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With the fifth-generation (5G) networks widely commercialized and fast deployed, the sixth-generation (6G) wireless communication is envisioned to provide competitive quality of service (QoS) in multiple aspects to global users. The critical and underlying research of the 6G is, firstly, highly dependent on the precise modeling and characterization of the wireless propagation when the spectrum is believed to expand to the terahertz (THz) domain. Moreover, future networks' power consumption and energy efficiency are critical factors to consider. In this research, based on a review of the fundamental mechanisms of reconfigurable intelligent surface (RIS) assisted wireless communications, we utilize the 3D ray-tracing method to analyze a realistic indoor THz propagation environment with the existence of human blockers. Furthermore, we propose a distributed RISs framework (DRF) to assist the indoor THz wireless communication to achieve overall energy efficiency. The numerical analysis of simulation results based on more than 2,900 indoor THz wireless communication sub-scenarios has demonstrated the significant efficacy of applying distributed RISs to overcome the mobile human blockage issue, improve the THz signal coverage, increase signal-to-noise ratios (SNRs), and QoS. With practical hardware design constraints investigated, we eventually envision how to utilize the existing integrated sensing and communication techniques to deploy and operate such a system in reality. Such a distributed RISs framework can also lay the foundation of efficient THz communications for Internet-of-Things (IoT) networks.