ABC is congruent to GHE. Describe a sequence of transformations from ABC to GHE that proves their congruence.
One possible sequence of transformations that would prove the congruence between triangles ABC and GHE is as follows:
1. Translation: Translate triangle GHE by the distance vector AB. This moves the entire triangle GHE over to the same position as triangle ABC.
2. Reflection: Reflect the translated triangle GHE across the line that contains side AB. This transforms triangle GHE into its mirror image, so that it aligns perfectly with triangle ABC.
3. Rotation: Rotate the reflected triangle GHE counterclockwise by the angle that is formed between sides AB and GH. This rotates triangle GHE into the same orientation as triangle ABC.
After these three transformations, triangle GHE will have been translated, reflected, and rotated into the exact position and orientation as triangle ABC. Therefore, triangle ABC and GHE are congruent.