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+% !TeX encoding = UTF-8
+% !TeX spellcheck = sl_SI
+\documentclass[]{article}
+\usepackage[utf8]{inputenc}
+\usepackage{etoolbox}
+\usepackage[hidelinks]{hyperref}
+\usepackage[a4paper, total={7in, 10in}]{geometry}
+\usepackage{graphicx}
+\usepackage{hologo}
+\usepackage{amssymb}
+\usepackage{pgfplots}
+\usepackage[inline]{enumitem}
+\usepackage{amsmath}
+\usepackage{siunitx}
+\usepackage{multicol}
+\usepackage{tabularcalc}
+\usepackage{amsmath}
+\usepackage{float}
+\usepackage{tasks}
+\usepackage{filecontents}
+\usepackage{textcomp}
+\usepackage{tkz-euclide}
+\usepackage{listings}
+% \usepackage{multienum} % weird with labels
+\usetikzlibrary{calc} %% not really needed............. idk.
+%\usetikzlibrary{external}
+% \usetkzobj{all} % tkz-euclide > 3.02 tega ne potrebuje več (:
+%\tikzexternalize
+\usepackage{xcolor}
+\sisetup{output-decimal-marker = {,}, quotient-mode=fraction,per-mode=fraction} % per-mode=symbol
+\newcommand\ddfrac[2]{\frac{\displaystyle #1}{\displaystyle #2}}
+\newcommand{\functionSamples}{100} % fix to fancier value upon release, keep low during development
+\newcommand{\razhroscevanje}{1}
+\definecolor{codegreen}{rgb}{0,0.6,0}
+\definecolor{codegray}{rgb}{0.5,0.5,0.5}
+\definecolor{codepurple}{rgb}{0.58,0,0.82}
+\definecolor{backcolour}{rgb}{0.95,0.95,0.92}
+
+\lstdefinestyle{mystyle}{
+ backgroundcolor=\color{backcolour},
+ commentstyle=\color{codegreen},
+ keywordstyle=\color{magenta},
+ numberstyle=\tiny\color{codegray},
+ stringstyle=\color{codepurple},
+ basicstyle=\ttfamily\footnotesize,
+ breakatwhitespace=false,
+ breaklines=true,
+ captionpos=b,
+ keepspaces=true,
+ numbers=left,
+ numbersep=5pt,
+ showspaces=false,
+ showstringspaces=false,
+ showtabs=false,
+ tabsize=2
+}
+
+\lstset{style=mystyle}
+\def\@maketitle{%
+ \newpage
+ \null
+ \vskip 2em%
+ \begin{center}%
+ \let \footnote \thanks
+ {\LARGE \@title \par}%
+ \vskip 1.5em%
+ {\large
+ \lineskip .5em%
+ \begin{tabular}[t]{c}% <------
+ \@author% <------ Authors
+ \end{tabular}\par}% <------
+ \vskip 1em%
+ {\large \@date}%
+ \end{center}%
+ \par
+ \vskip 1.5em}
+%opening
+\makeatletter
+\newcommand{\stevilkadn}{8}
+\newcommand{\snovdn}{Toge preslikave }
+\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}
+\makeatother
+\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma
+\newcommand*\textfrac[2]{
+ \frac{\text{#1}}{\text{#2}}
+}
+\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 5. oktobra 2020, in njihove
+ rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so
+ iz učbenika (stran 26) in vaj (stran 21). Kjer je bilo potrebno izbrati neke poljubne primere, sem jih vedno izbral naključno.
+\end{abstract}
+% \tableofcontents
+
+\section{Učbenik \textit{Matematika 2} --- stran 26}
+\begin{enumerate}[label=\textbf{\arabic*.}]
+ \item Prezrcali enakostranični trikotnik $ABC$, ki ima stranico dolgo \cm{1}, \textsuperscript{(kako lahko narišem razviden \cm{1} enakostranični trikotnik?!)}
+ \begin{enumerate}[label=\textbf{\xslalph*)}] % c, b
+ \begin{multicols}{2}
+ \setcounter{enumii}{1}
+ \item \color{cyan} čez nosilko stranice $BC$, \color{black}
+ \item \color{magenta} čez nosilko višine na osnovnico. \color{black}
+ \end{multicols}
+ \end{enumerate}
+ \begin{center}
+ \begin{tikzpicture}
+ \tkzDefPoint(0,0){A}
+ \tkzDefPoint(60:1){C}
+ \tkzDefPoint(1,0){B}
+ \tkzDrawLine(A,C) \tkzLabelLine[](A,C)
+ {$b=\color{magenta}a'\color{black}$}
+ \tkzDrawLine(C,B) \tkzLabelLine[pos = 0.25](C,B)
+ {$a=\color{magenta}b'\color{black}$}
+ \tkzDrawLine(B,A) \tkzLabelLine[below](B,A)
+ {$c=\color{magenta}c'\color{black}$}
+ \tkzDefMidPoint(C,B) \tkzGetPoint{CB}
+ \tkzCompass[color=cyan](C,CB) \tkzCompass[color=cyan](B,CB)
+ \tkzInterLC(A,CB)(CB,A) \tkzGetPoints{AAGAIN}{AX}
+ \tkzDrawLine[color=cyan](A,AX)
+ \tkzDrawPoint[color=cyan](AX)
+ \tkzLabelPoint[color=cyan](AX){$A'$}
+ \tkzDrawLine[color=cyan, add = 0 and 0](C,AX)
+ \tkzLabelLine[color=cyan](C,AX){$b'$}
+ \tkzDrawLine[color=cyan, add = 0 and 0](B,AX)
+ \tkzLabelLine[color=cyan](B,AX){$c'$}
+ \tkzDrawLine[color=cyan, add = 0 and 0](B,C)
+ \tkzLabelLine[color=cyan, pos = 0.75](C,B){$a'$}
+ \tkzDefMidPoint(A,B) \tkzGetPoint{AB}
+ \tkzCompass[color=magenta](A,AB) \tkzCompass[color=magenta](B,AB)
+ \tkzDrawLine[color=magenta](C,AB)
+ \tkzLabelPoint[below left](A){$A=\color{magenta}B'\color{black}$}
+ \tkzLabelPoint[](B)
+ {$B=\color{cyan}B'\color{black}=\color{magenta}A'\color{black}$}
+ \tkzLabelPoint[above](C)
+ {$C=\color{cyan}C'\color{black}=\color{magenta}C'\color{black}$}
+ \tkzDrawPoints(A,B,C)
+ \end{tikzpicture}
+ \end{center}
+ \item Načrtaj krožnico s središčem $S$ in polmerom \cm{3} ter premico $p$, ki je od točke $S$ oddaljena \cm{2}, ter prezrcali krožnico čez premico.
+ \begin{center}
+ \begin{tikzpicture}
+ \tkzDefPoint(0,0){S}
+ \tkzDefPoint(4,0){K}
+ \tkzCompass(S,K)
+ \tkzDefPoint(3,0){R}
+ \tkzDrawCircle(S,R)
+ \tkzDrawLine(S,K)
+ \tkzInterCC(S,K)(K,S) \tkzGetPoints{SK}{KS}
+ \tkzCompass(K,SK) \tkzCompass(K,KS) \tkzCompass(S,SK) \tkzCompass(S,KS)
+ \tkzDrawLine(SK,KS) \tkzLabelLine[left](SK,KS){$p$}
+ \tkzInterLL(SK,KS)(S,K) \tkzGetPoint{P}
+ \tkzMarkRightAngles(S,P,SK)
+ \tkzInterLC(S,K)(P,K) \tkzGetPoints{SAGAIN}{SX} \tkzCompass(P,SX)
+ \tkzInterLC(S,R)(P,R) \tkzGetPoints{RX}{RAGAIN} \tkzCompass(P,RX)
+ \tkzLabelPoint(SX){$S'$}
+ \tkzLabelPoint(RX){$R'$}
+ \tkzDrawCircle(SX,RX)
+ \tkzDrawPoints(S,R)
+ \tkzLabelPoints(S,R)
+ \end{tikzpicture}
+ \end{center}
+ \item Premici $p$ in $q$ se sekata v točki $T$. Prezrcali premico $p$ čez premico $q$, če premici oklepata kot:
+ \begin{enumerate}[label=\textbf{\xslalph*)}] % b, č
+ \begin{multicols}{2}
+ \setcounter{enumii}{1}
+ \item \color{cyan}\ang{60}\color{black}
+ \setcounter{enumii}{3}
+ \item \color{magenta}\ang{75}\color{black}
+ \end{multicols}
+ \end{enumerate}
+ \begin{center}
+ \begin{tikzpicture}
+ \tkzDefPoint(-4,0){P}
+ \tkzDefPoint(4,0){R}
+ \tkzDefPoint(30:4){Q}
+ \tkzDefPoint(210:4){W}
+ \tkzDefPoint(60:4){Q1}
+ \tkzDefPoint(240:4){W1}
+ \tkzDefMidPoint(P,R) \tkzGetPoint{T}
+ \tkzDrawLine(P,R) \tkzLabelLine[above, pos = 0.25](P,R){$p$}
+ \tkzDrawLine[color=cyan](Q,W) \tkzLabelLine[above, pos = 0.25, color=cyan](Q,W){$q$} % cayn
+ \tkzCompass[color=cyan](T,W) \tkzInterCC(T,W)(W,P) \tkzGetPoints{PX}{PAGAIN}
+ \tkzCompass[color=cyan](W,PX) \tkzCompass[color=cyan](T,PX) \tkzLabelPoint[color=cyan](PX){$P'$}
+ \tkzCompass[color=cyan](T,Q) \tkzInterCC(T,Q)(Q,R) \tkzGetPoints{RX}{RAGAIN}
+ \tkzCompass[color=cyan](Q,RX) \tkzCompass[color=cyan](T,RX) \tkzLabelPoint[color=cyan](RX){$R'$}
+ \tkzDrawLine[color=cyan](RX,PX)
+ \tkzDrawLine[color=magenta](Q1,W1) \tkzLabelLine[color=magenta, above, pos = 0.25](Q1,W1){$q$} % magen
+ \tkzCompass[color=magenta](T,W1) \tkzInterCC(T,W1)(W1,P) \tkzGetPoints{PX1}{PAGAIN1}
+ \tkzCompass[color=magenta](W1,PX1) \tkzCompass[color=magenta](T,PX1) \tkzLabelPoint[color=magenta](PX1){$P'$}
+ \tkzCompass[color=magenta](T,Q1) \tkzInterCC(T,Q1)(Q1,R) \tkzGetPoints{RX1}{RAGAIN1}
+ \tkzCompass[color=magenta](Q1,RX1) \tkzCompass[color=magenta](T,RX1) \tkzLabelPoint[color=magenta](RX1){$R'$}
+ \tkzDrawLine[color=magenta](RX1,PX1)
+ \tkzDrawPoints(P,R,T)
+ \tkzLabelPoints(P,R,T)
+ \end{tikzpicture}
+ \end{center}
+ \item Zavrti enakostranični trikotnik $ABC$ okrog oglišča $C$ za kot:
+ \begin{enumerate}[label=\textbf{\xslalph*)}] % č, b
+ \begin{multicols}{2}
+ \setcounter{enumii}{1}
+ \item \color{cyan} \ang{60} \color{black}
+ \setcounter{enumii}{3}
+ \item \color{magenta} \ang{120} \color{black}
+ \end{multicols}
+ \begin{center}
+ \begin{tikzpicture}
+ \tkzDefPoint(0,0){A}
+ \tkzDefPoint(4,0){B}
+ \tkzDefPoint(60:4){C}
+ \tkzDrawLine(A,B) \tkzLabelLine[above](A,B){$c$}
+ \tkzDrawLine(A,C) \tkzLabelLine[below](A,C){$b$}
+ \tkzDrawLine(C,B) \tkzLabelLine[below](C,B){$a=\color{cyan}b'$}
+ \tkzInterCC(C,B)(B,C) \tkzGetPoints{CBU}{CBUNAPAK}
+ \tkzCompass[color=cyan](C,CBU) \tkzCompass[color=cyan](B,CBU)
+ \tkzDrawLine[color=cyan](C,B)
+ \tkzDrawLine[color=cyan](C,CBU)
+ \tkzLabelLine[above](C,CBU)
+ {$\color{cyan}a'\color{black}=\color{magenta}b'$}
+ \tkzDrawLine[color=cyan](B,CBU)
+ \tkzLabelLine[color=cyan, above](B,CBU){$c'$}
+ \tkzDrawLine[color=magenta](C,CBU)
+ \tkzInterLC(A,C)(C,A) \tkzGetPoints{AAGAIn}{AX}
+ \tkzDrawLine[color=magenta](C,AX) \tkzCompass[color=magenta](C,AX)
+ \tkzLabelLine[above, color=magenta](C,AX){$a'$}
+ \tkzDrawLine[color=magenta](AX,CBU)
+ \tkzLabelLine[color=magenta, above](AX,CBU){$c'$}
+ \tkzLabelPoint[color=magenta](AX){$A'$}
+ \tkzLabelPoint(CBU){$\color{cyan}B'\color{black}=\color{magenta}A'$}
+ \tkzLabelPoint(B){$B=\color{cyan}A'$}
+ \tkzLabelPoint(C){$C=\color{cyan}C'\color{black}=\color{magenta}C'$}
+ \tkzDrawPoints(A,B,C) \tkzLabelPoints(A)
+ \end{tikzpicture}
+ \end{center}
+ \end{enumerate}
+ \item Zavrti okrog središča:
+ \begin{enumerate}[label=\textbf{\xslalph*)}] % c, a
+ \begin{multicols}{2}
+ \item kvadrat za \ang{90}
+ \begin{center}
+ \begin{tikzpicture}
+ \tkzDefPoint(0,1){D} \tkzDefPoint(1,1){C}
+ \tkzDefPoint(0,0){A} \tkzDefPoint(1,0){B}
+ \tkzDrawLine(A,B) \tkzDrawLine(B,C)
+ \tkzDrawLine(C,D) \tkzDrawLine(D,A)
+ \tkzDrawPoints(A,B,C,D)
+ \tkzLabelPoint[below left](A){$A=D'$}
+ \tkzLabelPoint[](B){$B=A'$}
+ \tkzLabelPoint[above right](C){$C=B'$}
+ \tkzLabelPoint[above left](D){$D=C'$}
+ \end{tikzpicture}
+ \end{center}
+ \setcounter{enumii}{2}
+ \item krožnico za \ang{90}
+ \begin{center}
+ \begin{tikzpicture}
+ \tkzDefPoint(0,0){S}
+ \tkzDefPoint(1,0){K}
+ \tkzDrawCircle(S,K)
+ \tkzDrawPoints(S)
+ \tkzLabelPoints(S)
+ \end{tikzpicture}
+ \end{center}
+ \end{multicols}
+ \end{enumerate}
+ \item Prezrcali
+ \begin{enumerate}[label=\textbf{\xslalph*)}] % c, b
+ \setcounter{enumii}{1}
+ \item pravilni šestkotnik $ABCDEF$ čez eno izmed oglišč,
+ \item krožnico čez eno izmed točk na njej.
+ \begin{multicols}{2}
+ \begin{center}
+ \begin{tikzpicture}
+ \tkzDefPoint(0,0){O}
+ % šestkotnik 360/6=60
+ \foreach[count=\i] \ANG in {60,60*2,60*3,60*4,60*5,60*6} {
+ \tkzDefPoint({2*cos(\ANG*pi/180)},{2*sin(\ANG*pi/180)}){P\i}
+ }
+ \foreach[count=\i] \ANG in {60,60*2,60*3,60*4,60*5,60*6} {
+ \tkzDefPoint({2*cos(\ANG*pi/180)+4},{2*sin(\ANG*pi/180)}){R\i}
+ }
+ \tkzDrawPolygon[](P1,P2,P3,P4,P5,P6)
+ \tkzDrawPoints(P1,P2,P3,P4,P5,P6)
+ \tkzDrawPolygon[color=magenta](R1,R2,R3,R4,R5,R6)
+ \tkzDrawPoints[color=magenta](R1,R2,R3,R4,R5,R6)
+ \tkzDrawLine[color=cyan](P2,R5) \tkzDrawLine[color=cyan](P4,R1)
+ \tkzDrawLine[add=0.1 and 0.1, color=cyan](P3,R6)
+ \tkzCompass[color=cyan](P6,R5) \tkzCompass[color=cyan](P6,R6)
+ \tkzCompass[color=cyan](P6,R1) \tkzCompass[color=cyan](P6,R2)
+ \tkzCompass[color=cyan](P6,R4)
+ \end{tikzpicture}
+ \end{center}
+ \begin{center}
+ \begin{tikzpicture}
+ \tkzDefPoint(0,0){S}
+ \tkzDefPoint(1.5,0){K}
+ \tkzDefPoint(3,0){SX}
+ \tkzDrawCircle(S,K)
+ \tkzDrawCircle[color=magenta](SX,K)
+ \tkzDrawLine[color=cyan](S,SX)
+ \tkzCompass[color=cyan](K,SX)
+ \tkzLabelPoint[color=magenta](SX){$S'$}
+ \tkzDrawPoints(S) \tkzLabelPoints(S)
+ \tkzDrawPoints[color=magenta](K)
+ \end{tikzpicture}
+ \end{center}
+ \end{multicols}
+ \end{enumerate}
+\end{enumerate}
+\section{Zbirka nalog \textit{Matematika 2} --- stran 21}
+\begin{enumerate}[label=\textbf{\arabic*.}] % 113, 108, 112, 105
+ \setcounter{enumi}{104}
+ \item Slike preriši na karirast papir v zvezek. Nariši zrcalne slike likov glede na narisano premico.
+ \setcounter{enumi}{107}
+ \item V pravokotnem sistemu nariši daljivo s krajiščema $A(3,-2)$ in $B(6,1)$. Nariši daljice:
+ \begin{itemize}
+ \item $A_1B_1$, ki je zrcalna slika daljice $AB$ glede na os $x$,
+ \item $A_2B_2$, ki je zrcalna slika daljice $AB$ glede na os $y$,
+ \item $A_3B_3$, ki je zrcalna slika daljice $AB$ glede na simetralo lihih kvadrantov,
+ \item $A_4B_4$, ki je zrcalna slika daljice $AB$ glede na simetralo sodih kvadrantov,
+ \end{itemize}
+ in zapiši koordinate krajišč teh daljic.
+ \setcounter{enumi}{111}
+ \item Nariši:
+ \begin{enumerate}[label=\textbf{\xslalph*)}]
+ \item trikotnik s podatki $a=\cm{5}$, $b=\cm{4}$ in $c=\cm{4}$ ter ga prezrcali čez stranico $c$,
+ \item enakostranični trikotnik $ABC$ s \cm{3} dolgo stranico ter ga prezrcali čez stranico $AC$,
+ \item kvadrat $ABCD$ s stranico, dolgo \cm{2}, in ga prezrcali čez stranico $AD$,
+ \item pravokotnik $ABCD$ s stranicama, dolgima $a=\cm{4}$ in $b=\cm{2}$, in ga prezrcali čez diagonalo $AC$.
+ \end{enumerate}
+ \item Slike preriši na karirast papir. Nariši vse simetrale.
+\end{enumerate}
+
+\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}