Protocols based on directed acyclic graphs (DAG) have been proposed as potential solution to the latency and throughput limitations of traditional consensus protocols. However, their adoption has been hindered by security concerns and a lack of a solid foundation to guarantee improvements in both throughput and latency. In this paper, we present a construction that rigorously demonstrates how DAG-based protocols can achieve superior throughput and latency compared to chain-based consensus protocols, all while maintaining the same level of security guarantees.