  String geometry theory is one of the candidates of non-perturbative
formulation of string theory. In this paper, we have shown that dimensionally
reduced string geometry theories have what we call T-symmetry. In case of the
dimensional reduction in space-like directions, the T-symmetry transformation
gives the T-dual transformation between the type IIA and IIB perturbative
vacua. In case of the dimensional reduction in the direction of string geometry
time $\bar{\tau}$, the T-symmetry transformation is independent of the T-dual
transformation, and gives a symmetry that cannot be seen in the perturbative
string theories.
