Pary prostych i pary płaszczyzn

Project ID: 
5000000036
Accepted: 
Template: 
Question: 
Dany jest sześcian $ABCDEFGH$, gdzie punkty $K$ i $L$ to środki krawędzi $AE$ i $BF$. Określ wzajemne położenie prostych i płaszczyzn.
Answer Header 1: 
są równoległe
Answer Header 2: 
przecinają się
Answer Header 3: 
są skośne
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}