Illustrator - Joining two rectangle with a line in between

[level3]

I wanted to make a logo looking like figure A, in doing so, I had to draw 3 triangle (figure B) and move them as close as possible and adjust them.

I could have drawn the outline of the shape of my logo and used line tool. But I want to shad those three segments in different colors. I could not shade three parts unless they have separators in between.

Is there any way in Illustrator to make those triangle and then join them together so in between lines are fixed?

I tried making compound path in object menu, but direct selection tool still can separate them