In this article, the problem of distributed synchronization of networked systems with actuator bias faults is investigated. To effectively use the limited network bandwidth and avoid the requirement of global information, a novel adaptive event-triggered state feedback controller and a dynamic triggering law are designed jointly by employing a projection operator approach. The proposed synchronization scheme is different from existing ones that have focused on designing controllers and triggering laws independently. Besides, our scheme is extended to design an observer-based distributed adaptive event-triggered controller and corresponding dynamic triggering law when the system states are unmeasurable. Theoretical analysis shows that under the two different distributed event-triggered synchronization schemes, the following three results can be obtained: 1) fully distributed synchronization can be achieved without knowing global information associated with the underlying communication topology and node’s scale; 2) continuous communication among adjacent nodes can be avoided for both designed controllers and dynamic triggering laws; and 3) exclusion of Zeno phenomenon is shown by contradiction. Finally, the effectiveness of the proposed algorithms is verified through three numerical examples.