% Title: Demonstration sans parole : regle des nombres moyens
% Author: Jacques Duma
% Site: http://math.et.info.free.fr/TikZ/index.html

\documentclass{article}

\usepackage{tikz}

\begin{document}

\pagestyle{empty}

\section*{R\`egle des nombres moyens}

\vfill

\begin{center}
\begin{tikzpicture} [scale=1.5,transform shape]
\fill[color=red!50] (0,0)--(6,2)--(8,5)--cycle;
\fill[color=blue!50] (0,0) -- (6,0)--(6,2)--cycle;
\fill[color=yellow!50] (6,0) rectangle (8,2);
\fill[color=green!50] (8,2)--(8,5)--(6,2)--cycle;
\node[above] at (4,0){$b$};
\node[above] at (7,0){$d$};
\node[above] at (7,2){$d$};
\node[left] at (8,1){$a$};
\node[left] at (6,1){$a$};
\node[left] at (8,3){$c$};
\end{tikzpicture}
\end{center}

\vfill


{\huge $$\frac{a}{b}<\frac{c}{d}Ê\quad \Rightarrow \quad \frac{a}{b}<\frac{a+c}{b+d} <\frac{c}{d}$$}

\vfill

\end{document}
