Use the image to answer the question. What is the sequence of transformations needed to move triangle ABC to triangle EGH to show that the triangles are congruent?
Based on the given image, the sequence of transformations needed to move triangle ABC to triangle EGH and show congruence are as follows:
1. Reflection over the x-axis: This will reflect triangle ABC over the x-axis, creating a new triangle with vertices A', B', and C'. This reflection will make segment AB align with segment EH, segment BC align with segment HG, and segment AC align with segment EG.
2. Translation: Move the reflected triangle A'B'C' horizontally to the right by the same amount as the horizontal distance between points E and G. This will place triangle A'B'C' over triangle EGH, aligning point A' with point E, B' with G, and C' with H.
After performing these two transformations (reflection over x-axis and translation), triangle ABC will coincide with triangle EGH, indicating that they are congruent.