Statements A, B, and F are true. The z-coordinates of corresponding points are equal, corresponding line segments have the same lengths, and the figures are congruent after translation and reflection.
After the translation and reflection operations on figure PQRST, let's analyze each statement:
A. ZS = ZS: The z-coordinate of point S is unchanged by translation or reflection. This statement is true.
B. PT = P'T: The translation and reflection do not affect the lengths of line segments; they only change the position. Thus, PT and P'T have the same length. This statement is true.
C. The area of P'Q'R'ST' is greater: The area of a figure is not affected by translation or reflection. The original and reflected figures have the same area. This statement is false.
D. The perimeter of PQRST is greater: The perimeter is determined by the lengths of the sides. Since the lengths remain the same after translation and reflection, the perimeters are equal. This statement is false.
E. The figures' orientations are the same: The reflection in the y-axis changes the orientation of the figure, so this statement is false.
F. The figures are congruent: Congruence implies that the figures have the same shape and size. In this case, the translation and reflection do not alter the size or shape of the figure, so the figures are congruent. This statement is true.