A method for cooling a shroud segment of a gas turbine engine is provided. The method includes providing a turbine shroud assembly including a shroud segment having an inner surface and a leading edge that is substantially perpendicular to the inner surface, and coupling a turbine nozzle to the turbine shroud segment such that a gap is defined between an aft edge of an outer band of the turbine nozzle and the leading edge. The method also includes directing cooling air into the gap, and directing the cooling air in the gap through at least one cooling hole extending between the leading edge and the inner surface.