This article studies the rendezvous problem of linear multiagent systems by parallel event-triggered connectivity-preserving control strategies. There are two distinguished features of our design. First, the event-triggered control laws can not only guarantee the convergence of the tracking error as existing event-triggered consensus control strategies but also have the additional ability to maintain the connectivity of the time-varying and position-dependent communication network as rendezvous control laws. Second, by combining the potential function technique, output regulation theory, and adaptive control technique, an event-triggered observer is applied to estimate both the leader's system matrix and trajectory, which can work in parallel with the connectivity-preserving event-triggered controller. The executive time instants for the observer and the controller are asynchronous and generated by different triggering functions based on their own locally available measurement errors.