A blade track used in gas turbine engines to define an outer boundary of the primary gas path through a turbine section of a gas turbine engine is disclosed. The blade track includes segments comprising ceramic matrix composite materials that are assembled such that the blade track segments keystone against one another to provide a self-supporting full hoop assembly. Circumferentially-extending splines may be used to couple adjacent segments to one. Also disclosed are other heat shielding assemblies used in gas turbine engines that share features with the illustratively disclosed blade track.