How can I draw two triangles in a row?

Question

I'm trying to illustrate the rigid transformations of the equilateral triangle: rotation and transposition. Therefore I would like to draw the triangle, then the $\to$ arrow with superscript say, $\rho$, and then the rotated triangle (and below all of this, something similar for $\tau$)

Here is how I'm drawing the triangle

\documentclass{article}
\usepackage{tikz-cd}
\usepackage{tikz}
\usepackage{xcolor}

\begin{document}

\begin{tikzpicture}
  \draw [line width=1pt, color=gray] (0,0) -- (60:2) -- (2,0) -- cycle;
  \coordinate[label=left:$A$]  (A) at (0,0);
  \coordinate[label=right:$B$] (B) at (2,0);
  \coordinate[label=above:$C$] (C) at (1,1.732);
\end{tikzpicture}

\end{document}

The question is, how can I put the mapping arrow next to it and then the resulting triangle.

Answer 1

Here is a suggestion using the a node with the regular polygon shape (from shapes.geometric).

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric,positioning}
\begin{document}

\begin{tikzpicture}[
  triangle/.style={
   regular polygon,
   regular polygon sides=3,
   minimum size=2cm,
   draw,
   label=corner 1:$A$,
   label=corner 2:$B$,
   label=corner 3:$C$}
]
\node [triangle] (a) {};
\node [triangle,rotate=40,right=3cm of a] (b) {};
\draw [->,shorten <=4mm,shorten >=4mm] (a) to[bend left] node[above]{$\rho$} (b);
\end{tikzpicture}

\end{document}