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% Document Info
\author{anjuscha}
\pdfinfo{
  /Title (foundations-of-euclidean-geometry-unit-1.pdf)
  /Creator (Cheatography)
  /Author (anjuscha)
  /Subject (Foundations of Euclidean Geometry - Unit 1 Cheat Sheet)
}

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    {\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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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Foundations of Euclidean Geometry - Unit 1 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{anjuscha} via \textcolor{DarkBackground}{\uline{cheatography.com/125991/cs/24589/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}anjuscha \\
  \uline{cheatography.com/anjuscha} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 1st October, 2020.\\
   Updated 1st October, 2020.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Euclidean Geometry}}  \tn
% Row 0
\SetRowColor{LightBackground}
theorem & a statement that has been proven based on previous theorems, postulates, or axioms \tn 
% Row Count 4 (+ 4)
% Row 1
\SetRowColor{white}
collinear & points that lie on the same line \tn 
% Row Count 6 (+ 2)
% Row 2
\SetRowColor{LightBackground}
deductive reasoning & the process of utilizing facts, properties, definitions, and theorems to form a logical argument \tn 
% Row Count 10 (+ 4)
% Row 3
\SetRowColor{white}
coplanar & contained within the same plane \tn 
% Row Count 12 (+ 2)
% Row 4
\SetRowColor{LightBackground}
postulate & a statement accepted without proof; also known as an axiom \tn 
% Row Count 15 (+ 3)
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Add}}  \tn
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\mymulticolumn{1}{x{5.377cm}}{Euclidean geometry is comprised of figures and diagrams that can all be constructed using just a straightedge and compass.% Row Count 3 (+ 3)
} \tn 
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% Row 0
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Point & Line & Plane \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
No dimensions & \seqsplit{One-dimensional} set of infinite points & \seqsplit{Two-dimensional} set of all points \tn 
% Row Count 4 (+ 3)
% Row 2
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Location on coordinate plane designated by an ordered pair (x/y) & Has no beginning or an end & Flat or level surface \tn 
% Row Count 9 (+ 5)
% Row 3
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Identified with a single capital letter & Identified with a lowercase italicized letter or two capital letters representing two points on the line & Identified with a capital italicized letter \tn 
% Row Count 17 (+ 8)
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Defining terms}}  \tn
% Row 0
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line segment & a part of a line that has two endpoints and a specific length \tn 
% Row Count 3 (+ 3)
% Row 1
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ray & part of a line that has one endpoint and extends indefinitely in one direction \tn 
% Row Count 6 (+ 3)
% Row 2
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circle & the set of all points in a plane that are a given distance away from a given point called the center \tn 
% Row Count 10 (+ 4)
% Row 3
\SetRowColor{white}
angle & a figure formed by two rays that share a common endpoint \tn 
% Row Count 13 (+ 3)
% Row 4
\SetRowColor{LightBackground}
parallel lines & lines that lie in the same plane and do not intersect \tn 
% Row Count 15 (+ 2)
% Row 5
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\seqsplit{perpendicularlines} & lines that intersect to form right, or 90-degree, angles \tn 
% Row Count 18 (+ 3)
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midpoint & a point on a line segment that is equidistant from the two endpoints \tn 
% Row Count 3 (+ 3)
% Row 1
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protractor & tool used to measure an angle in degrees \tn 
% Row Count 5 (+ 2)
% Row 2
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bisect & to divide into two congruent parts \tn 
% Row Count 7 (+ 2)
% Row 3
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congruent segments & two line segments that have the same length \tn 
% Row Count 9 (+ 2)
% Row 4
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Undefined terms: & Point: Points are locations in space. Line: Lines are infinite in two different directions. \tn 
% Row Count 13 (+ 4)
% Row 5
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Defined terms: & Line segment: A line segment has two endpoints. Ray: Rays have one endpoint. Angle: An angle is formed by two rays with a common endpoint. \tn 
% Row Count 19 (+ 6)
% Row 6
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adjacent angles & two angles within the same plane that share a common side and vertex, but do not share any common interior points \tn 
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% Row 7
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congruent angles & two angles that have the same measure \tn 
% Row Count 26 (+ 2)
% Row 8
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obtuse angle & an angle measuring greater than 90 degrees, but less than 180 degrees \tn 
% Row Count 29 (+ 3)
% Row 9
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straight angle & an angle whose measure is exactly 180 degrees \tn 
% Row Count 31 (+ 2)
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acute angle & an angle measuring between 0 and 90 degrees \tn 
% Row Count 2 (+ 2)
% Row 11
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right angle & an angle whose measure is exactly 90 degrees \tn 
% Row Count 4 (+ 2)
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Intro to proof}}  \tn
% Row 0
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conjecture & a statement thought to be true but not yet proved true or false \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
deductive reasoning & the process of utilizing facts, properties, definitions, and theorems to form a logical argument \tn 
% Row Count 7 (+ 4)
% Row 2
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reflexive property & the property that states that for any real number 𝑥, 𝑥 = 𝑥; or that a figure and its parts (e.g., sides, angles, triangles, etc.) are congruent to themselves \tn 
% Row Count 14 (+ 7)
% Row 3
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substitution property & the property stating that if two values are equal, then they are interchangeable in an equation; or if two figures are congruent, then they are interchangeable in a statement \tn 
% Row Count 21 (+ 7)
% Row 4
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symmetric property & \seqsplit{thepropertythatstatesthattheleftandright} sides of an equation or congruence statement are interchangeable \tn 
% Row Count 26 (+ 5)
% Row 5
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Proofs involve: & given information, in words or a diagram, a statement to be proven, an argument using deductive reasoning and justification of steps in a logical order. A conclusion \tn 
% Row Count 33 (+ 7)
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linear pair & 2 adjacentangles whose noncommon sides are opposite rays \tn 
% Row Count 2 (+ 2)
% Row 1
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vertical angles & opposite angles formed by two intersecting lines \tn 
% Row Count 4 (+ 2)
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% Row 0
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opposite rays & ays that are collinear and have the same endpoint but run infinitely in opposite directions \tn 
% Row Count 4 (+ 4)
% Row 1
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\seqsplit{supplementary} angles & two angles whose measures have a sum of 180 degrees \tn 
% Row Count 6 (+ 2)
% Row 2
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\seqsplit{complementary} angles & angles are two angles whose measures have a sum of 90 degrees \tn 
% Row Count 9 (+ 3)
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Example finding angle}}  \tn
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\mymulticolumn{1}{x{5.377cm}}{Find the following angle measures. \newline % Row Count 1 (+ 1)
𝑚∠1 = ? \newline % Row Count 2 (+ 1)
𝑚∠1 + 70° = 90° \newline % Row Count 3 (+ 1)
𝑚∠1 = 90° − 70 \newline % Row Count 4 (+ 1)
𝑚∠1 = 20% Row Count 5 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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% That's all folks
\end{multicols*}

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