This paper considers the distributed event-triggered consensus problem for general linear multiagent networks. Both the leaderless and leader-follower consensus problems are considered. Based on the local sampled state information, distributed adaptive event-triggered protocols are designed, which can ensure that the consensus of the agents is achieved, and the Zeno behavior is excluded by showing that the interval between any two triggering events is lower-bounded by a strictly positive value. Compared with the previous related works, our main contribution is that the proposed adaptive event-based protocols are fully distributed and scalable, which do not rely on any global information of the network graph and are independent of the network's scale. In these eventbased protocols, continuous communications are not required for either control laws updation or triggering functions monitoring.