勾股定理的欧几里得证明方法

\documentclass{minimal}

\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}

\begin{tikzpicture}[line width = 3pt]
    \newcommand{\la}[0]{2}
    \newcommand{\lb}[0]{4}

    \draw[help lines] (-\lb, -\la) grid (\la + \lb, \la + \lb);

    \coordinate (C) at (0, 0);
    \coordinate (A) at (\la, 0);
    \coordinate (B) at (0, \lb);
    \coordinate (D) at ($ (B) + (\lb, \la) $);
    \coordinate (E) at ($ (A) + (\lb, \la) $);
    \coordinate (G) at ($ (A)!(C)!(B) $);
    \coordinate (H) at ($ (D)!(C)!(E) $);

    \draw[fill = green] (C) rectangle (\la, -\la);
    \draw[fill = yellow] (C) rectangle (-\lb, \lb);

    \draw[fill = pink] (C) -- (A) -- (B) -- (C);
    \draw[fill = green] (E) -- (A) -- (G) -- (H) -- (E);
    \draw[fill = yellow] (H) -- (G) -- (B) -- (D) -- (H);
    \draw (C) -- (H);

    \tikzstyle{every node} = [circle, draw, fill, inner sep = 3pt, blue]

    \foreach \p/\l in {A/315, B/90, C/225, D/90, E/0, G/90, H/0} {
        \node[label = \l: $ \p $] at (\p) {};
    }

\end{tikzpicture}

\end{document}