I am plannning on laying down 3/8" glue down engineered wood on concrete.I have several rectangular,cross and diamond patterns which will make many cuts necessary.If I have a tongue piece that must go into a cut piece I can cut a groove in the cut piece with a table saw.What if I have the groove side piece that needs to be joined to a cut piece ? I assume I can't just glue the pieces with no tongue and groove connection ?

Thank you for anybody that has suggestions

You need a router to cut a grove, a table saw is asking for a wavy groove. then if you need a tounge you can pop a spline in and go.

You can either:
1) Use a bisquit joiner, sometimes called a plate joiner.
2) find a router bit that is the same size as your grooves and make your own grooves. I do that with either a router table or a I use a bearing guided grooving bit. You'll need to make your own tongues as well.

Whenever possible, you a T&G connection. However, sometimes that is not possible or impractical. The T&G help keep the flooring surface aligned so as not to have overwood/underwood. You can eliminate T&G's sometimes but you risk independant movement and more overwood.

First off, whose wood is it? Most manufacurers sell both splines and slot cutters to go with their varous products.