Joining Different Lines

Hello,

I have an odd situation, that I'd like some help with. I've got a
situation where I want to have a line bend around a corner. There are
just two difficult parts of this.

For the sake of example, lets say its running along the bottom border
of a window and is going to go up along the left-hand edge.

I can use a make a line segment path to do this and even get it to
curve properly (so as not to be a miter joint), but the real trouble is
that I want the vertical segment to be considerably thicker as a line
than the horizontal.

The intent is to have a "border" which will contain a button list on
the left hand side and I want it to appear to be part of that border.

Anyone think of a way to make this happen?

- Mike