\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{tikz}
\usepackage{tkz-euclide}
\usetkzobj{all}
\usetikzlibrary{shapes, calc, decorations}
\usepackage{amsmath,amssymb}
\usepackage{helvet}
\usepackage[eulergreek]{sansmath}

\begin{document}
\begin{preview}
\begin{tikzpicture}[very thick,font=\sansmath\sffamily]
    \tkzDefPoint(0,0){A}
    \tkzDefPoint(3.2,0){B}
    \tkzDefPoint(2.3,2.4){C}

    \tkzLabelPoints[below left,font=\sansmath\sffamily](A)
    \tkzLabelPoints[below right,font=\sansmath\sffamily](B)
    \tkzLabelPoints[above,font=\sansmath\sffamily](C)

    % Draw polygon
    \tkzDrawPolygon[thick,fill=gray!10](A,B,C)

    % Mark angles
    \tkzMarkAngle[arc=l,size=0.6cm,fill=green!30](B,A,C)
    \tkzLabelAngle[pos=0.3](B,A,C){$\alpha$}

    \tkzMarkAngle[arc=l,size=0.6cm,fill=red!30](C,B,A)
    \tkzLabelAngle[pos=0.4](C,B,A){$\beta$}

    \tkzMarkAngle[arc=l,size=0.6cm,fill=blue!30](A,C,B)
    \tkzLabelAngle[pos=0.4](A,C,B){$\gamma$}

    % left red square
    \tkzDefLine[perpendicular=through A,K=1](A,C)\tkzGetPoint{F}
    \tkzInterLC(A,F)(A,C) \tkzGetPoints{E}{F}

    \tkzDefLine[perpendicular=through C,K=1](A,C)\tkzGetPoint{G}
    \tkzInterLC(C,G)(A,C) \tkzGetPoints{C}{C}

    \tkzLabelPoints[above,font=\sansmath\sffamily](G)
    \tkzLabelPoints[left,font=\sansmath\sffamily](F)
    \tkzDrawPolygon[thick,fill=red!15!white](A,C,G,F)

    % right blue square
    \tkzDefLine[perpendicular=through B,K=-1](B,C)\tkzGetPoint{I}
    \tkzInterLC(B,I)(B,C) \tkzGetPoints{I}{I}

    \tkzDefLine[perpendicular=through C,K=-1](B,C)\tkzGetPoint{H}
    \tkzInterLC(C,H)(B,C) %\tkzGetPoints{X}{H} - TODO

    \tkzLabelPoints[above,font=\sansmath\sffamily](H)
    \tkzLabelPoints[right,font=\sansmath\sffamily](I)
    \tkzDrawPolygon[thick,fill=blue!15!white](C,B,I,H)

    % below blue square
    \tkzDefLine[perpendicular=through A,K=-1](A,B)\tkzGetPoint{Xtemp}
    \tkzInterLC(A,Xtemp)(A,B) \tkzGetPoints{notNeeded}{D}

    \tkzDefLine[perpendicular=through B,K=-1](A,B)\tkzGetPoint{X}
    \tkzInterLC(B,X)(B,A) \tkzGetPoints{notNeeded}{E}

    \tkzLabelPoints[below,font=\sansmath\sffamily](D,E)
    \tkzDrawPolygon[thick,fill=blue!15!white](B,A,D,E)

    % squares below
    \tkzDefLine[perpendicular=through C,K=-1](A,B)\tkzGetPoint{Xtemp}
    \tkzInterLL(C,Xtemp)(D,E)\tkzGetPoint{L}
    \tkzInterLL(C,Xtemp)(A,B)\tkzGetPoint{K}
    \tkzDrawPoints[size=2,fill=black](L,K)
    \tkzLabelPoints[below right,font=\sansmath\sffamily](L,K)

    \tkzDrawLines[dashed](C,L)

    \tkzDrawPolygon[fill=red!15!white](A,K,L,D)

    % Label lines
    \tkzLabelSegment[below](A,B){$c$}
    \tkzLabelSegment[left](A,C){$b$}
    \tkzLabelSegment[right](B,C){$a$}

    \tkzDrawLines(C,D B,F)

    % Draw polygons
    \tkzDrawPolygon[thick](A,B,C)
\end{tikzpicture}
\end{preview}
\end{document}