This article studies consensus of linear multi-agent systems (MASs) on undirected graphs. An adaptive event-triggering protocol is constructed for consensus control by using relative information between agents. Sufficient conditions are established for consensus of linear MASs without and with external disturbances , respectively. Zeno behavior is proved to be excluded. Moreover, a self-triggered realization based on sampled information is formulated for the protocol. Since the proposed protocol incorporates both adaptive control and event-triggered control, it can be implemented in a fully distributed way and only makes use of the sampled relative information between neighboring agents. Two numerical examples are finally provided for demonstrating the effectiveness and advantages of the theoretical results.