Automatic (calculated) position of nodes in tikz

Question

Say I have the following triangle, which is a pretty standard figure:

\documentclass[border=3pt]{standalone}

\usepackage[ngerman]{babel}
\usepackage{tikz}

\usetikzlibrary{angles,quotes,babel}

\begin{document}
    \begin{tikzpicture}%
        \draw[thick,xshift=6cm] (0,0) coordinate(A) node[below left] {$\mathrm{A^{\prime}}$}
        -- (0:5cm) coordinate(B) node[pos=0.5, below] {$\mathrm{c^{\prime}}$} node[below right] {$\mathrm{B^{\prime}}$}
        -- (40:5cm) coordinate(C) node[pos=0.5, right] {$\mathrm{a^{\prime}}$} node[above] {$\mathrm{C^{\prime}}$}
        -- cycle node[pos=0.5,above left] {$\mathrm{b^{\prime}}$}
        pic["$\beta^\prime$",draw,thin,angle radius=0.5cm,angle eccentricity=1.3] {angle=C--B--A}
        pic["$\gamma^\prime$",draw,thin,angle radius=0.5cm,angle eccentricity=1.45] {angle=A--C--B}
        pic["$\alpha^\prime$",draw,thin,angle radius=0.5cm,angle eccentricity=1.5] {angle=B--A--C}
        ;
    \end{tikzpicture}
\end{document}

I placed the nodes manually and I have the problem that they have to be manually adjusted, if I rotate the figure. An example of how horrible it can get is if I add [rotate=180] after \begin{tikzpicture}.

I read the whole section on nodes in the manual, but didn't find an answer to this:

1. For sides labels, is there a way to tell TikZ to place the nodes always half way (pos=0.5, but more "really 0.5") and especially to tell it to place it x pt (or mm) from the middle of the line in the direction of the perpendicular to the segment?

2. For vertex labels, is there a way to tell TikZ to place the node x pt (or mm) from the vertex, on the bisector of the angle at that vertex?

If there were such a way, there would possibly remain to manually "swap" the position (for when the figure is upside/down), but this kind of geometric figures would always look nice.

Answer 1

As suplement to @SebGlav answer (+1), mostly off-topic:

• used are quotes for labeling of edges
• edge labels lie on edges (used option sloped)
• defined common style for angle labels
• all math variables in picture are set by

\everymath=\expandafter{\the\everymath\mathrm}

• instead of ^#{prime} is used '

\documentclass[tikz, border=3pt]{standalone}
\usepackage[ngerman]{babel}
\usetikzlibrary{angles,
                calc,
                quotes,
                babel}
\tikzset{
Angle/.style = {draw, font=\footnotesize,
                angle radius=5mm,
                angle eccentricity=1.45},
every edge quotes/.style ={auto=right, rounded corners=5pt, inner sep=2pt},
        }


\begin{document}
    \begin{tikzpicture}
\everymath=\expandafter{\the\everymath\mathrm}
%
\draw[thick]    (0,0) coordinate (A)    to["$c'$"]   coordinate (c)
                (5,1) coordinate (B)    to["$a'$"]     coordinate (a)
                (2,3) coordinate (C)    to["$a'$"]     coordinate (b)
                cycle;
\path   pic[Angle, "$\beta'$"]  {angle=C--B--A}
        pic[Angle, "$\gamma'$"] {angle=A--C--B}
        pic[Angle, "$\alpha^\prime$"] {angle=B--A--C};
\path   (A) -- ($(A)!3mm!180:(a)$) node {A}
        (B) -- ($(B)!3mm!180:(b)$) node {B}
        (C) -- ($(C)!3mm!180:(c)$) node {C};
    \end{tikzpicture}

    \begin{tikzpicture}[rotate=45]
\everymath=\expandafter{\the\everymath\mathrm}
%
\draw[thick]    (0,0) coordinate (A)    to["$c'$"]   coordinate (c)
                (5,1) coordinate (B)    to["$a'$"]     coordinate (a)
                (2,3) coordinate (C)    to["$a'$"]     coordinate (b)
                cycle;
\path   pic[Angle, "$\beta^\prime$"]  {angle=C--B--A}
        pic[Angle, "$\gamma^\prime$"] {angle=A--C--B}
        pic[Angle, "$\alpha^\prime$"] {angle=B--A--C};
\path   (A) -- ($(A)!3mm!180:(a)$) node {A}
        (B) -- ($(B)!3mm!180:(b)$) node {B}
        (C) -- ($(C)!3mm!180:(c)$) node {C};
    \end{tikzpicture}
\end{document}

First example:

Second example: first one is rotated for 45 degrees

Answer 2

Here's a way to do this, using calc for the edges labels and angles,quotes for the vertices labels (similar to what you used to draw the inner angles).

This should remain correctly placed with any rotation angle.

\documentclass[tikz,border=3.14mm]{standalone}

\usetikzlibrary{calc,angles,quotes}

\begin{document}
    \begin{tikzpicture}[rotate=0]
        \coordinate (A) at (0,0);
        \coordinate (B) at (5,2);
        \coordinate (C) at (3,5);
        
        \draw (A) -- (B) coordinate[midway] (C') -- (C) coordinate[midway] (A') -- (A) coordinate[midway] (B') -- cycle
            pic["$A$",angle radius=15pt] {angle=C--A--B}
            pic["$B$",angle radius=15pt] {angle=A--B--C}
            pic["$C$",angle radius=15pt] {angle=B--C--A};
        
        \node (lbl_a) at ($(A')!10pt!-90:(C)$) {a};
        \node (lbl_b) at ($(B')!10pt!-90:(A)$) {b};
        \node (lbl_c) at ($(C')!10pt!-90:(B)$) {c}; 
    \end{tikzpicture}
\end{document}

Rotate = 0

Rotate = -30

Rotate = -60