We develop and analyze a distributed event-triggered linear iterative algorithm that enables the components of a distributed system, each with some initial value, to reach approximate average consensus on their initial values, after executing a finite number of iterations. The proposed protocol provides the nodes with a criterion that allows them to determine, in a distributed manner, when to terminate (because approximate average consensus has been reached) and also reduces the number of transmissions that are required. We consider an undirected graph, i.e., a symmetric graph with bi-directional communication links, and compare the number of iterations and transmissions required by the proposed protocol against a previously proposed stopping protocol for approximate average consensus.