Hi Involute, welcome to MoI and to the forum!

You can use the Edit > Join command to glue end-to-end touching segments into a longer connected curve that will select all as one unit.

Basically the Extrude command will automatically do a join of the curves you input into it anyway but it can be convenient for object management and such to join them directly.

The Join command is located here on the Edit palette:



- Michael

Also re: "I tried unioning them together but that had no effect."

The boolean functions are basically expecting for things to get cut with one another with some chunks of things being removed, if you have things that are touching end to end (or edge-to-edge for surfaces) rather than more sort of punching through each other, use Edit > Join instead of boolean union.

- Michael