which diagram can be used to prove △abc ~ △dec using similarity transformations?

Explanation:

Step1: Recall similarity - angle - angle (AA) criterion

For two triangles $\triangle ABC$ and $\triangle DEC$ to be similar using similarity transformations, we need to show that two pairs of corresponding angles are equal. In the first - given diagram, $\angle ACB=\angle DCE$ (vertically - opposite angles) and if we can show another pair of equal angles (for example, if $\angle B=\angle E$ or $\angle A=\angle D$), we can prove similarity. In the second diagram, it is not clear how we can directly apply similarity transformations to show $\triangle ABC\sim\triangle DEC$ as the angle - relationships are not as straightforward as in the first diagram.

Answer:

The first diagram (where $\angle ACB$ and $\angle DCE$ are vertically - opposite angles)