Final answer:
Option (c) is the correct transformation that could be used to prove ∆ABC ~ ∆ADE by AA similarity postulate. It correctly translates triangle ABC to align angles B and D, satisfying the AA similarity conditions. Therefore, option (c) is the correct transformation.
Step-by-step explanation:
If angle A is congruent to itself by the Reflexive Property, the correct transformation to prove ∆ABC ~ ∆ADE by AA similarity postulate could either involve a translation (to align a pair of corresponding angles) or dilation (to scale the triangle and align corresponding sides). However, the AA similarity postulate requires us to show that two pairs of corresponding angles are congruent.
Option (a) translates triangle ABC so that point C lies on point D to confirm ∠C ≅ ∠D. Whereas option (b) dilates ∆ABC from point A using a specified ratio, but it does not focus on angles. Option (c) translates triangle ABC so that point B lies on point D to confirm ∠B ≅ ∠D. This option does create a pair of congruent angles, which supports the use of AA similarity. Option (d) proposes dilation to confirm segment AE ~ segment AC, but again this focuses on sides rather than angles.
Therefore, option (c) is the correct transformation, as it aligns angles B and D, both corresponding to angle A, thereby satisfying the conditions for the AA similarity postulate.