Approximation of Lines Intersecting

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\documentclass[border=4pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{angles, quotes, calc}
\begin{document}
    
    \begin{tikzpicture}[line cap = round]
%       \draw (0,0) grid (10,10);
        
        \coordinate (Ai) at (5,3) {};
        \coordinate (Bi) at (6,7) {};
        \coordinate (Aj) at (4,3) {};
        \coordinate (Bj) at (3,7) {};
        \coordinate (P) at (4.5,2.5) {};
        \node[inner sep = 0.2cm] (DVreco) at ($(P)+(1,-0.8)$) {};
        \coordinate (P') at (4.5,1) {};
        \node[inner sep = 0.2cm] (DVtrue) at ($(P')+(-0.6,0)$) {};
        \node[inner sep = 0.2cm] (thetai) at (6,4) {};
        \node[inner sep = 0.2cm] (thetaj) at (3,4) {};
        
        \draw[very thick] (Ai) -- (Bi);
        \draw[thick, dashed] ($(Ai)!-0.55!(Bi)$) -- (Ai);
        \draw[very thick] (Aj) -- (Bj);
        \draw[thick, dashed] ($(Aj)!-0.55!(Bj)$) -- (Aj);
        \draw[dashed] (P) -- (Ai);
        \draw[dashed] (P) -- (Bi);
        \draw[dashed] (P) -- (Aj);
        \draw[dashed] (P) -- (Bj);
        
        \draw[fill=black] (Ai) circle (1.5pt);
        \draw[fill=black] (Bi) circle (1.5pt);
        \draw[fill=black] (Aj) circle (1.5pt);
        \draw[fill=black] (Bj) circle (1.5pt);
        \draw[fill=black] (P) circle (1.5pt);
        \draw[fill=black] (P) circle (1.5pt);
        \draw[fill=black] (P') circle (1.5pt);
        
        \pic[draw, thick, angle eccentricity=1.4, angle radius=0.6cm] {angle = Ai--P--Bi};
        \pic[draw, thick, angle eccentricity=1.4, angle radius=0.6cm] {angle = Bj--P--Aj};
        
 
 
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