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{\LARGE \@title \par}%
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{\large
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\begin{tabular}[t]{c}% <------
\@author% <------ Authors
\end{tabular}\par}% <------
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{\large \@date}%
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\par
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%opening
\makeatletter
\newcommand{\stevilkadn}{7}
\newcommand{\snovdn}{Zrcaljenje in simetrija }
\newcommand{\cm}[1]{\SI{#1}{\centi\meter}}
\newcommand{\xslalph}[1]{\expandafter\@xslalph\csname c@#1\endcsname}
\newcommand{\@xslalph}[1]{%
\ifcase#1\or a\or b\or c\or \v{c}\or d\or e\or f\or g\or h\or i%
\or j\or k\or l\or m\or n\or o\or p\or r\or s\or \v{s}%
\or t\or u\or v\or z\or \v{z}
\else\@ctrerr\fi%
}
\AddEnumerateCounter{\xslalph}{\@xslalph}{m}
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\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma
\newcommand*\textfrac[2]{
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\renewcommand\abstractname{Povzetek}
\date{30. september 2020}
\renewcommand\contentsname{Kazalo vsebine}
\renewcommand\figurename{Slika}
\renewcommand\abstractname{Povzetek}
\newcommand{\iic}{I\textsuperscript{2}C }
% \patchcmd{\thebibliography}{\section*{\refname}}{}{}{}
\title{%
\snovdn --- \stevilkadn. domača naloga \\
\large Matematika, Gimnazija Bežigrad}
\author{\begin{tabular}{rl}
\textbf{Profesor:} & prof. Vilko Domajnko \\
\textbf{Avtor:} & Anton Luka Šijanec, 2. a
% \textbf{Avtor:} & Anton Luka Šijanec \\ & Member 2 \\ & Member 3
\end{tabular}}
% \everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260
\begin{document}
\maketitle
\begin{abstract}
Ta dokument obsega naloge, naročene dijakom 30. septembra 2020, in njihove
rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so
iz učnega lista profesorja Domajnka.
\end{abstract}
% \tableofcontents
\section{Učni list \textit{\snovdn} -- naloge}
\begin{enumerate}[label=\textbf{\arabic*.}] % 2, 6, 3, 1
\item \begin{enumerate}[label=\textbf{\xslalph*)}]
\item Nariši \color{magenta}enakokraki trikotnik \color{black} s podatki: $|AC|=|BC|=2|AB|=\SI{8}{\cm}$. Prezrcali ta lik čez:
\begin{enumerate}[label=\textbf{a\textsubscript{\arabic*)}}]
\item premico skozi točki $A$ in $B$,
\item premico skozi točki $A$ in $C$,
\item premico, ki gre skozi točko $C$ in razpolovišče daljice $AB$,
\item premico, ki gre skozi razpolovišči daljic $AC$ in $BC$,
\item \color{cyan} premico skozi točko $A$, ki je vzporedna premici skozi točki $B$ in $C$. \color{black}
\end{enumerate}
\item Naj bo $ABC$ trikotnik, za katerega velja: $a=\SI{5}{\cm}, b=\SI{6}{\cm}, c=\SI{7}{\cm}$.
\begin{enumerate}[label=\textbf{b\textsubscript{\arabic*)}}]
\item Načrtaj trikotnik $ABC$.
\item Načrtaj pravokotno projekcijo točke $C$ na daljico $AB$.
\item Trikotnik $ABC$ prezrcali čez nosilko stranice $BC$.
\item Naj bo $D$ razpolovišče daljice $AB$. Načrtaj točko $D$. Trikotnik $ABC$ prezrcali čez premico skozi $c$ in $D$.
\item Naj bo $E$ taka točka na daljici $AB$, da je $AB\bot CE$. Načrtaj točko $E$. Trikotnik $ABC$ rezrcali čez premico skozi $C$ in $E$.
\end{enumerate}
\end{enumerate}
\item \begin{enumerate}[label=\textbf{\xslalph*)}]
\setcounter{enumii}{2}
\item Nariši premici $p$ in $q$, ki se sekata pod kotom \ang{30}. Prezrcali $p$ čez $q$.
\item \color{magenta} Nariši premici $p$ in $q$, ki sta vzporedni in oddaljeni \SI{5}{\cm}. Prezrcali $p$ čez $q$.\color{black}
\end{enumerate}
\item Naj bo \color{magenta}$AB$ \color{black} daljica. Poišči vse simetrale daljice \color{magenta}$AB$\color{black}.
\setcounter{enumi}{5}
\item \begin{enumerate}[label=\textbf{\xslalph*)}]
\item Poišči vse simetrale krožnice s središčem v točki $S$ in s polmerom $r$. (\textbf{Krožnica} je množica točk, ki so vse enako oddaljene od središča.). Dokaži.
\item Naj bo $ABCD$ romb. (\textbf{Romb} je štirikotnik, ki ima vse stranice enako dolge.). Poišči vse simetrale romba $ABCD$. Dokaži. Ali je romb simetričen lik?
\item Naj bo $ABCD$ deltoid. (\textbf{Deltoid} je štirikotnik, ki ima po dve stranici enako dolgi.). Poišči vse simetrale deltoida $ABCD$. Dokaži.
\item Naj bo $ABCD$ kvadrat. (\textbf{Kvadrat} je štirikotnik, ki ima vse stranice enako dolge, poljuben par sosednjih stranic pa oklepa pravi kot). Poišči vse simetrale kvadrata $ABCD$. Dokaži.
\item Naj bo $ABCD$ pravokotnik, kjer je: $|AB|=2|BC|$. (\textbf{Pravokotnik} je štirikotnik, ki ima po dve nasprotni stranici enako dolgi, poljuben par sosednjih stranic pa oklepa pravi kot.). Poišči vse simetrale pravokotnika $ABCD$. Dokaži.
\end{enumerate}
\end{enumerate}
\section{Rešitve}
\subsection{Nalogi 2 in 3}
\begin{center}
\begin{tikzpicture} % naloga 2
\tkzDefPoint(-4,0){P}
\tkzDefPoint(4,0){R}
\tkzDefPoint(15:4){Q}
\tkzDefPoint(195:4){W}
\tkzDrawLine(P,R) \tkzLabelLine[pos=0.25, above](P,R){$p$}
\tkzDrawLine(Q,W) \tkzLabelLine[pos=0.75, below](Q,W){$q$}
\tkzDefPoint(-2.5,0){P2} % naredimo preslikavo za P
\tkzInterLC(Q,W)(P,P2) \tkzGetPoints{PP1}{PP2}
\tkzCompass(P,PP1) \tkzCompass(P,PP2)
\tkzInterCC(PP1,PP2)(PP2,PP1) \tkzGetPoints{PPZ1}{PPZ2}
\tkzCompass(PP1,PPZ1) \tkzCompass(PP2,PPZ1)
\tkzDrawLine(P,PPZ1)
\tkzInterLL(P,PPZ1)(Q,W) \tkzGetPoint{PS}
\tkzInterLC(P,PPZ1)(PS,P) \tkzGetPoints{PP}{PPX}
\tkzCompass(PS,PPX) \tkzLabelPoint(PPX){$P'$}
\tkzMarkRightAngle(P,PS,PP2)
\tkzDefPoint(2.5,0){R2} % pa še za R
\tkzInterLC(Q,W)(R,R2) \tkzGetPoints{RP1}{RP2}
\tkzCompass(R,RP1) \tkzCompass(R,RP2)
\tkzInterCC(RP1,RP2)(RP2,RP1) \tkzGetPoints{RPZ1}{RPZ2}
\tkzCompass(RP1,RPZ1) \tkzCompass(RP2,RPZ1)
\tkzDrawLine(R,RPZ1)
\tkzInterLL(R,RPZ1)(Q,W) \tkzGetPoint{RS}
\tkzInterLC(R,RPZ1)(RS,R) \tkzGetPoints{RP}{RPX}
\tkzCompass(RS,RPX) \tkzLabelPoint(RPX){$R'$}
\tkzDrawPoints(P,R,PPX,RPX)
\tkzDrawLine(PPX,RPX) \tkzLabelLine[pos=0.75, below](PPX,RPX){$p'$}
\tkzLabelPoints(P,R)
\tkzMarkRightAngle(R,RS,RP2)
% pa naredimo tukaj še b primer ... z magento
\tkzDefPoint(-4,5){BQ} \tkzDefPoint(4,5){BW}
\tkzDrawLine[color=magenta](BQ,BW)
\tkzLabelLine[below, color=magenta](BQ,BW){$q$}
\tkzDrawPoints[color=magenta](BQ,BW)
\tkzLabelPoint[color=magenta](BQ){$Q$}
\tkzLabelPoint[color=magenta](BW){$W$}
\tkzInterLC(P,R)(BQ,P2) \tkzGetPoints{BPQC1}{BPQC2} % naredimo preslik. za Q
\tkzCompass[color=magenta](BQ,BPQC1) \tkzCompass[color=magenta](BQ,BPQC2)
\tkzInterCC(BPQC1,BPQC2)(BPQC2,BPQC1) \tkzGetPoints{BPP1}{BPP2}
\tkzCompass[color=magenta](BPQC1,BPP2)
\tkzCompass[color=magenta](BPQC2,BPP2)
\tkzInterLC(BQ,BPP2)(P,BQ) \tkzGetPoints{BQP}{BQPX}
\tkzCompass[color=magenta](P,BQPX)
\tkzDrawPoints[color=magenta](BQPX)
\tkzLabelPoint[color=magenta](BQPX){$Q'=A$}
\tkzDrawLine[color=magenta](BQ,BQPX)
\tkzInterLC(P,R)(BW,R2) \tkzGetPoints{BPWC1}{BPWC2} % pa še za W
\tkzCompass[color=magenta](BW,BPWC1) \tkzCompass[color=magenta](BW,BPWC2)
\tkzInterCC(BPWC1,BPWC2)(BPWC2,BPWC1) \tkzGetPoints{BRP1}{BRP2}
\tkzCompass[color=magenta](BPWC1,BRP1)
\tkzCompass[color=magenta](BPWC2,BRP1)
\tkzInterLC(BW,BRP1)(R,BW) \tkzGetPoints{BWP}{BWPX}
\tkzCompass[color=magenta](R,BWPX)
\tkzDrawPoints[color=magenta](BWPX)
\tkzLabelPoint[color=magenta](BWPX){$W'=B$}
\tkzDrawLine[color=magenta](BW,BWPX)
\tkzDrawLine[color=magenta](BQPX,BWPX)
\tkzLabelLine[color=magenta, above, pos=0.40](BQPX,BWPX){$q'=AB$}
% pa naredimo tukaj še tretjo nalogo
\tkzDefMidPoint(BQPX,BWPX) \tkzGetPoint{3M}
\tkzCompass(BQPX,3M) \tkzCompass(BWPX,3M)
\tkzDefMidPoint(BQPX,3M) \tkzGetPoint{3QM}
\tkzDefMidPoint(BWPX,3M) \tkzGetPoint{3WM}
\tkzCompass(3M,3WM) \tkzCompass(3M,3QM)
\tkzInterCC(3WM,3QM)(3QM,3WM) \tkzGetPoints{3S1}{3S2}
\tkzCompass(3WM,3S1) \tkzCompass(3QM,3S1)
\tkzCompass(3WM,3S2) \tkzCompass(3QM,3S2)
\tkzDrawLine(3S1,3S2) \tkzLabelLine[pos=0.25, left](3S1,3S2){simetrala}
\end{tikzpicture}
\end{center}
\newpage
\subsection{Naloga 1}
\begin{center}
\begin{tikzpicture}
\tkzDefPoint(-2,0){A} \tkzDefPoint(2,0){B}
\tkzDefPoint(-10,0){CCIRCLEHELPERA} \tkzDefPoint(10,0){CCIRCLEHELPERB}
\tkzCompass(A,B)
\tkzDrawLine[color=magenta](A,B)\tkzLabelLine[above,color=magenta](A,B){$c$}
\tkzInterCC(B,CCIRCLEHELPERB)(A,CCIRCLEHELPERA) \tkzGetPoints{CX}{C}
\tkzCompass(A,C) \tkzCompass(B,C) \tkzCompass(A,CX) \tkzCompass(B,CX)
\tkzDrawLine[color=magenta](A,C)
\tkzLabelLine[color=magenta,below right,pos=0.75](A,C){$b$}
\tkzDrawLine[color=magenta](B,C)
\tkzLabelLine[color=magenta,below left, pos=0.75](B,C){$a$}
\tkzDrawPoints[color=magenta](A,B,C)
\tkzLabelPoint(CX){$C'$} % prezrcali lik čez AB
\tkzDrawLine(A,CX) \tkzLabelLine[above right](A,CX){$b'$}
\tkzDrawLine(B,CX) \tkzLabelLine[above left](B,CX){$a'$}
\tkzLabelLine[below](A,B){$c'$}
\tkzInterLC(A,C)(B,A) \tkzGetPoints{ABUTAG}{BCIRC} \tkzCompass(B,BCIRC) % AC
\tkzInterCC(BCIRC,B)(A,B) \tkzGetPoints{BBUTAGAIN}{BX}
\tkzCompass(BCIRC,BX) \tkzCompass(A,BX) \tkzLabelPoint(CX){$C'$}
\tkzDrawLine(A,BX) \tkzLabelLine[above](A,BX){$c'$}
\tkzDrawLine(C,BX) \tkzLabelLine[below right](C,BX){$a'$}
\tkzLabelLine[left, pos=0.75](A,C){$b'$}
\tkzLabelLine[right, pos=0.75](B,C){$a'$} \tkzLabelPoint[right](BX){$B'$}
\tkzLabelPoint[color=magenta, above right](A){$A=A'$} % skozi C|AB
\tkzLabelPoint[color=magenta, above left](B){$B=B'$}
\tkzLabelPoint[color=magenta](C){$C=C'$}
\tkzDefMidPoint(A,C) \tkzGetPoint{ACM} \tkzCompass(A,ACM) \tkzCompass(C,ACM)
\tkzDefMidPoint(B,C) \tkzGetPoint{BCM} \tkzCompass(B,BCM) \tkzCompass(C,BCM)
\tkzDrawLine(ACM,BCM) \tkzInterCC(ACM,C)(BCM,C) \tkzGetPoints{CBUTAGAI}{CX2}
\tkzCompass(ACM,CX2) \tkzCompass(BCM,CX2)
\tkzLabelPoint(CX2){$C'$}
\tkzInterLC(BCM,ACM)(BCM,ACM) \tkzGetPoints{BCMOUTER}{BCMBUTAGAIN}
\tkzInterLC(BCM,ACM)(ACM,BCM) \tkzGetPoints{ABCMBUTAGAIN}{ACMOUTER}
\tkzCompass(ACM,ACMOUTER) \tkzCompass(BCM,BCMOUTER)
\tkzInterCC(BCMOUTER,B)(BCM,B) \tkzGetPoints{BBUTAGAI2}{BX2}
\tkzCompass(BCM,BX2) \tkzCompass(BCMOUTER,BX2)
\tkzLabelPoint[below left](BX2){$B'$}
\tkzInterCC(ACMOUTER,A)(ACM,A) \tkzGetPoints{AX}{ABUTAGAI2}
\tkzCompass(ACM,AX) \tkzCompass(ACMOUTER,AX)
\tkzLabelPoint[below right](AX){$A'$}
\tkzDrawLine(AX,BX2) \tkzLabelLine[pos=0.25](AX,BX2){$c'$}
\tkzDrawLine(BX2,CX2) \tkzLabelLine[](BX2,CX2){$a'$}
\tkzDrawLine(CX2,AX) \tkzLabelLine[](CX2,AX){$b'$}
\tkzCompass(B,BCMOUTER) \tkzCompass(A,ACMOUTER)
\tkzInterLC(B,C)(A,B) \tkzGetPoints{ACIRC}{BAGAIN} \tkzCompass(A,ACIRC)%cyan
\tkzDefMidPoint(B,ACIRC) \tkzGetPoint{BACIRCMID}
\tkzCompass[color=cyan](B,BACIRCMID)\tkzCompass[color=cyan](ACIRC,BACIRCMID)
\tkzDrawLine[color=cyan, add = 0.1 and 1.1](BACIRCMID,A)
\tkzMarkRightAngle[color=cyan](A,BACIRCMID,B)
\tkzInterLC(A,BACIRCMID)(A,BACIRCMID) \tkzGetPoints{BACIRCMIDP}{BACIRCMIDA}
\tkzCompass[color=cyan](A,BACIRCMIDP)
\tkzInterCC(BACIRCMID,BACIRCMIDP)(BACIRCMIDP,BACIRCMID)
\tkzGetPoints{BACIRCMID2P1}{BACIRCMID2P2}
\tkzCompass[color=cyan](BACIRCMIDP,BACIRCMID2P2)
\tkzCompass[color=cyan](BACIRCMID,BACIRCMID2P2)
\tkzDrawLine[color=cyan](BACIRCMID2P2,A)
\tkzInterLC(A,BACIRCMID2P2)(B,A) \tkzGetPoints{BCCIRC}{BAGAIN}
\tkzCompass[color=cyan](B,BCCIRC)
\tkzInterCC(A,B)(BCCIRC,B) \tkzGetPoints{ANOTHERB}{BP}
\tkzCompass[color=cyan](BCCIRC,BP) \tkzCompass[color=cyan](A,BP)
\tkzMarkRightAngle[color=cyan](BACIRCMID,A,BACIRCMID2P2)
\tkzInterLC(BACIRCMID2P2,A)(C,BACIRCMID2P2) \tkzGetPoints{CAGAIN}{CCIRC}
\tkzCompass[color=cyan](C,CCIRC)
\tkzInterCC(CCIRC,C)(BACIRCMID2P2,C) \tkzGetPoints{CAGAIN}{CP}
\tkzCompass[color=cyan](BACIRCMID2P2,CP) \tkzCompass[color=cyan](CCIRC,CP)
\tkzDrawPoints[color=cyan](CP,BP)
\tkzLabelPoint[color=cyan, right](CP){$C'$}
\tkzLabelPoint[color=cyan, above left](BP){$B'$}
\tkzDrawLine[color=cyan](BP,CP) \tkzLabelLine[color=cyan,right](BP,CP){$a'$}
\tkzDrawLine[color=cyan](BP,A) \tkzLabelLine[color=cyan, above](BP,A){$c'$}
\tkzDrawLine[color=cyan](A,CP) \tkzLabelLine[color=cyan, above](A,CP){$b'$}
\tkzDrawPoints(CX,BX,ACM,BCM,CX2,BX2,AX)
\end{tikzpicture}
\end{center}
\section{Zaključek}
Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in
\hologo{LaTeX}
izvorna koda, zgodovina sprememb in prejšnje različice, je na voljo mojem šolskem Git repozitoriju na
\url{https://github.com/sijanec/sola-gimb-2} v mapi
\href{https://github.com/sijanec/sola-gimb-2/tree/master/mat/domace_naloge/\stevilkadn/}{/mat/domace\_naloge/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/mat/domace_naloge/\stevilkadn/dokument.pdf} in/ali \url{https://github.com/sijanec/sola-gimb-2/raw/master/mat/domace_naloge/\stevilkadn/dokument.pdf}.
\if\razhroscevanje1
\section{Razhroščevalne informacije}
Te informacije so generirane, ker je omogočeno razhroščevanje. Prej objavo dokumenta izklopite razhroščevanje. To naredite tako, da nastavite ukaz \texttt{razhroscevanje} na 0 v začetku dokumenta.
Grafi imajo natančnost \functionSamples\space točk na graf.
Konec generiranja dokumenta: \input|"date -Ins"
\fi
% \item $$$$
\end{document}
