\documentclass[10pt,a4paper]{article} % Packages \usepackage{fancyhdr} % For header and footer \usepackage{multicol} % Allows multicols in tables \usepackage{tabularx} % Intelligent column widths \usepackage{tabulary} % Used in header and footer \usepackage{hhline} % Border under tables \usepackage{graphicx} % For images \usepackage{xcolor} % For hex colours %\usepackage[utf8x]{inputenc} % For unicode character support \usepackage[T1]{fontenc} % Without this we get weird character replacements \usepackage{colortbl} % For coloured tables \usepackage{setspace} % For line height \usepackage{lastpage} % Needed for total page number \usepackage{seqsplit} % Splits long words. %\usepackage{opensans} % Can't make this work so far. Shame. Would be lovely. \usepackage[normalem]{ulem} % For underlining links % Most of the following are not required for the majority % of cheat sheets but are needed for some symbol support. \usepackage{amsmath} % Symbols \usepackage{MnSymbol} % Symbols \usepackage{wasysym} % Symbols %\usepackage[english,german,french,spanish,italian]{babel} % Languages % Document Info \author{doxeado} \pdfinfo{ /Title (geometry-i.pdf) /Creator (Cheatography) /Author (doxeado) /Subject (Geometry I Cheat Sheet) } % Lengths and widths \addtolength{\textwidth}{6cm} \addtolength{\textheight}{-1cm} \addtolength{\hoffset}{-3cm} \addtolength{\voffset}{-2cm} \setlength{\tabcolsep}{0.2cm} % Space between columns \setlength{\headsep}{-12pt} % Reduce space between header and content \setlength{\headheight}{85pt} % If less, LaTeX automatically increases it \renewcommand{\footrulewidth}{0pt} % Remove footer line \renewcommand{\headrulewidth}{0pt} % Remove header line \renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit % This two commands together give roughly % the right line height in the tables \renewcommand{\arraystretch}{1.3} \onehalfspacing % Commands \newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour \newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols \newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns \newcommand{\tn}{\tabularnewline} % Required as custom column type in use % Font and Colours \definecolor{HeadBackground}{HTML}{333333} \definecolor{FootBackground}{HTML}{666666} \definecolor{TextColor}{HTML}{333333} \definecolor{DarkBackground}{HTML}{00C9A7} \definecolor{LightBackground}{HTML}{EFFBF9} \renewcommand{\familydefault}{\sfdefault} \color{TextColor} % Header and Footer \pagestyle{fancy} \fancyhead{} % Set header to blank \fancyfoot{} % Set footer to blank \fancyhead[L]{ \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{C} \SetRowColor{DarkBackground} \vspace{-7pt} {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}} } \end{tabulary} \columnbreak \begin{tabulary}{11cm}{L} \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Geometry I Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{doxeado} via \textcolor{DarkBackground}{\uline{cheatography.com/199990/cs/42249/}}} \end{tabulary} \end{multicols}} \fancyfoot[L]{ \footnotesize \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{LL} \SetRowColor{FootBackground} \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}} \\ \vspace{-2pt}doxeado \\ \uline{cheatography.com/doxeado} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Published 2nd February, 2024.\\ Updated 2nd February, 2024.\\ Page {\thepage} of \pageref{LastPage}. \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}} \\ \SetRowColor{white} \vspace{-5pt} %\includegraphics[width=48px,height=48px]{dave.jpeg} Measure your website readability!\\ www.readability-score.com \end{tabulary} \end{multicols}} \begin{document} \raggedright \raggedcolumns % Set font size to small. Switch to any value % from this page to resize cheat sheet text: % www.emerson.emory.edu/services/latex/latex_169.html \footnotesize % Small font. \begin{multicols*}{3} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Line}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{General equation}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{Ax+By+C=0}}} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\bf{Point slope equation}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{y-y1=m(x-x1)}}} \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{Slope of a straight line (m)}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{m=-A/B \{\{nl\}\} m=(y2-y1)/(x2-x1) \{\{nl\}\} m=tg(α)}}} \tn % Row Count 7 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Positions relative to two lines}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{Equations}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{Ax+By+C=0\{\{nl\}\}A'x+B'y+C'=0}}} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\bf{Secant lines}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{A/A'≠B/B'}}} \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{Parallel lines}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{A/A'=B/B'≠ C/C'}}} \tn % Row Count 6 (+ 2) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\bf{Coincident lines}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{A/A'=B/B'= C/C'}}} \tn % Row Count 8 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Parallel lines}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{Slope}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{m1=m2 \{\{nl\}\} -A/B=-A'/B'}}} \tn % Row Count 2 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Perpendicular lines}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{Slope}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{m1.m2=-1 \{\{nl\}\} -A/B=B'/A'}}} \tn % Row Count 2 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Points}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{Coordinates}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{P(x1,y1) \{\{nl\}\} Q(x2,y2) \{\{nl\}\} M(x3,y3)}}} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\bf{Distance between two points (P and Q)}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{d={\bf{}}√}}{\emph{{[}(x2-x1)\textasciicircum{}2+(y2-y1)\textasciicircum{}2{]}}}} \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{Midpoint (M)}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{x3=(x1+x2)/2 \{\{nl\}\} y3=(y1+y2)/2}}} \tn % Row Count 6 (+ 2) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\bf{Distance from a point (P) to a line}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{d=|(A.x1+B.y1+C)/{\bf{√}}(a\textasciicircum{}2+b\textasciicircum{}2)|}}} \tn % Row Count 8 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Circumference}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{Ordinary equation}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{(x-a)\textasciicircum{}2+(y-b)\textasciicircum{}2=r\textasciicircum{}2}}} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\bf{Elements}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{Center: C(a,b) \{\{nl\}\} Point: P(x,y) \{\{nl\}\} Radius: r}}} \tn % Row Count 5 (+ 3) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{General equation}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{x\textasciicircum{}2+y\textasciicircum{}2+Ax+By+C=0 \{\{nobreak\}\} \{\{nl\}\} }}If:{\emph{ \{\{nl\}\} (A/2)\textasciicircum{}2+(B/2)\textasciicircum{}2-C\textgreater{}0 \{\{nl\}\} x }}and{\emph{ y }}don't multiply \{\{nl\}\} {\emph{x\textasciicircum{}2}} and {\emph{y\textasciicircum{}2}} have {\emph{1}} as coefficient} \tn % Row Count 10 (+ 5) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\bf{Elements}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{A=-2a \{\{nl\}\} B=-2b \{\{nl\}\} C=a\textasciicircum{}2+b\textasciicircum{}2-r}}\{\{nobreak\}\}} \tn % Row Count 13 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Ellipse}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{Equation}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{{[}(x-x0)\textasciicircum{}2{]}/(a\textasciicircum{}2)+{[}(y-y0)\textasciicircum{}2{]}/(b\textasciicircum{}2)=1}} \{\{nl\}\} Center: {\emph{C(x0,y0)}} \{\{nl\}\} Horizontal radius: {\emph{a}} \{\{nl\}\} Vertical radius: {\emph{b}}} \tn % Row Count 4 (+ 4) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Parabola}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{General equation}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{Ax\textasciicircum{}2+Bxy+Cy\textasciicircum{}2+Dx+Ey+F=0}} \{\{nl\}\} If: \{\{nl\}\} {\emph{A≠0 v B≠0}} \{\{nl\}\} {\emph{B\textasciicircum{}2-4AC=0}}} \tn % Row Count 3 (+ 3) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\bf{Vertical Parabola Ordinary Equation}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{(x-x0)\textasciicircum{}2=2p(y-y0)}} \{\{nl\}\} Vertex: V(x0,y0) \{\{nl\}\} Parameter: p} \tn % Row Count 6 (+ 3) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{Horizontal Parabola Ordinary Equation}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{(y-y0)\textasciicircum{}2=2p(x-x0)}} \{\{nl\}\} Vertex: V(x0,y0) \{\{nl\}\} Parameter: p} \tn % Row Count 9 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Hyperbola}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{General equation}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{Ax\textasciicircum{}2+Bxy+Cy\textasciicircum{}2+Dx+Ey+F=0}} \{\{nl\}\} If: \{\{nl\}\} {\emph{A≠0 \textasciicircum{} B≠0}} \{\{nl\}\} {\emph{A.B\textless{}0}}} \tn % Row Count 3 (+ 3) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\bf{Ordinary Equation (horizontal focal axis)}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{{[}(x-x0)\textasciicircum{}2{]}/(a\textasciicircum{}2)-{[}(y-y0)\textasciicircum{}2{]}/(b\textasciicircum{}2)=1}}} \tn % Row Count 5 (+ 2) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{Ordinary Equation (vertical focal axis)}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{{[}(y-y0)\textasciicircum{}2{]}/(b\textasciicircum{}2)-{[}(x-x0)\textasciicircum{}2{]}/(a\textasciicircum{}2)=1}}} \tn % Row Count 7 (+ 2) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\bf{Equilateral Hyperbola Equation}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{a=b}}} \tn % Row Count 9 (+ 2) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\bf{Asymptotes}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}{\emph{y=x \{\{nl\}\} y=-x}}} \tn % Row Count 11 (+ 2) % Row 5 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\bf{Elements}}} \tn \mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Center: {\emph{O(x0,y0)}} \{\{nl\}\} Length of the semimajor axis of the hyperbola: {\emph{a}} \{\{nl\}\} Length of the semi-minor axis of the hyperbola: {\emph{b}}} \tn % Row Count 15 (+ 4) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}