A translation followed by a clockwise rotation and a dilation will map triangle ABC to triangle DFE; proving congruence can be done using the corresponding angles and sides congruence criteria (ASA).
To transform triangle ABC into triangle DFE, a sequence of transformations can be applied. Firstly, a translation is employed to shift the entire triangle to a new position. Following the translation, a clockwise rotation is executed, altering the orientation of the triangle. Finally, a dilation is applied to resize the triangle proportionally. It is essential to ensure that the corresponding angles and sides of the transformed triangle match those of the original, verifying congruence.
Proving the congruence of triangles ABC and DFE relies on the Angle-Side-Angle (ASA) criterion, where corresponding angles and the included side are equal. This sequence of transformations, combined with the congruence criteria, establishes a clear and systematic method for demonstrating the congruence between the two triangles.