Fire-barriers systems, including pre-assembled intersecting and straight-line fire-barriers having either all male-, all female-, or both types of coupling ends eliminate on-site cutting and construction of barriers required for intersection-spaces and provide easy, rapid, and safe one-step, drop-in installation and coupling. All male/female ended fire-barriers are constructed as single-piece units. All adjacent laid-flat layers are continuously connected having no gaps or folds. Straight-line and L-shaped barriers are certified according to the criteria mandated by both the ASTM E 1399-97 (Reapproved 2005), Standard Test Method for Cyclic Movement and Measuring the Minimum and Maximum Joint Widths of Architectural Joint Systems and the UL 2079 Fire Resistance of Building Joint Systems Test for air leakage (Revised and relocated as 1.14 Mar. 10, 2006).