Project ID:
5000000036
Accepted:
Template:
Question:
The picture shows a cube $ABCDEFGH$ with points $K$ and $L$ being the centers of edges $AE$ and $BF$. Determine the mutual positions of lines and planes.
Answer Header 1:
are parallel
Answer Header 2:
are intersecting
Answer Header 3:
are skew
Question Row 1:
\ifen lines $KH$ and $AB$\fi
\ifcs přímky $KH$ a $AB$\fi
\ifsk priamky $KH$ a $AB$\fi
\ifpl linie $KH$ i $AB$\fi
\ifes rectas $KH$ y $AB$ \fi
Answer Row 1:
3
Question Row 2:
\ifen planes $ABC$ and $HKL$\fi
\ifcs roviny $ABC$ a $HKL$\fi
\ifsk roviny $ABC$ a $HKL$\fi
\ifpl równia $ABC$ i $HKL$\fi
\ifes planos $ABC$ y $HKL$ \fi
Answer Row 2:
2
Question Row 3:
\ifen lines $LG$ and $BC$\fi
\ifcs přímky $LG$ a $BC$\fi
\ifsk priamky $LG$ a $BC$\fi
\ifpl linie $LG$ i $BC$\fi
\ifes rectas $LG$ y $BC$ \fi
Answer Row 3:
2
Question Row 4:
\ifen planes $KAC$ and $HFL$\fi
\ifcs roviny $KAC$ a $HFL$\fi
\ifsk roviny $KAC$ a $HFL$\fi
\ifpl równia $KAC$ i $HFL$\fi
\ifes planos $KAC$ y $HFL$ \fi
Answer Row 4:
2
Question Row 5:
\ifen lines $KL$ and $DC$\fi
\ifcs přímky $KL$ a $DC$\fi
\ifsk priamky $KL$ a $DC$\fi
\ifpl linie $KL$ i $DC$\fi
\ifes rectas $KL$ y $DC$ \fi
Answer Row 5:
1
Question Row 6:
\ifen planes $KAD$ and $FLG$\fi
\ifcs roviny $KAD$ a $FLG$\fi
\ifsk roviny $KAD$ a $FLG$\fi
\ifpl równia $KAD$ i $FLG$\fi
\ifes planos $KAD$ y $FLG$ \fi
Answer Row 6:
1
Question Row 7:
\ifen lines $KL$ and $HB$\fi
\ifcs přímky $KL$ a $HB$\fi
\ifsk priamky $KL$ a $HB$\fi
\ifpl linie $KL$ i $HB$\fi
\ifes rectas $KL$ y $HB$\fi
Answer Row 7:
3
Tex:
% tiket 32493
\let\oldQuestion\Question
\def\I{\mathrm{i}}
\def\Question{
\begin{minipage}[t]{0.6\linewidth}
\leavevmode
\oldQuestion
\end{minipage}
\hfill
\begin{minipage}[t]{0.35\linewidth}
\leavevmode
\kern -30pt
\def\delka{1.5cm}
\obrMsr[x=\delka,y=\delka]{-1}2{-1}2
{
\pgfmathsetmacro{\cubex}{1}
\pgfmathsetmacro{\cubey}{1}
\pgfmathsetmacro{\cubez}{1}
\coordinate (A) at (0,0,0);
\coordinate (B) at (\cubex,0,0);
\coordinate (C) at (\cubex.2,0,-\cubez);
\coordinate (D) at (0.2,0,-\cubez);
\coordinate (E) at (0,\cubey,0);
\coordinate (F) at (\cubex,\cubey,0);
\coordinate (G) at (\cubex.2,\cubey,-\cubez);
\coordinate (H) at (0.2,\cubey,-\cubez);
\coordinate (K) at ($(A)!0.5!(E)$);
\coordinate (L) at ($(B)!0.5!(F)$);
\draw[thick,dashed] (A) -- (D) node [yshift=-6pt,xshift=3pt]{$D$} -- (C) node [yshift=-5pt,xshift=5pt]{$C$};
\draw[thick,dashed] (D) -- (H);
\draw (K) node [left,xshift=-2pt]{$K$};
\draw[thick] (-0.05,1/2*\cubey,0) -- (0.05,1/2*\cubey,0);
\draw[thick] (\cubex-0.05,1/2*\cubey,0) -- (\cubex+0.05,1/2*\cubey,0);
\draw (L) node [left,xshift=-2pt]{$L$};
\draw[thick] (A) node [yshift=-5pt,xshift=-5pt]{$A$} -- (B) node [yshift=-6pt,xshift=3pt]{$B$} -- (F) node [yshift=6pt,xshift=-3pt]{$F$}-- (E) node [yshift=6pt,xshift=-3pt]{$E$} -- cycle;
\draw[thick] (B) -- (C) -- (G) -- (F);
\draw[thick] (G) node [yshift=6pt,xshift=3pt]{$G$} -- (H) node [yshift=6pt,xshift=-3pt]{$H$} -- (E);
}
\end{minipage}}
\pocetsloupcu{3}