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\author{frog.lover28}
\pdfinfo{
  /Title (geometry-finals-semester-2.pdf)
  /Creator (Cheatography)
  /Author (frog.lover28)
  /Subject (Geometry Finals (Semester 2) Cheat Sheet)
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Geometry Finals (Semester 2) Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{frog.lover28} via \textcolor{DarkBackground}{\uline{cheatography.com/147552/cs/32097/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}frog.lover28 \\
  \uline{cheatography.com/frog-lover28} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 16th May, 2022.\\
   Updated 16th May, 2022.\\
   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}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{chapter 6 - relating lines to planes}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{VOCAB} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{1}{x{8.4cm}}{plane - a surface such that if any two points on the surface are connected by a line, all points of the line are also on the surface.} \tn 
% Row Count 4 (+ 3)
% Row 2
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\mymulticolumn{1}{x{8.4cm}}{noncoplanar - not on the same plane.} \tn 
% Row Count 5 (+ 1)
% Row 3
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\mymulticolumn{1}{x{8.4cm}}{coplanar - on the same plane.} \tn 
% Row Count 6 (+ 1)
% Row 4
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\mymulticolumn{1}{x{8.4cm}}{foot - point of intersection of a line and a plane.} \tn 
% Row Count 8 (+ 2)
% Row 5
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% Row Count 8 (+ 0)
% Row 6
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\mymulticolumn{1}{x{8.4cm}}{POSTULATES} \tn 
% Row Count 9 (+ 1)
% Row 7
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\mymulticolumn{1}{x{8.4cm}}{Three noncollinear points determine a plane.} \tn 
% Row Count 10 (+ 1)
% Row 8
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\mymulticolumn{1}{x{8.4cm}}{If a line intersects a plane not containing it, then the intersection is exactly one point.} \tn 
% Row Count 12 (+ 2)
% Row 9
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\mymulticolumn{1}{x{8.4cm}}{If two planes intersect, their intersection is exactly one line.} \tn 
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% Row 10
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% Row Count 14 (+ 0)
% Row 11
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% Row 12
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\mymulticolumn{1}{x{8.4cm}}{A line and a point not on the line determine a plane.} \tn 
% Row Count 17 (+ 2)
% Row 13
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\mymulticolumn{1}{x{8.4cm}}{Two intersecting lines determine a plane.} \tn 
% Row Count 18 (+ 1)
% Row 14
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\mymulticolumn{1}{x{8.4cm}}{Two parallel lines determine a plane.} \tn 
% Row Count 19 (+ 1)
% Row 15
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\mymulticolumn{1}{x{8.4cm}}{If a line is perpendicular to 2 distinct lines that lie on a plane and that pass through its foot, then it is perpendicular to the plane.} \tn 
% Row Count 22 (+ 3)
% Row 16
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\mymulticolumn{1}{x{8.4cm}}{If a plane intersects 2 parallel planes, the lines of intersection are parallel.} \tn 
% Row Count 24 (+ 2)
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{chapter 8 - ratio and proportion}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{THEOREMS} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{1}{x{8.4cm}}{Means-Extremes Products Theorem - a/b = c/d   -\textgreater{}   ad=bc} \tn 
% Row Count 3 (+ 2)
% Row 2
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\mymulticolumn{1}{x{8.4cm}}{Means-Extremes Ratio Theorem - pq=rs   -\textgreater{}   p/r=s/q   etc.} \tn 
% Row Count 5 (+ 2)
% Row 3
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\mymulticolumn{1}{x{8.4cm}}{Arithmetic mean example: given 3 \& 7,     3+27/2= 15} \tn 
% Row Count 7 (+ 2)
% Row 4
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\mymulticolumn{1}{x{8.4cm}}{Geometric mean example: given 3 \& 7,     3/x = x/27     x=+ or - 9} \tn 
% Row Count 9 (+ 2)
% Row 5
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\mymulticolumn{1}{x{8.4cm}}{AAA (angles) - similar} \tn 
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% Row 6
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\mymulticolumn{1}{x{8.4cm}}{AA (angles) - similar} \tn 
% Row Count 11 (+ 1)
% Row 7
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\mymulticolumn{1}{x{8.4cm}}{Side-Splitter Theorem - ab/bc = ae/ed} \tn 
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% Row 8
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% Row 10
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% Row 11
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\mymulticolumn{1}{x{8.4cm}}{Similarity - same shape but not size} \tn 
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{chapter 10 - circles}}  \tn
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% Row 1
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\mymulticolumn{1}{x{8.4cm}}{chord - points connected by a segment on a circle} \tn 
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% Row 3
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% Row 4
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\mymulticolumn{1}{x{8.4cm}}{secants/tangents} \tn 
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% Row 5
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% Row 6
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% Row 7
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\mymulticolumn{1}{x{8.4cm}}{If a radius is perpendicular to a chord then it bisects it (reversed too).} \tn 
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% Row 8
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\mymulticolumn{1}{x{8.4cm}}{The perpendicular bisector of a chord passes through the center of a circle.} \tn 
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% Row 9
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\mymulticolumn{1}{x{8.4cm}}{If 2 chords are equidistant from the center then they are congruent (reversed too).} \tn 
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% Row 10
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\mymulticolumn{1}{x{8.4cm}}{secant/tangent theorems - example: 1/2 (large angle - medium angle) = small angle} \tn 
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% Row 11
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\mymulticolumn{1}{x{8.4cm}}{chords: ev . en = el . se} \tn 
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% Row 12
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\mymulticolumn{1}{x{8.4cm}}{tp (tangent) squared = (pr)(pq aka external part of secant)} \tn 
% Row Count 18 (+ 2)
% Row 13
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\mymulticolumn{1}{x{8.4cm}}{pb . pa (external part of secant) = pd . pc (external part of secant)} \tn 
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{chapter 7 - triangle application theorems}}  \tn
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\mymulticolumn{1}{x{8.4cm}}{THEOREMS} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{1}{x{8.4cm}}{The sum of the measures of the 3 angles of a triangle is 180.} \tn 
% Row Count 3 (+ 2)
% Row 2
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\mymulticolumn{1}{x{8.4cm}}{The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.} \tn 
% Row Count 6 (+ 3)
% Row 3
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\mymulticolumn{1}{x{8.4cm}}{A segment joining the midpoints of 2 sides of a triangle is parallel to the third side, and its length is one-half the length of the third side (midline theorem).} \tn 
% Row Count 10 (+ 4)
% Row 4
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\mymulticolumn{1}{x{8.4cm}}{No choice theorem - if 2 angles of a triangle are congruent then the remaining ones are also.} \tn 
% Row Count 12 (+ 2)
% Row 5
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\mymulticolumn{1}{x{8.4cm}}{AAS - angle angle side} \tn 
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% Row 6
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% Row Count 13 (+ 0)
% Row 7
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\mymulticolumn{1}{x{8.4cm}}{FORMULAS} \tn 
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% Row 8
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% Row 9
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\mymulticolumn{1}{x{8.4cm}}{exterior angles = 360} \tn 
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% Row 10
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% Row 11
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{chapter 9 - a lot of different things}}  \tn
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\mymulticolumn{1}{x{8.4cm}}{RADICAL REVIEW} \tn 
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% Row 1
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\mymulticolumn{1}{x{8.4cm}}{squared root of 48 = 4 radical 3} \tn 
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% Row 2
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\mymulticolumn{1}{x{8.4cm}}{squared root of 5/3 = squared root of 15/3} \tn 
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% Row 3
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% Row 4
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% Row 5
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\mymulticolumn{1}{x{8.4cm}}{circumference - pi d} \tn 
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% Row 6
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\mymulticolumn{1}{x{8.4cm}}{area - pi r squared} \tn 
% Row Count 6 (+ 1)
% Row 7
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\mymulticolumn{1}{x{8.4cm}}{sector - fraction of circle area} \tn 
% Row Count 7 (+ 1)
% Row 8
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\mymulticolumn{1}{x{8.4cm}}{arc - fraction of circumference} \tn 
% Row Count 8 (+ 1)
% Row 9
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\mymulticolumn{1}{x{8.4cm}}{secants - through circle} \tn 
% Row Count 9 (+ 1)
% Row 10
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\mymulticolumn{1}{x{8.4cm}}{tangent - edge of circle (external/internal)} \tn 
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% Row 11
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% Row Count 10 (+ 0)
% Row 12
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\mymulticolumn{1}{x{8.4cm}}{RIGHT TRIANGLE ALTITUDES} \tn 
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% Row 13
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\mymulticolumn{1}{x{8.4cm}}{h squared = x . y} \tn 
% Row Count 12 (+ 1)
% Row 14
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\mymulticolumn{1}{x{8.4cm}}{a squared = x . c} \tn 
% Row Count 13 (+ 1)
% Row 15
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\mymulticolumn{1}{x{8.4cm}}{b squared = y . c} \tn 
% Row Count 14 (+ 1)
% Row 16
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\mymulticolumn{1}{x{8.4cm}}{} \tn 
% Row Count 14 (+ 0)
% Row 17
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\mymulticolumn{1}{x{8.4cm}}{OTHER} \tn 
% Row Count 15 (+ 1)
% Row 18
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\mymulticolumn{1}{x{8.4cm}}{pythagorean theorem - a squared + b squared = c squared} \tn 
% Row Count 17 (+ 2)
% Row 19
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\mymulticolumn{1}{x{8.4cm}}{distance formula - squared root (x2 - x1) squared + (y2 - y1) squared} \tn 
% Row Count 19 (+ 2)
% Row 20
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\mymulticolumn{1}{x{8.4cm}}{30 60 90} \tn 
% Row Count 20 (+ 1)
% Row 21
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% Row Count 21 (+ 1)
% Row 22
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\mymulticolumn{1}{x{8.4cm}}{SOH CAH TOA} \tn 
% Row Count 22 (+ 1)
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{chapter 11 - area}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{I don't feel like writing all of the area formulas but here are the ones you need to know...} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{8.4cm}}{square/rectanle} \tn 
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% Row 2
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% Row 3
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\mymulticolumn{1}{x{8.4cm}}{parallelogram} \tn 
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% Row 4
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\mymulticolumn{1}{x{8.4cm}}{trapezoid (and median)} \tn 
% Row Count 6 (+ 1)
% Row 5
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\mymulticolumn{1}{x{8.4cm}}{kite} \tn 
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% Row 6
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\mymulticolumn{1}{x{8.4cm}}{polygons} \tn 
% Row Count 8 (+ 1)
% Row 7
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\mymulticolumn{1}{x{8.4cm}}{circle, sectors, segments} \tn 
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% Row 8
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\mymulticolumn{1}{x{8.4cm}}{} \tn 
% Row Count 9 (+ 0)
% Row 9
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\mymulticolumn{1}{x{8.4cm}}{hero formula: squared root of s(s-a)(s-b)(s-c)} \tn 
% Row Count 10 (+ 1)
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\par\addvspace{1.3em}


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

\end{document}