The development of scalable sources of non-classical light is fundamental to unlocking the technological potential of quantum photonics. Semiconductor quantum dots are emerging as near-optimal sources of indistinguishable single photons. However, their performance as sources of entangled-photon pairs are still modest compared to parametric down converters. Photons emitted from conventional Stranski-Krastanov InGaAs quantum dots have shown non-optimal levels of entanglement and indistinguishability. For quantum networks, both criteria must be met simultaneously. Here, we show that this is possible with a system that has received limited attention so far: GaAs quantum dots. They can emit triggered polarization-entangled photons with high purity (g(2)(0) = 0.002±0.002), high indistinguishability (0.93±0.07 for 2 ns pulse separation) and high entanglement fidelity (0.94±0.01). Our results show that GaAs might be the material of choice for quantum-dot entanglement sources in future quantum technologies.