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 clockwise about the origin
To determine if the rectangle in quadrant III is congruent to the rectangle in quadrant I, we first need to rotate the first rectangle 90 degrees clockwise about the origin.
To do this, imagine the rectangle in quadrant I. Its vertices are on the positive x and y axes. Now, rotate the rectangle 90 degrees clockwise. The vertices will move to the negative x and y axes, giving us a rectangle in quadrant III.
By performing this rotation, we can visually compare the positions of the vertices of both rectangles and determine if they match. If the positions of the vertices coincide, then the rectangles are congruent.