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% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
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\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
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% Document Info
\author{Celia (CCRoses)}
\pdfinfo{
  /Title (geometry-unit-6.pdf)
  /Creator (Cheatography)
  /Author (Celia (CCRoses))
  /Subject (Geometry Unit 6 Cheat Sheet)
}

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% Commands
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% Header and Footer
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\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 Unit 6 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Celia (CCRoses)} via \textcolor{DarkBackground}{\uline{cheatography.com/118676/cs/21871/}}}
\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}Celia (CCRoses) \\
  \uline{cheatography.com/ccroses} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 9th March, 2020.\\
   Updated 9th March, 2020.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
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  \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*}{2}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Polygons}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Number of Sides}} & {\bf{Name of Polygon}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
3 & Triangle \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
4 & Quadrilateral \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
5 & Pentagon \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
6 & Hexagon \tn 
% Row Count 5 (+ 1)
% Row 5
\SetRowColor{white}
7 & Heptagon \tn 
% Row Count 6 (+ 1)
% Row 6
\SetRowColor{LightBackground}
8 & Octagon \tn 
% Row Count 7 (+ 1)
% Row 7
\SetRowColor{white}
9 & Nonagon \tn 
% Row Count 8 (+ 1)
% Row 8
\SetRowColor{LightBackground}
10 & Decagon \tn 
% Row Count 9 (+ 1)
% Row 9
\SetRowColor{white}
12 & Dodecagon \tn 
% Row Count 10 (+ 1)
% Row 10
\SetRowColor{LightBackground}
{\emph{n}} & {\emph{n}}-gon \tn 
% Row Count 11 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.04 cm} x{4.96 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Vocabulary}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Term}} & {\bf{Definition}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Vertex of the polygon & The common endpoint of two sides of a polygon \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Diagonal & A segment connecting any two nonconsecutive vertices of a polygon \tn 
% Row Count 6 (+ 3)
% Row 3
\SetRowColor{white}
Regular polygon & An equilateral and equiangular polygon (always convex) \tn 
% Row Count 9 (+ 3)
% Row 4
\SetRowColor{LightBackground}
Concave polygon & A polygon with parts of a diagonal on the exterior of the polygon \tn 
% Row Count 12 (+ 3)
% Row 5
\SetRowColor{white}
Convex polygon & A polygon with every part of the diagonals on the interior \tn 
% Row Count 15 (+ 3)
% Row 6
\SetRowColor{LightBackground}
Rectangle & A quadrilateral with four right angles \tn 
% Row Count 17 (+ 2)
% Row 7
\SetRowColor{white}
Rhombus & A quadrilateral with four congruent sides \tn 
% Row Count 19 (+ 2)
% Row 8
\SetRowColor{LightBackground}
Square & A quadrilateral with four right angles and four congruent sides; it is a parallelogram, a rectangle, and a rhombus \tn 
% Row Count 24 (+ 5)
% Row 9
\SetRowColor{white}
Kite & A quadrilateral with exactly two pairs of consecutive sides \tn 
% Row Count 27 (+ 3)
% Row 10
\SetRowColor{LightBackground}
Trapezoid & A quadrilateral with exactly one pair of parallel sides \tn 
% Row Count 30 (+ 3)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{3.04 cm} x{4.96 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Vocabulary (cont)}}  \tn
% Row 11
\SetRowColor{LightBackground}
Base & One of the parallel sides of a trapezoid \tn 
% Row Count 2 (+ 2)
% Row 12
\SetRowColor{white}
Leg & One of the nonparallel sides of a trapezoid \tn 
% Row Count 4 (+ 2)
% Row 13
\SetRowColor{LightBackground}
Isosceles trapezoid & A trapezoid in which the legs are congruent \tn 
% Row Count 6 (+ 2)
% Row 14
\SetRowColor{white}
Midsegment of a trapezoid & The segment whose endpoints are the midpoints of the legs of a trapezoid \tn 
% Row Count 9 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.68 cm} x{4.32 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Theorems \& Postulates}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Name}} & {\bf{Theorem}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Polygon angle sum theorem & The sum of the interior angle measures of a convex polygon with {\emph{n}} sides is ({\emph{n}} - 2)180 degrees. \tn 
% Row Count 6 (+ 5)
% Row 2
\SetRowColor{LightBackground}
Polygon exterior angle sum theorem & The sum of the exterior angle measures, one angle at each vertex, of a convex polygon is 360 degrees. \tn 
% Row Count 11 (+ 5)
% Row 3
\SetRowColor{white}
Trapezoid Midsegment Theorem & The midsegment of a trapezoid is parallel to each base, and its length is one half the sum of the lengths of the bases \tn 
% Row Count 17 (+ 6)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.52 cm} x{4.48 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Formulas}}  \tn
% Row 0
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{\bf{Name}} & {\bf{Formula}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Sum of interior angle measures & ({\emph{n}} - 2)180 \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Midsegment of a trapezoid length & 1/2(base 1 + base 2) \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
Midpoint Formula & ({\emph{x}},{\emph{y}}) = {[}({\emph{x}}1 + {\emph{x}}2)/2{]},  {[}({\emph{y}}1 + {\emph{y}}2)/2{]} \tn 
% Row Count 8 (+ 3)
% Row 4
\SetRowColor{LightBackground}
Distance formula & √({\emph{x}}2 − {\emph{x}}1)\textasciicircum{}2\textasciicircum{}+({\emph{y}}2 − {\emph{y}}1)\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 10 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Properties of Parallelograms}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{{\bf{If a quadrilateral is a parallelogram, then...}}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Its opposite sides are congruent AND} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Its opposite angles are congruent AND} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Its consecutive angles are supplementary AND} \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Its diagonals bisect each other.} \tn 
% Row Count 5 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{} \tn 
% Row Count 5 (+ 0)
% Row 6
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\mymulticolumn{1}{x{8.4cm}}{{\bf{If...}}} \tn 
% Row Count 6 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{One pair of opposite sides of a quadrilateral are parallel and congruent OR} \tn 
% Row Count 8 (+ 2)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Both pairs of opposite sides of a quadrilateral are congruent OR} \tn 
% Row Count 10 (+ 2)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Both pairs of opposite angles of a quadrilateral are congruent OR} \tn 
% Row Count 12 (+ 2)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{An angle of a quadrilateral is supplementary to both of its consecutive angles OR} \tn 
% Row Count 14 (+ 2)
% Row 11
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{The diagonals of a quadrilateral bisect each other,} \tn 
% Row Count 16 (+ 2)
% Row 12
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{{\bf{then the quadrilateral is a parallelogram.}}} \tn 
% Row Count 17 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Properties of Rectangles \& Rhombuses}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{{\bf{If a quadrilateral is a rectangle, then...}}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{It is a parallelogram AND} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Its diagonals are congruent.} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{} \tn 
% Row Count 3 (+ 0)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{{\bf{If a quadrilateral is a rhombus, then...}}} \tn 
% Row Count 4 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{It is a parallelogram AND} \tn 
% Row Count 5 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Its diagonals are perpendicular AND} \tn 
% Row Count 6 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Each diagonal bisects a pair of opposite angles.} \tn 
% Row Count 7 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Properties of Kites and Trapezoids}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{{\bf{If a quadrilateral is a kite, then...}}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Its diagonals are perpendicular AND} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Exactly one pair of opposite angles are congruent.} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{} \tn 
% Row Count 3 (+ 0)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{{\bf{If a quadrilateral is an isosceles trapezoid, then...}}} \tn 
% Row Count 5 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Each pair of base angles are congruent AND} \tn 
% Row Count 6 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Its diagonals are congruent.} \tn 
% Row Count 7 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{} \tn 
% Row Count 7 (+ 0)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{{\bf{If...}}} \tn 
% Row Count 8 (+ 1)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{A trapezoid has one pair of congruent base angles OR} \tn 
% Row Count 10 (+ 2)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{A trapezoid has congruent diagonals,} \tn 
% Row Count 11 (+ 1)
% Row 11
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{{\bf{then the trapezoid is isosceles.}}} \tn 
% Row Count 12 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}