\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{ColdZera} \pdfinfo{ /Title (geometry-final.pdf) /Creator (Cheatography) /Author (ColdZera) /Subject (Geometry Final 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}{25A358} \definecolor{LightBackground}{HTML}{F1F9F4} \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 Final Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{ColdZera} via \textcolor{DarkBackground}{\uline{cheatography.com/28389/cs/8343/}}} \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}ColdZera \\ \uline{cheatography.com/coldzera} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Published 4th June, 2016.\\ Updated 4th June, 2016.\\ 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*}{2} \begin{tabularx}{8.4cm}{x{3.76 cm} x{4.24 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Vocabulary}} \tn % Row 0 \SetRowColor{LightBackground} Segment & Part of a line consisting of two end points and the points between them \tn % Row Count 4 (+ 4) % Row 1 \SetRowColor{white} Ray & Part of a line consisting of an end point and all the points to one side \tn % Row Count 8 (+ 4) % Row 2 \SetRowColor{LightBackground} Opposite rays & 2 collinear rays with the same endpoint; forms a line \tn % Row Count 11 (+ 3) % Row 3 \SetRowColor{white} Parallel Lines & Coplaner lines that do not intersect \tn % Row Count 13 (+ 2) % Row 4 \SetRowColor{LightBackground} Skew Lines & Non-coplaner lines that do not intersect \tn % Row Count 15 (+ 2) % Row 5 \SetRowColor{white} Parallel Planes & Planes that do not intersect \tn % Row Count 17 (+ 2) % Row 6 \SetRowColor{LightBackground} Congruent Segments & 2 segments with the same length \tn % Row Count 19 (+ 2) % Row 7 \SetRowColor{white} Midpoint & Point on a segment that divides a segment into 2 congruent segments \tn % Row Count 23 (+ 4) % Row 8 \SetRowColor{LightBackground} Angle & Formed by two rays with the same endpoint. \tn % Row Count 25 (+ 2) % Row 9 \SetRowColor{white} Acute Angle & Angle Greater than 0 and less than 90 \tn % Row Count 27 (+ 2) % Row 10 \SetRowColor{LightBackground} Right angle & 90 degree angle \tn % Row Count 28 (+ 1) % Row 11 \SetRowColor{white} Obtuse angle & Angle greater than 90 but less than 180 \tn % Row Count 30 (+ 2) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{3.76 cm} x{4.24 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Vocabulary (cont)}} \tn % Row 12 \SetRowColor{LightBackground} Straight Angle & 180 degree angle \tn % Row Count 1 (+ 1) % Row 13 \SetRowColor{white} Congruent angles & Angles with the same measure \tn % Row Count 3 (+ 2) % Row 14 \SetRowColor{LightBackground} Vertical angles & Opposite angles formed by intersecting lines \tn % Row Count 6 (+ 3) % Row 15 \SetRowColor{white} Adjecent angles & 2 coplaner angles that share a common vertex and a common side \tn % Row Count 9 (+ 3) % Row 16 \SetRowColor{LightBackground} Complementary angles & 2 angles that add up to 90 degrees \tn % Row Count 11 (+ 2) % Row 17 \SetRowColor{white} Supplementry angles & 2 angles that add up to 180 degrees \tn % Row Count 13 (+ 2) % Row 18 \SetRowColor{LightBackground} Conditional & An if/then statement \tn % Row Count 14 (+ 1) % Row 19 \SetRowColor{white} Hypothesis & What follows the If in a conditional \tn % Row Count 16 (+ 2) % Row 20 \SetRowColor{LightBackground} Conclusion & What follows the then in a conditional \tn % Row Count 18 (+ 2) % Row 21 \SetRowColor{white} Truth Value & If a conditional is true or false \tn % Row Count 20 (+ 2) % Row 22 \SetRowColor{LightBackground} Converse & Palendrome of a conditional \tn % Row Count 22 (+ 2) % Row 23 \SetRowColor{white} Biconditional & The combination of a conditional statement and its converse \tn % Row Count 25 (+ 3) % Row 24 \SetRowColor{LightBackground} Deductive Reasoning/Logical Thinking & The process of reasoning from a given statement to a conclusion \tn % Row Count 28 (+ 3) % Row 25 \SetRowColor{white} Negation & Opposite of the truth value \tn % Row Count 30 (+ 2) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{3.76 cm} x{4.24 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Vocabulary (cont)}} \tn % Row 26 \SetRowColor{LightBackground} Inverse & Negates both the hypothesis and the conclusion \tn % Row Count 3 (+ 3) % Row 27 \SetRowColor{white} Contraposotove & Switches the hypothesis and the conclusion and negates both \tn % Row Count 6 (+ 3) % Row 28 \SetRowColor{LightBackground} Transversal & A line that intersects 2 or more coplaner lines at distinct points \tn % Row Count 10 (+ 4) % Row 29 \SetRowColor{white} Equiangular Triangle & All angles are congruent \tn % Row Count 12 (+ 2) % Row 30 \SetRowColor{LightBackground} Acute Tringle & all angles are acute \tn % Row Count 13 (+ 1) % Row 31 \SetRowColor{white} Right Triangle & one right angle \tn % Row Count 14 (+ 1) % Row 32 \SetRowColor{LightBackground} Obtuse Triangle & one obtuse angle \tn % Row Count 15 (+ 1) % Row 33 \SetRowColor{white} Equalateral Triangle & All sides are congruent \tn % Row Count 17 (+ 2) % Row 34 \SetRowColor{LightBackground} Isosceles Triangle & 2 congruent sides \tn % Row Count 18 (+ 1) % Row 35 \SetRowColor{white} Scalene Triangle & No congruent sides \tn % Row Count 19 (+ 1) % Row 36 \SetRowColor{LightBackground} Exterior angle & Angle formed by a side and an extention of an adjacent side \tn % Row Count 22 (+ 3) % Row 37 \SetRowColor{white} Polygon & A closed plane figure with at least 3 sides that are segments. The sides only intersect at end points, no adjacent sides are congruent \tn % Row Count 29 (+ 7) % Row 38 \SetRowColor{LightBackground} Convex Polygons & No "dents" \tn % Row Count 30 (+ 1) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{3.76 cm} x{4.24 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Vocabulary (cont)}} \tn % Row 39 \SetRowColor{LightBackground} Concave polygon & Has a "dent" or "dents" \tn % Row Count 2 (+ 2) % Row 40 \SetRowColor{white} Equilateral Polygon & a polygon where all sides are congruent \tn % Row Count 4 (+ 2) % Row 41 \SetRowColor{LightBackground} Equiangular polygon & a polygon where all angles are congruent \tn % Row Count 6 (+ 2) % Row 42 \SetRowColor{white} regular polygon & a polygon that is both equiangular and equalateral \tn % Row Count 9 (+ 3) % Row 43 \SetRowColor{LightBackground} Congruent Polygons & Polygons with congruent corresponding sides and angles \tn % Row Count 12 (+ 3) % Row 44 \SetRowColor{white} Corollary & a statement that follows directly from a theorem \tn % Row Count 15 (+ 3) % Row 45 \SetRowColor{LightBackground} Midsegment & a segment that connects the midpoints of 2 sides of a triangle \tn % Row Count 18 (+ 3) % Row 46 \SetRowColor{white} Perpendicular Bisector & a line segment or ray that is perpendicular to a segment through its midpoint \tn % Row Count 22 (+ 4) % Row 47 \SetRowColor{LightBackground} Concurrent & When 3 or more lines intersect in one point \tn % Row Count 25 (+ 3) % Row 48 \SetRowColor{white} Point of concurrency & Point where 3 concurrent lines intersect \tn % Row Count 27 (+ 2) % Row 49 \SetRowColor{LightBackground} Circumcenter & The point of concurrency of the perpendicular bisectors of a triangle \tn % Row Count 31 (+ 4) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{3.76 cm} x{4.24 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Vocabulary (cont)}} \tn % Row 50 \SetRowColor{LightBackground} circumscribed circle & circle that passes through all the vertices of a triangle \tn % Row Count 3 (+ 3) % Row 51 \SetRowColor{white} Obtuse Circumcenter & Lies outside the triangle \tn % Row Count 5 (+ 2) % Row 52 \SetRowColor{LightBackground} Right Circumcenter & midpoint of the hypotenuse \tn % Row Count 7 (+ 2) % Row 53 \SetRowColor{white} Acute circumcenter & Lies within the triangle \tn % Row Count 9 (+ 2) % Row 54 \SetRowColor{LightBackground} Angle Bisector & Ray that divides an angle into to congruent segments \tn % Row Count 12 (+ 3) % Row 55 \SetRowColor{white} Incenter & Point of concurrency of the angle bisectors of a triangle \tn % Row Count 15 (+ 3) % Row 56 \SetRowColor{LightBackground} Inscribed Circle & Largest circle contained in a triangle that touches all three sides \tn % Row Count 19 (+ 4) % Row 57 \SetRowColor{white} Median & Segment whose endpoints are a vertex and the midpoint of the opposite side \tn % Row Count 23 (+ 4) % Row 58 \SetRowColor{LightBackground} centroid & point of concurrency of the medians; always lies within the triangle \tn % Row Count 27 (+ 4) % Row 59 \SetRowColor{white} Altitude & Height of a triangle \tn % Row Count 28 (+ 1) % Row 60 \SetRowColor{LightBackground} Quadrilateral & Polygon with 4 sides \tn % Row Count 29 (+ 1) % Row 61 \SetRowColor{white} Parallelogram & A quadrilateral with 2 pairs of opposite parallel sides \tn % Row Count 32 (+ 3) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{3.76 cm} x{4.24 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Vocabulary (cont)}} \tn % Row 62 \SetRowColor{LightBackground} Rhombus & Quadrilateral with all sides congruent and 2 pairs of opposite parallel sides \tn % Row Count 4 (+ 4) % Row 63 \SetRowColor{white} Rectangle & Parallelogram with four right angles \tn % Row Count 6 (+ 2) % Row 64 \SetRowColor{LightBackground} Square & A parallelogram with four congruent sides and four right angles \tn % Row Count 9 (+ 3) % Row 65 \SetRowColor{white} Kite & Quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent \tn % Row Count 14 (+ 5) % Row 66 \SetRowColor{LightBackground} Trapezoid & A quadrilateral with exaclty one pair of parallel sides \tn % Row Count 17 (+ 3) % Row 67 \SetRowColor{white} Isosceles Trapezoid & A trapezoid whose non-parallel sides are congruent \tn % Row Count 20 (+ 3) % Row 68 \SetRowColor{LightBackground} Consecutive Angles & Angles of a polygon that share a side; are supplementary \tn % Row Count 23 (+ 3) % Row 69 \SetRowColor{white} Base angles & two angles that share a base of a trapezoid \tn % Row Count 26 (+ 3) % Row 70 \SetRowColor{LightBackground} Proportion & a statement that 2 ratios are equal \tn % Row Count 28 (+ 2) % Row 71 \SetRowColor{white} Indirect Measurement & Used to find the lengths of objects that are too difficult to measure directly \tn % Row Count 32 (+ 4) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{3.76 cm} x{4.24 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Vocabulary (cont)}} \tn % Row 72 \SetRowColor{LightBackground} Vector & any quantity with magnitude (size) and direction \tn % Row Count 3 (+ 3) % Row 73 \SetRowColor{white} Magnitude & Distance from initial point to terminal point \tn % Row Count 6 (+ 3) % Row 74 \SetRowColor{LightBackground} Tangent line to a circle & A line on the same plane as a circle that intersects the circle at exactly one point \tn % Row Count 10 (+ 4) % Row 75 \SetRowColor{white} point of tangency & point where a circle and tangent line intersect \tn % Row Count 13 (+ 3) % Row 76 \SetRowColor{LightBackground} Apothem & Perpendicular distance from the center of a regular polygon \tn % Row Count 16 (+ 3) % Row 77 \SetRowColor{white} Circle & The set of all points in a plane equidistant to a given point called the center \tn % Row Count 20 (+ 4) % Row 78 \SetRowColor{LightBackground} radius & a segment w/ one endpoint at the center and the other in the circle \tn % Row Count 24 (+ 4) % Row 79 \SetRowColor{white} Diameter & a segment that contains the center and has both endpoints on a circle \tn % Row Count 28 (+ 4) % Row 80 \SetRowColor{LightBackground} Congruent circles & circles with congruent radii or diameters \tn % Row Count 30 (+ 2) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{3.76 cm} x{4.24 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Vocabulary (cont)}} \tn % Row 81 \SetRowColor{LightBackground} central angle & an angle whose vertex is the center of the circle \tn % Row Count 3 (+ 3) % Row 82 \SetRowColor{white} Arc & Part of circle \tn % Row Count 4 (+ 1) % Row 83 \SetRowColor{LightBackground} Semi-circle & Half a circle \tn % Row Count 5 (+ 1) % Row 84 \SetRowColor{white} Minor Arc & Smaller than a semi-circle \tn % Row Count 7 (+ 2) % Row 85 \SetRowColor{LightBackground} Major arc & Greater than a semi circle \tn % Row Count 9 (+ 2) % Row 86 \SetRowColor{white} adjacent arc & arcs of the same circle that have exactly one point in common \tn % Row Count 12 (+ 3) % Row 87 \SetRowColor{LightBackground} Circumference & Perimeter of a circle \tn % Row Count 13 (+ 1) % Row 88 \SetRowColor{white} concentric circles & coplanar circles that share a center \tn % Row Count 15 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{x{3.92 cm} x{4.08 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{All the other crap continued}} \tn % Row 0 \SetRowColor{LightBackground} Theorem 12-1 & If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency \tn % Row Count 6 (+ 6) % Row 1 \SetRowColor{white} Theorem 12-2 & If a line is in the plane of a circle is a radius at its endpoint on the circle, then the line is tangent to the circle \tn % Row Count 12 (+ 6) % Row 2 \SetRowColor{LightBackground} Theorem 12-3 & The two segments tangent to a circle from a point outside the circle are congruent \tn % Row Count 17 (+ 5) % Row 3 \SetRowColor{white} Perimiter of a Square & 4S \tn % Row Count 19 (+ 2) % Row 4 \SetRowColor{LightBackground} Area of a Square & S\textasciicircum{}2\textasciicircum{} \tn % Row Count 20 (+ 1) % Row 5 \SetRowColor{white} Perimiter of a \seqsplit{Rectangle/Parallelogram} & 2B+2H \tn % Row Count 22 (+ 2) % Row 6 \SetRowColor{LightBackground} Area of a \seqsplit{Rectangle/Parallelogram} & BH \tn % Row Count 24 (+ 2) % Row 7 \SetRowColor{white} Circumference & PiD or 2PiR \tn % Row Count 25 (+ 1) % Row 8 \SetRowColor{LightBackground} Area of a Circle & PiR\textasciicircum{}2\textasciicircum{} \tn % Row Count 26 (+ 1) % Row 9 \SetRowColor{white} Perimiter of a Triangle & S1+S2+S3 \tn % Row Count 28 (+ 2) % Row 10 \SetRowColor{LightBackground} Area of a Triangle & .5(b*h) \tn % Row Count 29 (+ 1) % Row 11 \SetRowColor{white} Area of a Trapezoid & .5(b1*b2)h \tn % Row Count 30 (+ 1) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{3.92 cm} x{4.08 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{All the other crap continued (cont)}} \tn % Row 12 \SetRowColor{LightBackground} Area of a Rhombus/Kite & .5(d1*d2) \tn % Row Count 2 (+ 2) % Row 13 \SetRowColor{white} Area of Regular Polygons & .5AP \tn % Row Count 4 (+ 2) % Row 14 \SetRowColor{LightBackground} Arc Addition Postulate & The whole is equal to the sum of its parts \tn % Row Count 7 (+ 3) % Row 15 \SetRowColor{white} \mymulticolumn{2}{x{8.4cm}}{Arc Length} \tn % Row Count 8 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Postulates, Formulas, etc...}} \tn % Row 0 \SetRowColor{LightBackground} Ruler Postulate & The points of a line can be put into 1:1 correspondence with the real numbers AB=|A-B| \tn % Row Count 5 (+ 5) % Row 1 \SetRowColor{white} Segment addition postulate & If three points (A,B,C) are colliner and B is between A and C, then AB+BC=AC; The whole is equal to te sum of its parts \tn % Row Count 11 (+ 6) % Row 2 \SetRowColor{LightBackground} Vertical Angles Theorem & Vertical angles are congruent \tn % Row Count 13 (+ 2) % Row 3 \SetRowColor{white} Law of detachment & If P-\textgreater{}Q and P is true, then Q is true \tn % Row Count 15 (+ 2) % Row 4 \SetRowColor{LightBackground} Law of syllogism & If P-\textgreater{}Q and Q-\textgreater{}R are true, then P-\textgreater{}R is true \tn % Row Count 18 (+ 3) % Row 5 \SetRowColor{white} Addition Property & A=B, then A+C=B+C \tn % Row Count 19 (+ 1) % Row 6 \SetRowColor{LightBackground} Subtraction Property & A=B, then A-C=B-C \tn % Row Count 20 (+ 1) % Row 7 \SetRowColor{white} Multiplication Property & A=B, then A{\emph{C=B}}C \tn % Row Count 22 (+ 2) % Row 8 \SetRowColor{LightBackground} Division Property & A=B and C is not 0, then (A/C)=(B/C) \tn % Row Count 24 (+ 2) % Row 9 \SetRowColor{white} Reflexive Property & A=A \tn % Row Count 25 (+ 1) % Row 10 \SetRowColor{LightBackground} Symmetric Property & A=B and B=A \tn % Row Count 26 (+ 1) % Row 11 \SetRowColor{white} Transitive Property & A=B and B=C, then A=C \tn % Row Count 28 (+ 2) % Row 12 \SetRowColor{LightBackground} Substitution Property & A=B, so B can replace A in equations \tn % Row Count 30 (+ 2) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Postulates, Formulas, etc... (cont)}} \tn % Row 13 \SetRowColor{LightBackground} Distributive property & A(B+C)= AB+AC \tn % Row Count 2 (+ 2) % Row 14 \SetRowColor{white} Congruent Supplements Theorem & If 2 ngles are supplements of the same angle or of congruent angles, then that angles are congruent \tn % Row Count 7 (+ 5) % Row 15 \SetRowColor{LightBackground} Congruent Complements Theorem & If 2 angles are complements of the same angle or of congruent angles, then the 2 angles are congruent \tn % Row Count 13 (+ 6) % Row 16 \SetRowColor{white} Right Angle Congruence & All right angles are congruent \tn % Row Count 15 (+ 2) % Row 17 \SetRowColor{LightBackground} Corresponding angles are congruent & Implys parallel lines \tn % Row Count 17 (+ 2) % Row 18 \SetRowColor{white} Alternate Interior angles are congruent & Implys parallel lines \tn % Row Count 19 (+ 2) % Row 19 \SetRowColor{LightBackground} Same side Interior angles are supplementry & Implys parallel lines \tn % Row Count 22 (+ 3) % Row 20 \SetRowColor{white} Alternate exterior angles are congruent & Implys parallel lines \tn % Row Count 24 (+ 2) % Row 21 \SetRowColor{LightBackground} Same side Exterior angles are supplementry & Implys parallel lines \tn % Row Count 27 (+ 3) % Row 22 \SetRowColor{white} If two lines are parallel to the same line & Then they are Parallel \tn % Row Count 30 (+ 3) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Postulates, Formulas, etc... (cont)}} \tn % Row 23 \SetRowColor{LightBackground} If 2 coplaner lines are perpendicular to the same line & then they are parallel \tn % Row Count 3 (+ 3) % Row 24 \SetRowColor{white} Sum of a triangle's angle measures & 180 degrees \tn % Row Count 5 (+ 2) % Row 25 \SetRowColor{LightBackground} Triangle exterior angle Theorem & The measure of each exterior angle of a triangle equals the sum of it's two remote exterior angles \tn % Row Count 10 (+ 5) % Row 26 \SetRowColor{white} Degrees in a Quadrilateral & 360 \tn % Row Count 12 (+ 2) % Row 27 \SetRowColor{LightBackground} Degrees on a Pentagon & 540 \tn % Row Count 14 (+ 2) % Row 28 \SetRowColor{white} Degrees in a hexagon & 720 \tn % Row Count 15 (+ 1) % Row 29 \SetRowColor{LightBackground} Degrees in a octagon & 1080 \tn % Row Count 16 (+ 1) % Row 30 \SetRowColor{white} Theorem 4-1 & If two angles of one triangle are congruent to two angles of another triangle, then they are congruent \tn % Row Count 22 (+ 6) % Row 31 \SetRowColor{LightBackground} CPCTC & Corresponding Parts of Congruent Triangles are congruent \tn % Row Count 25 (+ 3) % Row 32 \SetRowColor{white} SSS; Side Side Side & If 3 sides of a triangle are congruent to 3 sides of another triangle, then they are congruent \tn % Row Count 30 (+ 5) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Postulates, Formulas, etc... (cont)}} \tn % Row 33 \SetRowColor{LightBackground} SAS; Side Angle Side & If 2 sides and 1 included angle of a triangle are congruent to the 2 sides and angle of another triangle, then they are congruent \tn % Row Count 7 (+ 7) % Row 34 \SetRowColor{white} ASA; Angle Side Angle & If 2 angles and an included side of a triangle are congruent to 2 angles and included side of another triangle, then they are congruent \tn % Row Count 14 (+ 7) % Row 35 \SetRowColor{LightBackground} AAS; Angle Angle Side & If 2 angles and a non-included side of a triangle are congruent to 2 angles and non-included side of another triangle, then they are congruent \tn % Row Count 22 (+ 8) % Row 36 \SetRowColor{white} Isosceles Triangle Theorem & If the 2 sides of a triangle are congruent, then the base angles are congruent \tn % Row Count 26 (+ 4) % Row 37 \SetRowColor{LightBackground} Converse Isosceles Triangle Theorem & If the 2 base angles of a triangle are congruent, then the sides are congruent \tn % Row Count 30 (+ 4) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Postulates, Formulas, etc... (cont)}} \tn % Row 38 \SetRowColor{LightBackground} HL; Hypotenuse Leg & If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then they are congruent \tn % Row Count 7 (+ 7) % Row 39 \SetRowColor{white} Triangle Midsegment theorem & If a segment joins the midpoints if 2 sides of a triangle, then the segment is parallel to the third side and is half the length \tn % Row Count 14 (+ 7) % Row 40 \SetRowColor{LightBackground} Perpendicular Bisector theorem & If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment \tn % Row Count 20 (+ 6) % Row 41 \SetRowColor{white} Converse of the Perpendicular Bisector theorem & If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment \tn % Row Count 26 (+ 6) % Row 42 \SetRowColor{LightBackground} Angle Bisector theorem & If a point is on the angle bisector of an angle, then the point is wquidistant to the sides of the angle \tn % Row Count 32 (+ 6) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Postulates, Formulas, etc... (cont)}} \tn % Row 43 \SetRowColor{LightBackground} the converse of the Angle Bisector theorem & If a point in the interior of an angle is equidistant to the sides of the angle, then the point is on the angle bisector \tn % Row Count 6 (+ 6) % Row 44 \SetRowColor{white} Theorem 5-6 & The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices \tn % Row Count 12 (+ 6) % Row 45 \SetRowColor{LightBackground} Theorem 5-7 & The Bisectors of the angles of a triangle are concurrent at a point equidistant from the sides \tn % Row Count 17 (+ 5) % Row 46 \SetRowColor{white} Theorem 5-8 & The mediams of a triangle are concurrent at a point that is two thirds the distnce from each vertex to the mid point of the opposite side \tn % Row Count 24 (+ 7) % Row 47 \SetRowColor{LightBackground} Theorem 5-9 & The Lines that contain the altitudes of a triangle are concurrent \tn % Row Count 28 (+ 4) % Row 48 \SetRowColor{white} Comparison Property & If A=B+C and C\textgreater{}0, then A\textgreater{}B \tn % Row Count 30 (+ 2) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Postulates, Formulas, etc... (cont)}} \tn % Row 49 \SetRowColor{LightBackground} \mymulticolumn{2}{x{8.4cm}}{Distance formula} \tn % Row Count 1 (+ 1) % Row 50 \SetRowColor{white} \mymulticolumn{2}{x{8.4cm}}{Midpoint Formula} \tn % Row Count 2 (+ 1) % Row 51 \SetRowColor{LightBackground} Slope Intercept Form & Y=Mx+B \tn % Row Count 3 (+ 1) % Row 52 \SetRowColor{white} Standard Form & Ax+By=C \tn % Row Count 4 (+ 1) % Row 53 \SetRowColor{LightBackground} Point Slope Form & Y-Y\textasciicircum{}1\textasciicircum{}=M(X-X\textasciicircum{}1\textasciicircum{}) \tn % Row Count 5 (+ 1) % Row 54 \SetRowColor{white} Theorem 6-1 & Opposite sides of a parallelogram are congruent \tn % Row Count 8 (+ 3) % Row 55 \SetRowColor{LightBackground} Theorem 6-2 & Opposite angles of a parallelogram are congruent \tn % Row Count 11 (+ 3) % Row 56 \SetRowColor{white} Theorem 6-3 & The diagonals of a parallelogram bisect each other \tn % Row Count 14 (+ 3) % Row 57 \SetRowColor{LightBackground} Theorem 6-4 & If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal \tn % Row Count 21 (+ 7) % Row 58 \SetRowColor{white} Theorem 6-5 & If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram \tn % Row Count 27 (+ 6) % Row 59 \SetRowColor{LightBackground} Theorem 6-6 & If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram \tn % Row Count 33 (+ 6) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Postulates, Formulas, etc... (cont)}} \tn % Row 60 \SetRowColor{LightBackground} Theorem 6-7 & If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram \tn % Row Count 5 (+ 5) % Row 61 \SetRowColor{white} Theorem 6-8 & if one pair of opposite sides of a quadrilateral are both parallel and congruent, then the quadrilateral is a parallelogram \tn % Row Count 12 (+ 7) % Row 62 \SetRowColor{LightBackground} Theorem 6-9 & Each diagonal of a rhombus bisects 2 angles of the rhombus \tn % Row Count 15 (+ 3) % Row 63 \SetRowColor{white} Theorem 6-10 & The diagonals of a rhombus are perpendicular \tn % Row Count 18 (+ 3) % Row 64 \SetRowColor{LightBackground} Theorem 6-11 & The Diagonals of a rectangle are congruent \tn % Row Count 21 (+ 3) % Row 65 \SetRowColor{white} Theorem 6-12 & If one diagonal of a parallelogram bisects 2 angles of the parallelogram, then it is a rhombus \tn % Row Count 26 (+ 5) % Row 66 \SetRowColor{LightBackground} Theorem 6-13 & If the diagonals of a parallelogram are perpendicular, then it is a rhombus \tn % Row Count 30 (+ 4) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Postulates, Formulas, etc... (cont)}} \tn % Row 67 \SetRowColor{LightBackground} Theorem 6-14 & If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle \tn % Row Count 5 (+ 5) % Row 68 \SetRowColor{white} Theorem 6-15 & The Base angles of an isosceles trapezoid are congruent \tn % Row Count 8 (+ 3) % Row 69 \SetRowColor{LightBackground} theorem 6-16 & Diagonals of an isosceles trapezoid are congruent \tn % Row Count 11 (+ 3) % Row 70 \SetRowColor{white} AA\textasciitilde{}; angle angle similarity & If 2 angles of one triangle are congruent to 2 angles of another triangle, then they are similar \tn % Row Count 16 (+ 5) % Row 71 \SetRowColor{LightBackground} SAS\textasciitilde{}; Side Angle Side similarity & If an angle of one triangle is congruent to an angle of an angle of a second triangle, and the sides surrounding the angle are propotional, then they are similar \tn % Row Count 25 (+ 9) % Row 72 \SetRowColor{white} SSS\textasciitilde{}; Side Side Side similarity & If the corresponding sides of two triangles are proportional, then they are similar \tn % Row Count 30 (+ 5) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Postulates, Formulas, etc... (cont)}} \tn % Row 73 \SetRowColor{LightBackground} Theorem 7-3 & The altitude to the hypotenuse of a right triangle divides the triangle into 2 triangles that are similar to the original and eachother \tn % Row Count 7 (+ 7) % Row 74 \SetRowColor{white} Corollary 1 to Theorem 7-3 & The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse \tn % Row Count 14 (+ 7) % Row 75 \SetRowColor{LightBackground} Corollary 2 to Theorem 7-3 & The altitude of the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse \tn % Row Count 26 (+ 12) % Row 76 \SetRowColor{white} Side-Splitter Theorem & If a line is parallel to one side of a triangle and intersects the other two sides, then its divides those sides proportionally \tn % Row Count 33 (+ 7) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Postulates, Formulas, etc... (cont)}} \tn % Row 77 \SetRowColor{LightBackground} Corollary to Side-Splitter & If three parallel lines intersect 2 transversals, then the segments intercepted on the transversals are proportional \tn % Row Count 6 (+ 6) % Row 78 \SetRowColor{white} Theorem 7-5 & If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle \tn % Row Count 14 (+ 8) % Row 79 \SetRowColor{LightBackground} Pythagorean Theorem & A\textasciicircum{}2\textasciicircum{}+B\textasciicircum{}2\textasciicircum{}=C\textasciicircum{}2\textasciicircum{} \tn % Row Count 15 (+ 1) % Row 80 \SetRowColor{white} Pythagoren Triples & \{3,4,5\} \{5,12,13\} \{8,15,17\} \{7,24,25\} \tn % Row Count 17 (+ 2) % Row 81 \SetRowColor{LightBackground} C\textasciicircum{}2\textasciicircum{}=A\textasciicircum{}2\textasciicircum{}+B\textasciicircum{}2\textasciicircum{} & Right Triangle \tn % Row Count 18 (+ 1) % Row 82 \SetRowColor{white} C\textasciicircum{}2\textasciicircum{}\textgreater{}A\textasciicircum{}2\textasciicircum{}+B\textasciicircum{}2\textasciicircum{} & Obtuse Triangle \tn % Row Count 19 (+ 1) % Row 83 \SetRowColor{LightBackground} C\textasciicircum{}2\textasciicircum{}\textless{}A\textasciicircum{}2\textasciicircum{}+B\textasciicircum{}2\textasciicircum{} & Acute Triangle \tn % Row Count 20 (+ 1) % Row 84 \SetRowColor{white} 45-45-90 Triangle & In a 45-45-90 triangle, both legs are congruent and the length of the hypotenuse is square root of 2 times the length of a leg \tn % Row Count 27 (+ 7) % Row 85 \SetRowColor{LightBackground} 30-60-90 Triangle & The Hypotenuse is double the length of the shortest leg and the length of the longer leg is square root of 3 times the length of the shorter leg \tn % Row Count 35 (+ 8) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Postulates, Formulas, etc... (cont)}} \tn % Row 86 \SetRowColor{LightBackground} Tangent & Opposite/Adjacent \tn % Row Count 1 (+ 1) % Row 87 \SetRowColor{white} Sine & Opposite/Hypotenuse \tn % Row Count 2 (+ 1) % Row 88 \SetRowColor{LightBackground} Cosine & Adjacent/Hypotenuse \tn % Row Count 3 (+ 1) % Row 89 \SetRowColor{white} SohCahToa & You know what this means, dummy \tn % Row Count 5 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}