth $\angle B$ and $\angle D$ are right angles, so $\angle B \cong \angle D$.\n4. AA argument: Since $\angle A \cong \angle A$ and $\angle B \cong \angle D$, by AA we conclude $\triangle ABC \sim \triangle ADE$.\n5. Transformation that realizes the similarity: A dilation centered at $A$ with scale factor $s=\dfrac{AB}{AD}$ maps $D$ to $B$ because $s\cdot AD=AB$.\n6. Consequence: Under this dilation $E$ maps to $C$ and corresponding angles coincide, so the dilation realizes the correspondence and complements the AA argument.\n7. Final answer: Use a dilation about $A$ with factor $\dfrac{AB}{AD}$ (equivalently dilate $\triangle ABC$ by $\dfrac{AD}{AB}$) to align the triangles and confirm $\triangle ABC \sim \triangle ADE$ by AA.\n