How to solve mismatch of thick curves in tikz?

Question

Consider following MWE:

\begin{tikzpicture}
\draw (0,0) -- (1,1) -- (2,0);
\draw plot [smooth, tension=1.5] coordinates{(0,0) (1,-1) (2,0)};
\begin{scope}[xshift=3cm]
    \draw[line width=1.5] (0,0) -- (1,1) -- (2,0);
    \draw[line width=1.5] plot [smooth, tension=1.5] coordinates{(0,0) (1,-1) (2,0)};
\end{scope}
\end{tikzpicture}

that produces following picture:

In the right-hand part, because of the line width, there are 2 small "gaps" where the lines and the smooth curve join.

In some cases, it might be barely noticeable in print. But if it is the case, is there something you can do in Tikz that is smarter than vertically shifting the begin and end points of the curve, on order to obtain more overlap?

Answer 1

\draw[line width=1.5] (1,1) -- (0,0) -- plot [smooth, tension=1.5] coordinates{(0,0) (1,-1) (2,0)} -- cycle; is ok?

Answer 2

Draw a single path as advised by @DavidCarlisle, and a simple arc will suffice for this semicircular part of the diagram, no need for a plot.

\documentclass[tikz,border=5pt]{standalone}

\begin{document}

\begin{tikzpicture} [line width=1.5]
  \draw (0,0) arc (-180:0:1) -- (1,1) -- cycle;
\end{tikzpicture}

\end{document}