In this problem we have that
triangle DEC is congruent to triangle ABC by ASA congruence theorem
therefore
It is possible to map triangle ABC to triangle DEC with a rigid transformation, because are conguent figures
Example
with two reflections is possible
First reflection triangle ABC across the segment EB
Second reflection triangle A'B'C' across the segment DC
Another way
Rotation triangle ABC 180 degrees with center of rotation point C