qoch is not the word for "partner" when referring to socks and gloves and the like.  The word for that is nelwI'.  With nel, the subject is one sock (or glove or shoe or whatever) of the pair and the object is the other.  To talk about a sock (or glove or...) matching (that is fitting onto) a foot (or hand or...), use the verb mey:

        mumey waqmeywIj "my shoes fit" (literally, "my shoes fit me")

        torgh lumey waqmey  "the shoes fit Torg"

        waqmeywIj vImey  "I fit my shoes" 

When a piece of a jigsaw puzzle fits into the right spot, you can say:

        Qay'mol mey (Qay'mol) teSra'  "the (puzzle) piece fits (into) the puzzle" (In this context, you don't have to repeat Qay'mol, but it's fine if you do.)

        or

        nelchu' Qay'mol teSra' "the puzzle piece fits perfectly"

The first focuses on the interlocking of the pieces; the second focuses on the piece in question occupying the identically shaped space where it goes.