How to Generate Perpendicular Bisectors in Graphs Using Tkz-Graph

I am trying to demonstrate a geometric way to determine the symmetries of a graph generated using tkz-graph.

I was able to use a not-so-elegant way to get one of the perpendicular bisectors. How may I generate the other ones without figuring out the coordinates they would pass through?

Also, how could I add curved arrows between the vertices to illustrate the rotational symmetries.

Here is what I have so far.

\documentclass{article}
\usepackage{pgf,tikz}
\usepackage{tkz-graph}
\begin{document}
\begin{tikzpicture}[scale=1.75,rotate=90]
\draw[dashed,blue,thick] (1.5,0) -- (-1,0) node[below] {$l_1$};
\GraphInit[vstyle=Classic]
\begin{scope}[VertexStyle/.append style = {minimum size = 4pt, inner sep = 0pt}]
\Vertices[ Math, Lpos=90]{circle}{1,3,2}
\Edges(1,3,2,1)
\end{scope}
\end{tikzpicture}
\end{document}
• "to illustrate the rotational symmetries" >>> use rotate, and reflect (a built-in in Asymptote, but not in TikZ). Essence of the figure is not about perpendicular bisectors Oct 7, 2022 at 22:12
• Related: Q233246 Oct 8, 2022 at 1:36

The perpendicular bisectors can be made with e.g. tkz-euclide(same author - Alain Matthes as tkz-graph).

A figure like this would better be made purely in tkz-euclide, but they can be mixed. This code can be improved in many ways:

\documentclass[tikz, border=1cm]{standalone}
\usepackage{tkz-graph, tkz-euclide}
\begin{document}
\begin{tikzpicture}
\GraphInit[vstyle=Classic]
\tikzset{VertexStyle/.append style={minimum size=4pt, inner sep=0pt}}
\SetGraphUnit{2}
\begin{scope}[rotate=90]
\SetVertexNoLabel
\Vertices{circle}{A,B,C}
\end{scope}
\Edges(A,B,C,A)

\node[above right] at (A) {$1$};
\node[below] at (B) {$3$};
\node[above right] at (C) {$2$};

\tkzDefLine[mediator](A,B)
\tkzGetPoints{P}{Q}
\tkzDrawLines[dashed, blue, thick, add=0.2 and -0.3](P,Q)
\tkzLabelLine[below, pos=0.7](P,Q){$l_2$}
\tkzDefMidPoint(A,B)
\tkzGetPoint{M}
\tkzMarkRightAngle(P,M,B)

\tkzDefLine[mediator](B,C)
\tkzGetPoints{P}{Q}
\tkzDrawLines[dashed, blue, thick, add=0.2 and -0.3](P,Q)
\tkzLabelLine[below, pos=0.7](P,Q){$l_1$}
\tkzDefMidPoint(B,C)
\tkzGetPoint{M}
\tkzMarkRightAngle(P,M,C)

\tkzDefLine[mediator](C,A)
\tkzGetPoints{P}{Q}
\tkzDrawLines[dashed, blue, thick, add=0.2 and -0.3](P,Q)
\tkzLabelLine[below, pos=0.7](P,Q){$l_3$}
\tkzDefMidPoint(C,A)
\tkzGetPoint{M}
\tkzMarkRightAngle(P,M,C)

\end{tikzpicture}
\end{document}