A hood-latching system for a vehicle that has an engine-compartment hood that can be moved between a closed position and one or more open positions. The hood-latching system comprises one or more novel hood latches that are operable, when secured in a latched state to apply hood retention forces to the engine-compartment hood and thus, to secure the engine-compartment hood in its closed position. The novel hood latches of the hood latching system comprise prop legs that support the novel hood latches out of a path of travel of the engine-compartment hood when the novel hood latches are not secured in a latched state. The prop legs of the novel hood latches, thus, enable one person to close the engine-compartment hood of the vehicle without pinching the novel hood latches between the engine-compartment hood and latch-anchor components to which the novel hood latches are mounted.