What is the term for the cutout made to receive a leaf of the hinge?

The correct term for the cutout made to receive a leaf of the hinge is "mortise." A mortise is a rectangular or square cut made into a piece of wood or material to accommodate the thickness of a hinge leaf. This joint allows the hinge to sit flush with the surface of the door or frame, enabling it to operate smoothly without protruding.

Understanding the concept of a mortise is crucial in construction and woodworking because it ensures that doors operate correctly and are aesthetically pleasing, as the hinge is integrated into the door or cabinet. Proper mortising techniques also contribute to the durability and strength of the hinge connection, as it provides a solid foundation for the hinge to pivot against.

In contrast, the terms gain, slot, and recess refer to different types of cuts or adjustments made in woodworking or construction contexts, but they do not specifically describe the cut for hinge placement. These distinctions are essential for ensuring precision and functionality in building applications.