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The correct sequence of steps used to move triangle DFG in Quadrant IV to the triangle in Quadrant III to show that the triangles are congruent is:
1. Translation: Move the entire triangle to the left or right without any rotation.
2. Reflection: Reflect the triangle across the x-axis.
3. Translation: Move the reflected triangle up or down without any rotation.
These steps will prove that the triangles are congruent by showing that one can be transformed into the other through a series of rigid transformations.