The strong-field ionization behavior when a Rydberg atom is exposed to a terahertz single-cycle pulse is studied. Fully three-dimensional time-dependent Schrödinger equations and classical trajectory Monte Carlo calculations are performed. Results from stationary eigenstates and Rydberg wave packets are presented, and it is found that the ionization properties can be different for the two cases. All of the pulse parameters and physical quantities are scaled versus the principal quantum number n . The ionized electron's scaled radial, energy, and angular distributions are investigated for different n , and the quantum results are interpreted using a semiclassical method. The scaling relations of quantum interference amplitudes are discussed.