Generating nonclassical states of photons such as polarization-entangled states on a monolithic chip is a crucial step towards practical applications of optical quantum information processing such as quantum computing and quantum key distribution. Here we demonstrate two polarization-entangled photon sources in a single monolithic semiconductor waveguide. The first source is achieved through the concurrent utilization of two spontaneous parametric down-conversion (SPDC) processes, namely, type-0 and type-I SPDC processes. The chip can also generate polarization-entangled photons via the type-II SPDC process, enabling the generation of both copolarized-and cross-polarized polarization-entangled photons in the same device. In both cases, polarization entanglement is generated directly on the chip without the use of any off-chip compensation, interferometry, or bandpass filtering. This enables direct, chip-based generation of both Bell states (|H,H + |V ,V )/ √ 2 and (|H,V + |V ,H )/ √ 2 simultaneously utilizing the same pump source. In addition, based on compound semiconductors, this chip can be directly integrated with it own pump laser. This technique ushers an era of self-contained, integrated, electrically pumped, room-temperature polarization-entangled photon sources.