the first step to determine that the rectangle in Quadrant III is congruent to the rectangle in Quadrant I was to rotate the first rectangle 90 degrees clockwise about the origin. What is the next step?

The next step would be to show that the sides and angles of the two rectangles are congruent. This can be done by measuring the lengths of the sides and the angles between the sides of the rectangles in both Quadrant III and Quadrant I. If all the corresponding sides and angles are equal, then the rectangles are congruent.