triangle ABC is congruent to triangle GHE. Describes a sequence of transformations from triangle ABC to triangle GHE that proves their congruence
One possible sequence of transformations from triangle ABC to triangle GHE that proves their congruence is as follows:
1) Start by reflecting triangle ABC over line GH, creating a new triangle A'B'C'.
2) Next, translate triangle A'B'C' horizontally by the vector GH, resulting in a new triangle A''B''C''.
3) Finally, rotate triangle A''B''C'' clockwise around point H by an angle of measure 180 degrees, creating triangle GHE.
This sequence of transformations demonstrates congruence between triangle ABC and triangle GHE, as each transformation preserves shape and size. The reflection ensures that corresponding sides and angles are equal, the translation preserves side lengths and angles, and the rotation preserves side lengths and angles as well. Therefore, triangle ABC and triangle GHE are congruent.