In this study, new compositions of Tsai-type 1/1 quasicrystal approximants Gd(14)Au(70)Si(16), Gd(14)Au(67)Ge(19), Tb(14)Au(70)Si(16) and Yb(16)Au(65)Ge(19)are synthesized using both self-flux and arc-melting-annealing techniques. Both syntheses routes resulted single phase samples. The crystal structures of the compounds are determined by collecting single crystal X-ray and/or powder X-ray and powder neutron diffraction intensities.  The atomic structure refinements indicated that the compounds are essentially iso-structural with the prototype Tsai-type 1/1 approximant crystal, YbCd6. However, there are subtle structural variations at their cluster centers and in the so-called cubic interstices which affects some of their physical properties. Thermoelectric and magnetic properties of the compounds are investigated. Significant differences are observed in the thermoelectric properties of Gd(14)Au(70)Si(16), Gd(14)Au(67)Ge(19) and Yb(16)Au(65)Ge(19) compounds which are explained on the bases of their crystal structures and chemical compositions. Magnetic susceptibility and specific heat measurements revealed ferromagnetic transitions at low temperatures, Tc ≈ 22.5 K for Gd(14)Au(70)Si(16) and Tc ≈ 13.1 K for Gd(14)Au(67)Ge(19), whereas, for the Tb(14)Au(70)Si(16) compound a ferrimagnetic-like transition is observed at Tc ≈ 9 K. Moreover, a re-entrant spin-glass transition is observed at TRSG ≈ 3.3 K for Gd(14)Au(67)Ge(19) compound. Finally, the magnetic structure of the Tb(14)Au(70)Si(16) compound was determined from powder neutron diffraction data which is to our knowledge the first magnetic structure refinement report in the family of quasicrystals and approximants.