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Diffstat (limited to 'mat/domace_naloge/14/dokument.tex')
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1 files changed, 156 insertions, 29 deletions
diff --git a/mat/domace_naloge/14/dokument.tex b/mat/domace_naloge/14/dokument.tex index 0b3d4af..42d9cdc 100644 --- a/mat/domace_naloge/14/dokument.tex +++ b/mat/domace_naloge/14/dokument.tex @@ -80,7 +80,7 @@ \par \vskip 1.5em} %opening -\newcommand{\snovdn}{Trikotnik --- konstrukcije } +\newcommand{\snovdn}{Obodni in središčni kot } \newcommand{\predmdn}{mat} \newcommand{\stevilkadn}{14} \newcommand{\cm}[1]{\SI{#1}{\centi\meter}} @@ -100,7 +100,7 @@ \frac{\text{#1}}{\text{#2}} } \renewcommand\abstractname{Povzetek} -\date{22. oktober 2020} +\date{26. oktober 2020} \renewcommand\contentsname{Kazalo vsebine} \renewcommand\figurename{Slika} \renewcommand\abstractname{Povzetek} @@ -121,42 +121,169 @@ \maketitle \begin{abstract} -Ta dokument obsega naloge, naročene dijakom 22. oktobra 2020, in njihove rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so iz učnega lista profesorja Domajnka in vaj. +Ta dokument obsega naloge, naročene dijakom 23. oktobra 2020, in njihove rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so iz učnega lista profesorja Domajnka in vaj. Kjer je bilo potrebno izbrati neke poljubne naloge, sem jih vedno izbral naključno. \end{abstract} \tableofcontents \section{Vaje \textit{Matematika 2}: stran 29 --- Trikotnik} \begin{enumerate}[label=\textbf{\arabic*.}] - \setcounter{enumi}{164} - \item[\textbf{165.*}] Načrtaj trikotnik $ABC$ z dano vsoto dolžin stranic. Napiši postopek načrtovanja. - - % Nihče ni rekel, v katerem jeziku, zato bom postopek opisal kar v \hologo{LaTeX} jeziku \texttt{PGF/Ti\textit{k}Z}. Kako prikladno, ne? - \begin{enumerate}[label=\textbf{\xslalph*)}] % b č a d - \item $a+c=\cm{10}, \alpha=\ang{30}, b=\cm{4}$ - \input{165a} - \lstinputlisting[language=TeX]{165a.tex} - \item $a+c=\cm{10}, \gamma=\ang{30}, b=\cm{4}$ - \input{165b} - \lstinputlisting[language=TeX]{165b.tex} - \setcounter{enumii}{3} - \item $b+c=\cm{7}, v_b=\cm{3}, a=\cm{4}$ - % \input{165cstresica} % ne, to nalogo sem si kar v možganih izmislil... - % \lstinputlisting[language=TeX]{165cstresica.tex} - \item $a+b+c=\cm{12}, \alpha=\ang{30}, \beta=\ang{75}$ - % Nisem povsem prepričan, če smem uporabljati \textit{matematiko} \textsuperscript{(kaj sploh je to?)}, ampak nekako \textit{očitno} je, da so stranice trikotnika v razmerju $75:75:30$, torej je najkrajša dolga $\frac{1}{6}\cm{12}$. - %\begin{center} - % \begin{tikzpicture} - % \tkzDefPoint(0,0){A} \tkzDefPoint(3,0){12} - % \tkz - % \tkzDrawPoints() - % \end{tikzpicture} - %\end{center} - \end{enumerate} + \setcounter{enumi}{165} \item[\textbf{166.*}] Načrtaj trikotnik $ABC$ z dano razliko dolžin stranic. Napiši postopek načrtovanja. \begin{enumerate}[label=\textbf{\xslalph*)}] % c b \setcounter{enumii}{1} \item $a-c=\cm{2}, \gamma=\ang{30}, v_a=\cm{4}$ - \item $b-c=\cm{1}, \gamma=\ang{60}, a=\cm{3}$ + \input{166b.tex} + \lstinputlisting[language=TeX]{166b.tex} + \item $b-c=\cm{1}, \gamma=\ang{60}, a=\cm{3}$ + \input{166c.tex} + \lstinputlisting[language=TeX]{166c.tex} + \end{enumerate} +\end{enumerate} +\section{Učni list \textit{\snovdn}} +\begin{enumerate}[label=\textbf{\arabic*.}] + \item Načrtaj trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % b + \begin{enumerate}[label=\textbf{\alph*)}] + \setcounter{enumii}{1} + \item $b=6, \alpha=\ang{30}, \beta=\ang{15}$ + \begin{figure}[!h] + \makebox[\textwidth][c]{ + \begin{tikzpicture} + \tkzDefPoint(0,0){A} \tkzDefPoint(6,0){K0} + \tkzInterCC(A,K0)(K0,C) \tkzGetPoints{K60}{K60X} + \tkzDefMidPoint(K60,K0) \tkzGetPoint{K30} + \tkzInterLC(K30,A)(A,K0) \tkzGetPoints{C}{CX} + \tkzInterLC(C,A)(C,A) \tkzGetPoints{AX}{AAGAIN} + \tkzDrawLine(A,AX) \tkzLabelLine[above left](A,C){$b$} + \tkzCompass(C,AX) \tkzCompass(A,K0) \tkzCompass(A,C) + \tkzInterCC(C,AX)(AX,C) \tkzGetPoints{G60X}{G60} + \tkzCompass(C,G60) \tkzCompass(AX,G60) + \tkzDefMidPoint(AX,G60) \tkzGetPoint{G30} + \tkzCompass(AX,G30) \tkzCompass(G60,G30) + \tkzInterLC(C,G30)(C,AX) \tkzGetPoints{XX}{X} + \tkzCompass(C,X) \tkzDrawLine(C,G30) + \tkzDefMidPoint(X,G60) \tkzGetPoint{G45} + \tkzCompass(X,G45) \tkzCompass(G60,G45) + \tkzInterLL(C,G45)(A,K0) \tkzGetPoint{B} + \tkzDrawLine(A,B) \tkzLabelLine[below](A,B){$c$} + \tkzDrawLine(C,B) \tkzLabelLine[above right](C,B){$a$} + \tkzDrawPolygon[fill=blue!30, opacity=.30](A,B,C) + \tkzDrawPoints(A) \tkzLabelPoints(A,C,B) + \end{tikzpicture} + } + \end{figure} + \end{enumerate} + \item Načrtaj trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % a + \begin{enumerate}[label=\textbf{\alph*)}] + \item $a=6, b=5, c=10$ + \begin{center} + \begin{tikzpicture} + \tkzDefPoint(0,0){A} \tkzDefPoint(10,0){B} + \tkzDefPoint(5,0){bH} \tkzDefPoint(4,0){aH} + \tkzDrawLine(A,B) \tkzLabelLine[below](A,B){$c$} \tkzCompass(A,B) + \tkzInterCC(A,bH)(B,aH) \tkzGetPoints{C}{CX} + \tkzCompass(A,C) \tkzCompass(B,C) + \tkzDrawLine(A,C) \tkzLabelLine[above left](A,C){$b$} + \tkzDrawLine(B,C) \tkzLabelLine[above right](B,C){$a$} + \tkzDrawPolygon[fill=blue!30, opacity=.30](A,B,C) + \tkzDrawPoints(A) \tkzLabelPoints(A,B,C) + \end{tikzpicture} + \end{center} + \end{enumerate} + \if\false1 + \item[\textbf{*3.}] Načrtaj trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % ~c~=>b + \setcounter{enumi}{3} + \begin{enumerate}[label=\textbf{\alph*)}] + \setcounter{enumii}{1} + \item $c=8, a-b=2, \beta=\ang{60}$ + \begin{center} + \begin{tikzpicture} + \tkzDefPoint(0,0){A} \tkzDefPoint(8,0){B} + \tkzCompass(A,B) \tkzDrawLine(A,B) \tkzLabelLine[above](A,B){$c$} + \tkzInterCC(A,B)(B,A) \tkzGetPoints{aH}{aHX} \tkzDrawLine(B,aH) + \tkzCompass(A,aH) \tkzCompass(B,aH) + + \tkzDrawPoints(A) \tkzLabelPoints(A,B) + \end{tikzpicture} + \end{center} + \end{enumerate} + \fi + \item Načrtaj enakokraki trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % 2 + \begin{enumerate}[label=\textbf{\alph*)}] + \setcounter{enumii}{1} + \item $c=7, \gamma=\ang{30}$ + \begin{center} + \begin{tikzpicture} + \tkzDefPoint(0,0){A} \tkzDefPoint(7,0){B} + \tkzDefMidPoint(A,B)\tkzGetPoint{M}\tkzCompass(A,M) \tkzCompass(B,M) + \tkzInterLC(A,B)(B,M) \tkzGetPoints{AAGAIN}{AX} \tkzCompass(B,AX) + \tkzInterLC(A,B)(A,M) \tkzGetPoints{BX}{BAGAIN} \tkzCompass(A,BX) + \tkzCompass(A,B) \tkzDrawLine[add=0 and 0](BX,AX) \tkzLabelLine[above](A,B){$c$} + \tkzInterCC(A,BX)(BX,A) \tkzGetPoints{A60X}{A60} + \tkzCompass(A,A60) \tkzCompass(BX,A60) + \tkzInterCC(B,AX)(AX,B) \tkzGetPoints{B60}{B60X} + \tkzCompass(B,B60) \tkzCompass(AX,B60) + \tkzInterCC(A60,A)(A,A60) \tkzGetPoints{A120}{BXAGAIN} + \tkzCompass(A,A120) \tkzCompass(A60,A120) + \tkzInterCC(B60,B)(B,B60) \tkzGetPoints{AXAGAIN}{B120} + \tkzCompass(B,B120) \tkzCompass(B60,B120) + \tkzDefMidPoint(A60,A120) \tkzGetPoint{A90} + \tkzInterLC(A,A90)(A,A120) \tkzGetPoints{A90CX}{A90C} + \tkzCompass(A,A90C) \tkzDrawLine(A,A90C) + \tkzDefMidPoint(B60,B120) \tkzGetPoint{B90} + \tkzInterLC(B,B90)(B,B120) \tkzGetPoints{B90CX}{B90C} + \tkzCompass(B,B90C) \tkzDrawLine(B,B90C) + \tkzDefMidPoint(A120,A90C) \tkzGetPoint{A75} + \tkzCompass(A120,A75) \tkzCompass(A90C,A75) + \tkzDefMidPoint(B120,B90C) \tkzGetPoint{B75} + \tkzCompass(B120,B75) \tkzCompass(B90C,B75) + \tkzInterLL(A,A75)(B,B75) \tkzGetPoint{C} + \tkzDrawLine(A,C) \tkzLabelLine[above left](A,C){$b$} + \tkzDrawLine(B,C) \tkzLabelLine[above right](B,C){$a$} + \tkzDrawPolygon[fill=blue!30, opacity=.30](A,B,C) + \tkzDrawPoints(A) \tkzLabelPoints(A,B,C) + \end{tikzpicture} + \end{center} + \end{enumerate} + \if\false1 + \item Načrtaj pravokotni trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % a + \begin{enumerate}[label=\textbf{\alph*}] + \item[\textbf{*b)}] $a+c=12, \alpha=\ang{60}$ + \end{enumerate} + \fi + \item[\textbf{*6.}] Načrtaj enakostranični trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % a + \begin{enumerate}[label=\textbf{\alph*)}] + \item $a+v=10$ + \begin{figure}[H] + \begin{tikzpicture} + \tkzDefPoint(0,0){M} \tkzDefPoint(0,10){N} + \tkzInterCC(M,N)(N,M) \tkzGetPoints{K60}{K60X} + \tkzCompass(M,K60) \tkzCompass(N,K60) \tkzCompass(M,N) + \tkzDefMidPoint(M,K60) \tkzGetPoint{K30} + \tkzDrawLine(N,K30) \tkzInterLC(N,K30)(N,M) \tkzGetPoints{A4L}{K30C} + \tkzCompass(N,K30C) \tkzDefMidPoint(K30C,M) \tkzGetPoint{K15} + \tkzDefMidPoint(M,N) \tkzGetPoint{MN} + \tkzCompass(M,MN) \tkzCompass(N,MN) + \tkzInterLC(M,N)(M,MN) \tkzGetPoints{NX}{NAGAIN} \tkzCompass(M,NX) + \tkzDrawLine(NX,N) \tkzLabelLine[above left](M,N){$v+a$} + \tkzInterCC(MN,NX)(NX,MN) \tkzGetPoints{P}{R} + \tkzInterLL(P,R)(N,K15)\tkzGetPoint{A}\tkzDrawLine[add=0 and 0](P,R) + \tkzDrawLine(N,K15) \tkzInterCC(A,N)(N,A) \tkzGetPoints{AL}{L60} + \tkzCompass(A,L60) \tkzCompass(N,L60) + \tkzDefMidPoint(L60,N) \tkzGetPoint{L30} \tkzInterLC(A,L30)(A,N) + \tkzGetPoints{L30CX}{L30C}\tkzCompass(A,L30C)\tkzDrawLine(A,L30) + \tkzDefMidPoint(L30C,N) \tkzGetPoint{L15} \tkzDrawLine(A,L15) + \tkzCompass(L30C,L15) \tkzCompass(N,L15) + \tkzCompass(K60,K30) \tkzCompass(A,K30) + \tkzCompass(N,L30) \tkzCompass(L60,L30) + \tkzInterLL(M,N)(A,L15) \tkzGetPoint{C} + \tkzInterLC(A,M)(M,A) \tkzGetPoints{AAGAIN}{B} \tkzCompass(M,B) + \tkzDrawLine(C,B) \tkzLabelLine[above right](C,B){$a$} + \tkzLabelLine[above left](C,A){$b$} + \tkzLabelLine[above left](A,B){$c$} + \tkzDrawPolygon[fill=blue!30, opacity=.30](A,B,C) + \tkzDrawPoints(M) \tkzLabelPoints(A,C,B) \tkzMarkRightAngles(P,M,N) + \end{tikzpicture} + \end{figure} \end{enumerate} \end{enumerate} \section{Zaključek} |