Perigals Dissection

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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{intersections}
\usetikzlibrary{math}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{0.125pt}
%
% File name: perigals-dissection.tex
% Description: 
% A geometric proof of the Pythagorean theorem 
% known as the Perigal's dissection is shown.
% 
% Date of creation: July, 30th, 2021.
% Date of last modification: October, 9th, 2022.
% Author: Efraín Soto Apolinar.
% https://www.aprendematematicas.org.mx/author/efrain-soto-apolinar/instructing-courses/
% Source: page 126 of the 
% Glosario Ilustrado de Matem\'aticas Escolares.
% https://tinyurl.com/5udm2ufy
%
% Terms of use:
% According to TikZ.net
% https://creativecommons.org/licenses/by-nc-sa/4.0/
% Your commitment to the terms of use is greatly appreciated.
%
\begin{document}
    %
    \begin{tikzpicture}[scale=0.75]
    \tikzmath{function rotacionx(\x,\y,\angulo) {return \x*cos(\angulo) + \y*sin(\angulo);};}
    \tikzmath{function rotaciony(\x,\y,\angulo) {return -\x*sin(\angulo) + \y*cos(\angulo);};}
    \pgfmathsetmacro{\dx}{0.25}
    % Vertices of the triangle
    \pgfmathsetmacro{\Ax}{0}
    \pgfmathsetmacro{\Ay}{0}
    \coordinate (A) at (\Ax,\Ay);
    \pgfmathsetmacro{\Bx}{4}
    \pgfmathsetmacro{\By}{0}
    \coordinate (B) at (\Bx,\By);
    \pgfmathsetmacro{\Cx}{4}
    \pgfmathsetmacro{\Cy}{3}
 
 
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