A sequence of transformations from \(\triangle ABC\) to \(\triangle GHE\) that proves their congruence is:Translate \(\triangle ABC\) horizontally and vertically so that the corresponding vertices of the triangles coincide.Rotate \(\triangle ABC\) so that the corresponding angles of the triangles coincide.Dilate \(\triangle ABC\) so that the corresponding sides of the triangles coincide.
The sequence of transformations to prove the congruence between \(\triangle ABC\) and \(\triangle GHE\) is as follows:
1. Translation: Translate \(\triangle ABC\) horizontally and vertically so that the corresponding vertices of the triangles coincide. This means moving \(\triangle ABC\) to a new position where the corresponding vertices of \(\triangle ABC\) and \(\triangle GHE\) overlap.
2. Rotation: Rotate \(\triangle ABC\) so that the corresponding angles of the triangles coincide. This means rotating \(\triangle ABC\) around a point until the corresponding angles of \(\triangle ABC\) and \(\triangle GHE\) match.
3. Dilation: Dilate \(\triangle ABC\) so that the corresponding sides of the triangles coincide. This means scaling \(\triangle ABC\) up or down uniformly until the corresponding sides of \(\triangle ABC\) and \(\triangle GHE\) coincide in length.
By performing these three transformations in sequence, we will have proven the congruence between \(\triangle ABC\) and \(\triangle GHE\) by making their corresponding parts completely overlap.