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% Document Info
\author{Celia (CCRoses)}
\pdfinfo{
  /Title (geometry-unit-10.pdf)
  /Creator (Cheatography)
  /Author (Celia (CCRoses))
  /Subject (Geometry Unit 10 Cheat Sheet)
}

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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Geometry Unit 10 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Celia (CCRoses)} via \textcolor{DarkBackground}{\uline{cheatography.com/118676/cs/22893/}}}
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\noindent
\begin{multicols}{3}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Celia (CCRoses) \\
  \uline{cheatography.com/ccroses} \\
  \end{tabulary}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 1st June, 2020.\\
   Page {\thepage} of \pageref{LastPage}.
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{x{2.64 cm} x{5.36 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Vocabulary}}  \tn
% Row 0
\SetRowColor{LightBackground}
interior of a circle & the set of all points inside the circle \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
exterior of a circle & the set of all points outside the circle \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
chord & a segment whose endpoints lie in a circle \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
secant & a line that intersects a circle at two points \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
tangent & a line in the same plane as a cicle that intersects it at exactly one point \tn 
% Row Count 11 (+ 3)
% Row 5
\SetRowColor{white}
point of tangency & the point where the tangent and a circle intersect is called the point of tangency \tn 
% Row Count 15 (+ 4)
% Row 6
\SetRowColor{LightBackground}
common tangent & a line that is tangent to two circles \tn 
% Row Count 17 (+ 2)
% Row 7
\SetRowColor{white}
central angle & an angle whose vertex is the center of a circle \tn 
% Row Count 19 (+ 2)
% Row 8
\SetRowColor{LightBackground}
adjacent arcs & arcs of the same circle that intersect at exactly one point \tn 
% Row Count 22 (+ 3)
% Row 9
\SetRowColor{white}
congruent arcs & two arcs within a circle or two circles that have the same measure \tn 
% Row Count 25 (+ 3)
% Row 10
\SetRowColor{LightBackground}
sector of a circle & a region bounded by two radii of the circle and their intercepted arc \tn 
% Row Count 28 (+ 3)
% Row 11
\SetRowColor{white}
segment of a circle & a region bounded by an arc and its chord \tn 
% Row Count 30 (+ 2)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{2.64 cm} x{5.36 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Vocabulary (cont)}}  \tn
% Row 12
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arc length & the distance along an arc measured in linear units \tn 
% Row Count 2 (+ 2)
% Row 13
\SetRowColor{white}
inscribed angle & an angle whose vertex is on a circle and whose sides contain chords of the circle \tn 
% Row Count 6 (+ 4)
% Row 14
\SetRowColor{LightBackground}
intercepted arc & consists of endpoints that lie on the sides of an inscribed angle and all the points of the circle between them \tn 
% Row Count 11 (+ 5)
% Row 15
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subtends & a chord or arc subtends an angle if its endpoints lie on the sides of the angle \tn 
% Row Count 15 (+ 4)
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% Row 0
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\mymulticolumn{2}{x{8.4cm}}{*m = arc measurement in degrees*} \tn 
% Row Count 1 (+ 1)
% Row 1
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area of a sector of a circle & A = 𝜋r\textasciicircum{}2\textasciicircum{}(m/360) \tn 
% Row Count 3 (+ 2)
% Row 2
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area of a segment of a circle & A = area of sector - area of the triangle formed inside the sector \tn 
% Row Count 6 (+ 3)
% Row 3
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arc length & L = 2𝜋r(m/360) \tn 
% Row Count 7 (+ 1)
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\begin{tabularx}{8.4cm}{x{2.96 cm} x{5.04 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Angle Relationships in Circles}}  \tn
% Row 0
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{\bf{vertex of the angle}} & {\bf{measure of angle}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
on a circle & half the measure of its intercepted arc \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
inside a circle & half the sum of  the measures of its intercepted arcs \tn 
% Row Count 7 (+ 3)
% Row 3
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outside a circle & half the difference of the measures of its intercepted arcs \tn 
% Row Count 10 (+ 3)
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\begin{tabularx}{8.4cm}{x{2.96 cm} x{5.04 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Angle Relationships in Circles}}  \tn
% Row 0
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{\bf{vertex of the angle}} & {\bf{measure of angle}} \tn 
% Row Count 2 (+ 2)
% Row 1
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on a circle & half the measure of its intercepted arc \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
inside a circle & half the sum of  the measures of its intercepted arcs \tn 
% Row Count 7 (+ 3)
% Row 3
\SetRowColor{white}
outside a circle & half the difference of the measures of its intercepted arcs \tn 
% Row Count 10 (+ 3)
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\begin{tabularx}{8.4cm}{x{2.48 cm} x{5.52 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Pairs of Circles}}  \tn
% Row 0
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congruent circles & if and only if they have congruent radii \tn 
% Row Count 2 (+ 2)
% Row 1
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concentric circles & coplanar circles with the same center \tn 
% Row Count 4 (+ 2)
% Row 2
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tangent circles & two coplanar circle that intersect at exactly one point \tn 
% Row Count 7 (+ 3)
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\begin{tabularx}{8.4cm}{x{0.836 cm} x{3.42 cm} x{3.344 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{8.4cm}}{\bf\textcolor{white}{Arcs}}  \tn
% Row 0
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minor arc & an arc whose points are on or in the interior of a central angle & the measure of a minor arc is equal to the measure of its central angle \tn 
% Row Count 5 (+ 5)
% Row 1
\SetRowColor{white}
major arc & an arc whose points are on or in the eterior of a central angle & the measure of a major arc is equal to 360 degrees minus the measure of its central angle \tn 
% Row Count 11 (+ 6)
% Row 2
\SetRowColor{LightBackground}
\seqsplit{semicircle} & when the endpoints of an arc lie on a diameter & the measure of a semicircle is equal to 180 degrees \tn 
% Row Count 14 (+ 3)
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\begin{tabularx}{8.4cm}{x{3.44 cm} x{4.56 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Theorems \& Postulates}}  \tn
% Row 0
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12-1-1 & if a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency \tn 
% Row Count 5 (+ 5)
% Row 1
\SetRowColor{white}
12-1-2 & if a line is perpendicular to a radius of a circle, then the line is tangent to the circle \tn 
% Row Count 10 (+ 5)
% Row 2
\SetRowColor{LightBackground}
12-1-3 & if two segments are tangent to the same external point, then the segments are congruent \tn 
% Row Count 14 (+ 4)
% Row 3
\SetRowColor{white}
12-2-3 & in a circle, if a radius (or diameter) is perpendicular to a chord, then it bisects the chord and its arc \tn 
% Row Count 19 (+ 5)
% Row 4
\SetRowColor{LightBackground}
12-2-4 & in a circle, the perpendicular bisector of a chord is a radius (or diameter) \tn 
% Row Count 23 (+ 4)
% Row 5
\SetRowColor{white}
12-4-1 inscribed angle theorem & the measure of an inscribed angle is half the measure of its intercepted arc \tn 
% Row Count 27 (+ 4)
% Row 6
\SetRowColor{LightBackground}
12-4-2 & if inscribed angles of a circle intercept the same arc or are subtended by the same chord or arc then the angles are congruent \tn 
% Row Count 33 (+ 6)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
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\begin{tabularx}{8.4cm}{x{3.44 cm} x{4.56 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Theorems \& Postulates (cont)}}  \tn
% Row 7
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12-4-3 & an inscribed angle subtends a semicircle is and only if the angle is a right angle \tn 
% Row Count 4 (+ 4)
% Row 8
\SetRowColor{white}
12-4-4 & if a quadrilateral is inscribed in a circle, then its opposite angles are supplementary \tn 
% Row Count 8 (+ 4)
% Row 9
\SetRowColor{LightBackground}
12-5-1 & if a tangent and a secant (or chord) intersect on a circle at the point of tangency, then the measure of the angle formed is half the measure of its intercepted arc \tn 
% Row Count 16 (+ 8)
% Row 10
\SetRowColor{white}
12-5-2 & if two secants or chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs \tn 
% Row Count 24 (+ 8)
% Row 11
\SetRowColor{LightBackground}
12-5-3 & if a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs \tn 
% Row Count 33 (+ 9)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Theorem 12-2-2}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{{\emph{in a circle or congruent circles...}}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{1. congruent central angles have congruent chords} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{2. congruent chords have congruent arcs} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{3. congruent arcs have congruent central angles} \tn 
% Row Count 4 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}


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

\end{document}