We present, for the first time, the design of two antennas for the terahertz photomixers that have reconfigurable operation frequency or reconfigurable input impedance as an alternative to the state-of-the-art high-impedance, narrow band or low-impedance, wide-band antennas. Both antennas have folded-dipole structures, which inherently have high radiation resistances, and the dimensions of the antennas are modified in the horizontal and vertical dimensions by means of ideal switches, changing the operation frequency of the antenna or the input impedance of the antenna at a given operation frequency. We also propose a real-life solution for the ideal switches for the antennas, namely miniature Micro-Electro-Mechanical Systems (MEMS) switches, which have an area of 10 um x 10 um and is, to the best of our knowledge, the smallest MEMS switch reported in the literature. The first antenna is capable of operating at three different frequencies of 200, 400, and 600 GHz, whereas the input impedance of the second antenna can be adjusted between 4 k Omega and 7.5 k Omega at an operation frequency of 385 GHz. The proposed antennas can also be used as a photoconductive antenna for the terahertz frequency band.