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To move triangle ABC to triangle EGH and show that they are congruent, we would need to perform the following transformations:
1. Reflection over the x-axis: This will change the orientation of the triangle. Let's call the image of triangle ABC after the reflection A'B'C'.
2. Translation of (E - A', G - B'): After the reflection, we need to translate triangle A'B'C' so that point A' aligns with point E, and point B' aligns with point G. Let's call the image of triangle A'B'C' after the translation E'G'H'.
After these two transformations, triangle ABC would be congruent to triangle EGH.