What is the proper joint for an inside corner when installing molding?

A coped joint is the proper joint for an inside corner when installing molding because it provides a clean and aesthetically pleasing finish. In a coped joint, one piece of molding is shaped to fit over the profile of the other piece, allowing for a seamless connection at the corner. This method compensates for slight variations in wall angles and ensures the joint remains tight over time, as wood can expand and contract. The coped joint also minimizes the visibility of any gaps that might develop due to these changes.

The other joint types mentioned are not suitable for inside corners. A scarf joint involves two pieces of molding being joined at an angle, which is better suited for longer runs of molding rather than corners. A half-lap joint involves cutting away half of each piece to create a flush fitting, but this is not appropriate for molding at corners. Likewise, a lap joint simply overlaps the ends of two pieces without the intricate fitting that a coped joint provides. Thus, for aesthetics and functionality in molding installation, the coped joint is the preferred choice.