Bound states in the continuum (BIC) in metamaterials have recently attracted attention for their promising applications in photonics. Here, we investigate the transition from Fano resonances to BIC, at terahertz (THz) frequencies, of a one-dimensional photonic crystal slab made of rectangular dielectric rods. Simulations performed by an analytical exact solution of the Maxwell equations showed that symmetry-protected, high-quality factor (Q), BIC emerge at normal incidence. For non-normal incidence, BIC couple with the freely propagating waves and appear in the scattering field as a Fano resonance. Simulations were verified by realizing the photonic crystal slab by 3D-printing technique. THz time-domain spectroscopy measurements as a function of the incidence angle matched the simulation to good accuracy and confirmed the evolution of Fano resonances to high-Q resonances typical of BIC. These results point out the design of highly sensitive and low-cost THz devices for sensing for a wide range of applications.