\medskip

\begin{center}
\begin{tikzpicture}[scale=1.5]
\coordinate (A) at (0,0);
\coordinate (E) at (0,2);
\coordinate (F) at (2,2);
\coordinate (B) at (2,0);
\coordinate (C) at (2.7,.7);
\coordinate (G) at (2.7,2.7);
\coordinate (H) at (.7,2.7);
\coordinate (D) at (.7,.7);
\coordinate (I) at ($0.5*(H)+0.5*(G)$);
\coordinate (J) at ($0.5*(E)+0.5*(H)$);
\coordinate (K) at ($0.8*(B)+0.2*(D)$);
%\tkzDrawLine[add=0 and 1,color=gray!20](F,G)
\draw[gray!20] (F) -- (G);
\draw[gray!20] (F) -- (E);
%\tkzDrawLine[add=0 and 1,color=gray!20](F,E)
\fill (K) circle (1pt);
\draw (E) node[left] {E} -- (A) node[left] {A} -- (B) node[below] {B} -- (F) node[above] {F} -- (E) -- (H) node[above] {H} -- (G) node[right] {G} -- (C) node[below] {C} -- (B);
\draw (F) -- (G);
\draw[dashed] (A) -- (D) node[left] {D} -- (H);
\draw[dashed] (D) -- (C);
\node[above] at (I) {I};
\node[above left] at (J) {J};
\node[above left] at (K) {K};
%\tkzDrawLine[add=1.2 and 1.2,color=gray!20](I,J)
\draw[gray!20] (I) -- (J);
\draw[thick,red] (I) -- (J);
\tkzDefLine[parallel=through K](I,J) \tkzGetPoint{k'}
%\tkzDrawLine[add=1 and 1,color=gray!20](K,k')
\draw[gray!20] (K) -- (k');
\tkzInterLL(K,k')(B,C) \tkzGetPoint{P}
\tkzInterLL(K,k')(B,A) \tkzGetPoint{Q}
\draw[thick,red,dashed] (P) -- (Q);
\tkzInterLL(F,G)(I,J) \tkzGetPoint{M}
%\tkzDrawLine[color=gray!20](P,M)
\draw[gray!20] (P) -- (M);
\tkzInterLL(P,M)(C,G) \tkzGetPoint{N}
\draw[thick,red] (N) -- (P);
\draw[thick,red,dashed] (N) -- (I);
\tkzInterLL(E,F)(I,J) \tkzGetPoint{L}
%\tkzDrawLine[color=gray!20](Q,L)
\draw[gray!20] (Q) -- (L);
\tkzInterLL(A,E)(L,Q) \tkzGetPoint{S}
\draw[thick,red] (S) -- (Q);
\draw[thick,red,dashed] (S) -- (J);
\end{tikzpicture}
\end{center}
