In triangle XYZ, if the segments MZ, MX, and MY are all equal, this implies that point M is the centroid of the triangle. A centroid is the point where the three medians of the triangle intersect, and it is equidistant from all three vertices of the triangle when the triangle is equilateral.
This means that triangle XYZ must be an equilateral triangle. In an equilateral triangle, all sides are the same length, and all angles measure 60 degrees. Thus, if MZ = MX = MY, then XYZ cannot be any other type of triangle. Therefore, the statement that must be true about triangle XYZ is that it is equilateral.