\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tkz-euclide}
\usepackage{tikz}
\usetikzlibrary{patterns}

\begin{document}
\usetkzobj{all}
\begin{tikzpicture}
    \tkzSetUpPoint[shape=circle,size=10,color=black,fill=black]
    \tkzSetUpLine[line width=1]
    \tkzDefPoints{0/0/A, 4/0/B, 3/3/C}

    \tkzDefLine[orthogonal=through A,/tikz/overlay](B,C) \tkzGetPoint{helper}
    \tkzInterLL(B,C)(A,helper) \tkzGetPoint{La}
    \tkzDefLine[orthogonal=through C,/tikz/overlay](A,B) \tkzGetPoint{helper}
    \tkzInterLL(A,B)(C,helper) \tkzGetPoint{Lc}

    \tkzInterLL(A,La)(C,Lc) \tkzGetPoint{orthocenter}

    \tkzMarkAngle[arc=l,size=1.0cm,color=red,fill=red!20](B,A,La)
    \tkzLabelAngle[pos=0.8](B,A,La){$\alpha$}

    \tkzMarkAngle[arc=l,size=1.0cm,color=red,fill=red!20](Lc,C,B)
    \tkzLabelAngle[pos=0.8](Lc,C,B){$\alpha$}

    \tkzMarkAngle[arc=ll,size=0.6cm,color=green,fill=green!20](A,orthocenter,Lc)
    \tkzLabelAngle[pos=0.4](A,orthocenter,Lc){$\gamma$}

    \tkzMarkAngle[arc=ll,size=0.4cm,color=green,fill=green!20](La,orthocenter,C)
    \tkzLabelAngle[pos=0.2](La,orthocenter,C){$\gamma$}

    \tkzDrawPolygon(A,B,C)

    \node at ($(A)+(-0.47,-0.2)$){$A$};
    \node at ($(B)+(0.35,-0.2)$) {$B$}; % \tkzLabelPoint[below](B){$B$} is not accurate enough
    \node at ($(C)+(0.05,0.3)$)  {$C$};
    \node at ($(La)+(0.25,0.1)$)  {$L_A$};
    \node at ($(Lc)+(0,-0.25)$)  {$L_C$};

    \tkzDrawSegment(C,Lc)
    \tkzDrawSegments(A,La)
    \tkzDrawPolygon[pattern=north east lines](A,B,La)
    \tkzDrawPolygon[pattern=north west lines](Lc,B,C)
    \tkzDrawPoints(A,B,C,La,Lc)
    %\tkzLabelSegment[pos=0.7,below](A,B){$c$}
\end{tikzpicture}
\end{document}
