In quasi-one-or quasi-two-dimensional traps with strong transverse confinements, quantum gases behave like strictly one-or two-dimensional systems at large length scales. However, at short distance, the two-body scattering intrinsically has three-dimensional characteristics such that an exact description of any universal thermodynamic relation requires three-dimensional contacts, no matter how strong the confinement is. A fundamental question arises as to whether one-or twodimensional contacts, which were originally defined for strictly one or two dimensions, are capable of describing quantum gases in quasi-one-or quasi-two-dimensional traps. Here, we point out an exact relation between the three-and low-dimensional contacts in these highly anisotropic traps. Such relation allows us to directly connect physical quantities at different length scales, and to characterise the quasi-one-or quasi-two-dimensional traps using universal thermodynamic relations that were derived for strict one or two dimensions.