Detail cutting in general and when you fit two pieces of trim at the corner you can either cut them at a 45 degree angle or you can "cope" them. To do this, you put the first piece in place full length with a straight cut on the end. Cut a 45 degree angle on the second piece and that will give you the profile of the molding. Use the coping saw to cut the exposed wood away at the edge of the cut so that only the face remains. This will fit into the first piece and give you a better fit than a simple 45 degree cut. If the room is not exactly square, this type of cut allows for that since all you see is the finished edge.
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