# Glueing and pasting in geometry

everyone. I need to draw a picture which looks like below

Can any one recommend what package I should use? and some ideas to do it? I reall have no idea.

Here the first 5 pictures obtained using tkz-euclide and tikz. Then you can arrange the pictures in yours order and enviroment.

Remove comment % to look at points coordinates.

\documentclass{scrartcl}
\usepackage{tikz}
\usepackage{tikz-cd}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{angles}
\usepackage{tkz-euclide}
\usetkzobj{all}

\begin{document}
\tikzset{->-/.style={decoration={
markings,
mark=at position #1 with {\arrow{>}}},postaction={decorate}}}
\tikzset{->>-/.style={decoration={
markings,
mark=at position #1 with {\arrow{>>}}},postaction={decorate}}}

%1
\begin{tikzpicture}
\tkzDefPoints{0/0/O,-1/0/A,1/0/B}
\draw[->-=.5,green!75!black] (A) arc (180:0:1);
\node at (0,1.25) {\textcolor{green!75!black}{$a$}};
\draw[->-=.5,green!75!black] (B) arc (0:-180:1);
\node at (0,-1.25) {\textcolor{green!75!black}{$a$}};
\tkzDrawPoints[color=green!75!black](A,B)
%\tkzLabelPoints(A,B)
\end{tikzpicture}

\vspace{1cm}
%2
\begin{tikzpicture}
\tkzDefPoints{0/0/O,-1/0/A,1/0/B,-.3/0/a,.3/0/b}
\draw[->-=.5,green!75!black] (A) arc (180:0:1);
\node at (0,1.25) {\textcolor{green!75!black}{$a$}};
\draw[->-=.5,green!75!black] (B) arc (0:-180:1);
\node at (0,-1.25) {\textcolor{green!75!black}{$a$}};
\tkzDrawCircle[color=red](O,a)
\tkzDrawPoints[color=green!75!black](A,B)
%\tkzLabelPoints(A,B,a,b)
\end{tikzpicture}

\vspace{1cm}
%3
\begin{tikzpicture}
\tkzDefPoints{0/.25/O,-1/.25/A,1/.25/B,-.3/.25/a,.3/.25/b}
\tkzDefPoints{0/-.25/O'}
\tkzDefPointsBy[translation=from O to O'](A,B,a,b){A',B',a',b'}
\draw[->-=.5,green!75!black] (A) arc (180:0:1);
\draw[->-=.5,green!75!black] (B') arc (0:-180:1);
\tkzDrawSegments[->>-=.65,color=red](A,a b,B A',a' b',B')
\tkzDrawArc[color=red](O,b)(a)
\tkzDrawArc[color=red](O',a')(b')
%\tkzLabelPoints(A,B,a,b,A',B',a',b')
\end{tikzpicture}

\vspace{1cm}
%4
\begin{tikzpicture}
\tkzDefPoints{0/.25/O,-1/.25/A,1/.25/B,-1/.75/a,1/.75/b}
\tkzDefPoints{0/-.5/O'}
\tkzDefPointsBy[translation=from O to O'](A,B,a,b){A',B',a',b'}
\tkzDrawSegments[->-=.5,color=green!75!black](a,b)
\tkzDrawSegments[->>-=.65,color=red](a,A B,b A',a' b',B')
\tkzDrawSegments[color=red](A,B a',b')
\tkzDrawSegments[->-=.5,color=green!75!black](B',A')
%\tkzLabelPoints(A,B,a,b,A',B',a',b')
\end{tikzpicture}

\vspace{1cm}
%5
\begin{tikzpicture}
\tkzDefPoints{0/.25/O,-1/.25/A,1/.25/B,-1/.75/a,1/.75/b}
\tkzDefPoints{0/-.5/O'}
\tkzDefPointsBy[translation=from O to O'](A,B,a,b){A',B',a',b'}
\tkzDrawSegments[->-=.5,color=green!75!black](B,A)
\tkzDrawSegments[->>-=.65,color=red](a,A B,b a',A' B',b')
\tkzDrawSegments[color=red](a,b A',B')
\tkzDrawSegments[->-=.5,color=green!75!black](b',a')
%\tkzLabelPoints(A,B,a,b,A',B',a',b')
\end{tikzpicture}
\end{document}