The true statement are SZ = ZN and ZT = ZS
The figure formed by connecting points S, M, T, and N must be a square. - False. This statement is not necessarily true. While the arcs centered at S and T with the same radius might intersect in two points, these points might not lie exactly on the perpendicular bisector of ST, resulting in a rectangle or another quadrilateral instead of a square.
ΔNZT = ΔMST - False. This statement is also not necessarily true. The angles formed by the intersection of the arcs and the segments ST and MN depend on the specific locations of the points. There's no guarantee that they will be congruent, making ANZT and AMST potentially unequal in both angle measure and side lengths.
SZ = ZN - True. This statement is true. Since the perpendicular bisector passes through the midpoint (Z) of ST, the distances from Z to S and Z to N are equal. This property holds true for any perpendicular bisector construction, not just the method described.
ZT = ZS - True. Similar to statement 3, this statement is also true. By definition, the perpendicular bisector divides the segment ST into two segments with equal lengths. Therefore, ZT and ZS must be equal.
In conclusion, only statements 3 (SZ = ZN) and 4 (ZT = ZS) are necessarily true based on the provided steps for constructing the perpendicular bisector of ST. The other two statements (figure is a square and angles are congruent) depend on the specific locations of the points and are not guaranteed to be true in every case.