% Author: Izaak Neutelings (December 2021) % Inspiration: % https://en.wikipedia.org/wiki/Quadrilateral#Taxonomy % https://commons.wikimedia.org/wiki/File:Quadrilateral_hierarchy_svg.svg \documentclass[border=3pt,tikz]{standalone} \usetikzlibrary{calc} \usetikzlibrary{shadows.blur} % for blur shadow \usepackage[outline]{contour} % glow around text \contourlength{1.3pt} \tikzset{>=latex} % for LaTeX arrow head \colorlet{myred}{red!80!black} \colorlet{myblue}{blue!80!black} \colorlet{mygreen}{green!80!black} \colorlet{mypurple}{red!70!blue!80!black} \colorlet{mydarkred}{red!60!black} \colorlet{mylightred}{red!50!black!8} \colorlet{mydarkblue}{blue!50!black} \colorlet{mydarkgreen}{green!50!black} \colorlet{mylightblue}{blue!50!black!8} \colorlet{mydarkorange}{orange!80!black} \colorlet{mydarkpurple}{red!60!blue!65!black} \tikzstyle{myshape}=[ thick,draw=mydarkblue,fill=mylightblue,rounded corners=0.01, blur shadow={shadow blur steps=40,shadow xshift=1pt,shadow yshift=-1pt}] \tikzstyle{myset}=[draw=mydarkred,fill=mydarkred!3,rounded corners=6,line width=0.55] \tikzstyle{mygreenset}=[myset,draw=mydarkgreen,fill=mydarkgreen!3] \tikzstyle{myorangeset}=[myset,draw=mydarkorange,fill=mydarkorange!3] \tikzstyle{mydashed}=[very thin,dashed,draw=black!50,opacity=0.4] \tikzstyle{purple line}=[thick,draw=mydarkpurple] \tikzstyle{frontline}=[white,double=black,double distance=0.4,line width=0.5] \tikzset{ narcs/.initial=1, % number of (dark) arcs nmarks/.initial=0, % number of marks to indicate equal angles marklen/.initial=0.27, % length of marks markdist/.initial=3, % distance between marks markshift/.initial=0, % shift from origin/center angshift/.initial=1, % shift from origin/center angcol/.style={draw=#1,fill=#1!40}, % shorthand to fill (light) & draw (dark) angcol/.default={myblue}, pics/mark angle/.style args={(#1)-(#2)-(#3):#4}{ % arc: any angle code={ \tikzset{narcs/.get=\narcs} \tikzset{nmarks/.get=\nmarks} \tikzset{marklen/.get=\marklen} \tikzset{markdist/.get=\markdist} \tikzset{angshift/.get=\angshift} \pgfmathanglebetweenpoints{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#1}{center}} \pgfmathsetmacro\tmpAngA{\pgfmathresult} \pgfmathanglebetweenpoints{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#3}{center}} \pgfmathsetmacro\tmpAngB{\tmpAngA<\pgfmathresult?\pgfmathresult:\pgfmathresult+360} \pgfmathsetmacro\tmpAveAng{(\tmpAngA+\tmpAngB)/2} \coordinate (tmpS) at (\tmpAveAng:{\angshift*0.01/abs(sin((\tmpAngB-\tmpAngA)/2))}); % shift \coordinate (tmp#2) at ($(#2)+(tmpS)$); \coordinate (tmpA) at ($(tmp#2)+(\tmpAngA:#4)$); \fill[pic actions,draw=none] % fill circle segment (tmp#2) -- (tmpA) arc(\tmpAngA:\tmpAngB:#4) -- cycle; \draw[pic actions,fill=none] (tmpA) arc(\tmpAngA:\tmpAngB:#4); \ifnum\narcs>0 \foreach \i [evaluate={\dr=0.02*\markdist*(\i-1);}] in {1,...,\narcs}{ \draw[pic actions,fill=none] % draw angle mark (tmpA)++(\tmpAngA:-\dr) arc(\tmpAngA:\tmpAngB:#4-\dr); } \fi \ifnum\nmarks>0 \foreach \i [evaluate={\a=\tmpAveAng+\markdist/(#4)*(\i-0.5-\nmarks/2);}] in {1,...,\nmarks}{ \draw (tmp#2)++(\a:{#4-\marklen*max(#4/2,\marklen)}) --++ ({(\a+2*\tmpAveAng)/3}:{2*\marklen*max(#4/2,\marklen)}); } \fi } }, pics/right angle/.style args={(#1)-(#2)-(#3):#4}{ % right angle code={ \tikzset{angshift/.get=\angshift} \pgfmathanglebetweenpoints{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#1}{center}} \pgfmathsetmacro\tmpAngA{\pgfmathresult} %\pgfmathanglebetweenpoints{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#1}{center}} %\pgfmathsetmacro\tmpAveAng{(\tmpAngA+(\tmpAngA>\pgfmathresult?\pgfmathresult:\pgfmathresult+360))/2} \coordinate (tmpS) at (\tmpAngA+45:\angshift*0.01); % shift \coordinate (tmp#1) at ($(#1)+(tmpS)$); \coordinate (tmp#2) at ($(#2)+(tmpS)$); \coordinate (tmp#3) at ($(#3)+(tmpS)$); \coordinate (tmpRA) at ($(tmp#2)+(\tmpAngA+45:#4)$); \fill[pic actions,draw=none] % fill square area ($(tmp#2)!(tmpRA)!(tmp#1)$) -- (tmpRA) -- ($(tmp#2)!(tmpRA)!(tmp#3)$) -- (tmp#2) -- cycle; \draw[pic actions,fill=none] % draw orthogonal mark ($(tmp#2)!(tmpRA)!(tmp#1)$) -- (tmpRA) -- ($(tmp#2)!(tmpRA)!(tmp#3)$); } }, pics/mark line/.style args={(#1)-(#2):#3}{ % mark equal lengths code={ \tikzset{nmarks/.get=\nmarks} \tikzset{marklen/.get=\marklen} \tikzset{markdist/.get=\markdist} \tikzset{markshift/.get=\markshift} \pgfmathanglebetweenpoints{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#1}{center}} \pgfmathsetmacro\tmpAng{\pgfmathresult} \pgfmathsetmacro\nmarks{int(\nmarks==0?1:\nmarks)} \coordinate (tmpM) at ($(#1)!0.5+\markshift!(#2)$); % midpoint \foreach \i [parse=true] in {1,...,\nmarks)}{ \draw ($(tmpM)+(\tmpAng:{(\i-0.5-\nmarks/2)*0.015*\markdist})$) ++(\tmpAng+#3-180:0.3*\marklen) --++ (\tmpAng+#3:0.6*\marklen); } } } } %\def\name#1#2{\node[below=-1,align=center] at (#1) {\contour{white}{#2}};} \pgfdeclarelayer{back} % to draw on background \pgfsetlayers{back,main} % set order \begin{document} %%%%%%%%%%%%%%%%%%%%%%% % COMMON TRAPEZIA % %%%%%%%%%%%%%%%%%%%%%%% \def\xsquare{0.5} % x position square \def\ysquare{0.0} % y position square \def\yrectangle{1.0} % y position rectangle \def\yrighttrap{2.0} % y position right-angled trapezium \def\colpara{white} % contour color for parallelograms \def\coltrap{white} % contour color for isosceles trapezia \def\commontraps{ % trapezia common in each picture \message{^^J Common trapezia} %%%% LEVEL 1 %%%%%%%%%%%%%%%%%%%%%%%%%% % SQUARE \def\a{1.0} % length of each sides \begin{scope}[shift={(\xsquare*\W,\ysquare*\H)}] \node[below=1] at (0,0) {\contour{white}{square}}; \coordinate (SW) at (-\a/2, 0); \coordinate (NW) at (-\a/2,\a); \coordinate (NE) at ( \a/2,\a); \coordinate (SE) at ( \a/2, 0); \coordinate (square) at (0,\a/2); \draw[myshape] (SW) rectangle (NE); \pic[angcol=myblue] {right angle={(SE)-(SW)-(NW):0.22}}; \pic[angcol=myblue] {right angle={(SW)-(NW)-(NE):0.22}}; \pic[angcol=myblue] {right angle={(NW)-(NE)-(SE):0.22}}; \pic[angcol=myblue] {right angle={(NE)-(SE)-(SW):0.22}}; \pic[myblue] {mark line={(NE)-(NW):90}}; \pic[myblue] {mark line={(NW)-(SW):90}}; \pic[myblue] {mark line={(SW)-(SE):90}}; \pic[myblue] {mark line={(NE)-(SE):90}}; \end{scope} %%%% LEVEL 2 %%%%%%%%%%%%%%%%%%%%%%%%%% % RHOMBUS \def\ang{60} % smaller vertex angle (N or SW) \pgfmathsetmacro\h{\a*sqrt(2-2*cos(\ang))} % height / diagonal \begin{scope}[shift={(-0.5*\W,\H)}] \node[below=-1] at (0,0) {\contour{\colpara}{rhombus}}; %\coordinate (SW) at (-\a/2,0); %\coordinate (SE) at (\a/2,0); %\coordinate (NW) at ($(SW)+(\ang:\a)$); %\coordinate (NE) at ($(SE)+(\ang:\a)$); %\draw[myshape] (SW) -- (SE) -- (NE) -- (NW) -- cycle; %\pic[nmarks=1,angcol=myred] {mark angle={(SE)-(SW)-(NW):0.20}}; %\pic[nmarks=2,angcol=mygreen] {mark angle={(SW)-(NW)-(NE):0.20}}; %\pic[nmarks=1,angcol=myred] {mark angle={(NW)-(NE)-(SE):0.20}}; %\pic[nmarks=2,angcol=mygreen] {mark angle={(NE)-(SE)-(SW):0.20}}; \coordinate (S) at (0,0); \coordinate (E) at (\ang/2:\a); \coordinate (W) at (180-\ang/2:\a); \coordinate (N) at (0,\h); \coordinate (rhombus) at (0,\h/2); \draw[myshape] (S) -- (W) -- (N) -- (E) -- cycle; \pic[nmarks=2,angcol=mygreen] {mark angle={(W)-(N)-(E):0.20}}; \pic[nmarks=2,angcol=mygreen] {mark angle={(E)-(S)-(W):0.20}}; \pic[nmarks=1,angcol=myred] {mark angle={(N)-(E)-(S):0.20}}; \pic[nmarks=1,angcol=myred] {mark angle={(S)-(W)-(N):0.20}}; \pic[myblue] {mark line={(S)-(E):90}}; \pic[myblue] {mark line={(E)-(N):90}}; \pic[myblue] {mark line={(N)-(W):90}}; \pic[myblue] {mark line={(W)-(S):90}}; \end{scope} % RECTANGLE \def\a{1.0} % length of short side \def\b{1.5} % length of long side \begin{scope}[shift={(0.5*\W,\yrectangle*\H)}] \node[below=-1] at (0,0) {\contour{white}{rectangle}}; \coordinate (SW) at (-\b/2,0); \coordinate (NW) at (-\b/2,\a); \coordinate (NE) at ( \b/2,\a); \coordinate (SE) at ( \b/2,0); \coordinate (rectangle) at (0,\a/2); \draw[myshape] (SW) rectangle (NE); \draw[purple line] (SW) -- (NW) (SE) -- (NE); \pic[angcol=myblue] {right angle={(SE)-(SW)-(NW):0.22}}; \pic[angcol=myblue] {right angle={(SW)-(NW)-(NE):0.22}}; \pic[angcol=myblue] {right angle={(NW)-(NE)-(SE):0.22}}; \pic[angcol=myblue] {right angle={(NE)-(SE)-(SW):0.22}}; \pic[nmarks=1,markshift=0.07,myblue] {mark line={(NW)-(NE):90}}; \pic[nmarks=1,markshift=0.03,myblue] {mark line={(SW)-(SE):90}}; \pic[nmarks=2,mypurple] {mark line={(NW)-(SW):90}}; \pic[nmarks=2,mypurple] {mark line={(NE)-(SE):90}}; \end{scope} % 3-equal-sides TRAPEZIUM \def\a{1.1} % length of short sides \def\ang{68} % length of long side \begin{scope}[shift={(1.5*\W,\H)}] \node[below=-1,align=center] at (0,0) { \contour{\coltrap}{3-equal-sides}\\[-0.3em] \contour{\coltrap}{trapezium}}; \coordinate (SW) at ({-\a*(cos(\ang)+0.5)},0); \coordinate (NW) at (-\a/2,{\a*sin(\ang)}); \coordinate (NE) at ( \a/2,{\a*sin(\ang)}); \coordinate (SE) at ({\a*(cos(\ang)+0.5)},0); \coordinate (3 trapezium) at (0,\a/2); \draw[myshape] (SW) -- (SE) -- (NE) -- (NW) -- cycle; \pic[nmarks=2,angcol=mygreen] {mark angle={(SW)-(NW)-(NE):0.20}}; \pic[nmarks=2,angcol=mygreen] {mark angle={(NW)-(NE)-(SE):0.20}}; \pic[nmarks=1,angcol=myred] {mark angle={(SE)-(SW)-(NW):0.21}}; \pic[nmarks=1,angcol=myred] {mark angle={(NE)-(SE)-(SW):0.21}}; \pic[myblue,markshift=-0.07] {mark line={(NE)-(NW):90}}; \pic[myblue,markshift= 0.0] {mark line={(NW)-(SW):90}}; \pic[myblue,markshift= 0.0] {mark line={(NE)-(SE):90}}; \end{scope} %%%% LEVEL 3 %%%%%%%%%%%%%%%%%%%%%%%%%% % PARALLELOGRAM \begin{scope}[shift={(-0.5*\W,2*\H)}] \node[below=-1] at (0,0) {\contour{\colpara}{parallelogram}}; \def\a{1.0} % length short sides \def\b{1.4} % length long sides \def\ang{60} % smaller vertex angle (SW) \coordinate (SW) at ({-\b/2-0.4*\a*cos(\ang)},0); \coordinate (SE) at ($(SW)+(\b,0)$); \coordinate (NW) at ($(SW)+(\ang:\a)$); \coordinate (NE) at ($(SE)+(\ang:\a)$); \coordinate (parallelogram) at (0,{\a*sin(\ang)/2}); \draw[myshape] (SW) -- (SE) -- (NE) -- (NW) -- cycle; \draw[purple line] (SW) -- (NW) (SE) -- (NE); \pic[nmarks=2,angcol=mygreen] {mark angle={(SW)-(NW)-(NE):0.20}}; \pic[nmarks=2,angcol=mygreen] {mark angle={(NE)-(SE)-(SW):0.20}}; \pic[nmarks=1,angcol=myred] {mark angle={(SE)-(SW)-(NW):0.22}}; \pic[nmarks=1,angcol=myred] {mark angle={(NW)-(NE)-(SE):0.22}}; \pic[nmarks=1,markshift=0.02,myblue] {mark line={(NW)-(NE):90}}; \pic[nmarks=1,markshift=0.05,myblue] {mark line={(SW)-(SE):90}}; \pic[nmarks=2,mypurple] {mark line={(NW)-(SW):90}}; \pic[nmarks=2,mypurple] {mark line={(NE)-(SE):90}}; \end{scope} % RIGHT-ANGLED TRAPEZIUM \begin{scope}[shift={(0.5*\W,\yrighttrap*\H)}] \node[below=-1,align=center] at (0,0) { \contour{white}{right-angled}\\[-0.3em] \contour{white}{trapezium}}; \def\h{1.0} % height \def\a{0.9} % length of short horizontal sides \def\b{1.7} % length of long horizontal sides \coordinate (SW) at (-\b/2,0); \coordinate (NW) at (-\b/2,\h); \coordinate (NE) at (\a-\b/2,\h); \coordinate (SE) at (\b/2,0); \coordinate (right trapezium) at (0,\h/2); \draw[myshape] (SW) -- (SE) -- (NE) -- (NW) -- cycle; \pic[angcol=myblue] {right angle={(SE)-(SW)-(NW):0.22}}; \pic[angcol=myblue] {right angle={(SW)-(NW)-(NE):0.22}}; \end{scope} % ISOSCELES TRAPEZIUM \begin{scope}[shift={(1.5*\W,2*\H)}] \node[below=-1,align=center] at (0,0) { \contour{\coltrap}{isosceles}\\[-0.3em] \contour{\coltrap}{trapezium}}; \def\h{1.0} % height \def\a{0.9} % length of short horizontal sides \def\b{1.7} % length of long horizontal sides \coordinate (SW) at (-\b/2,0); \coordinate (NW) at (-\a/2,\h); \coordinate (NE) at ( \a/2,\h); \coordinate (SE) at ( \b/2,0); \coordinate (2 trapezium) at (0,\h/2); \draw[myshape] (SW) -- (SE) -- (NE) -- (NW) -- cycle; \pic[nmarks=2,angcol=mygreen] {mark angle={(SW)-(NW)-(NE):0.20}}; \pic[nmarks=2,angcol=mygreen] {mark angle={(NW)-(NE)-(SE):0.20}}; \pic[nmarks=1,angcol=myred] {mark angle={(SE)-(SW)-(NW):0.21}}; \pic[nmarks=1,angcol=myred] {mark angle={(NE)-(SE)-(SW):0.21}}; \pic[myblue,markshift= 0.0] {mark line={(NW)-(SW):90}}; \pic[myblue,markshift= 0.0] {mark line={(NE)-(SE):90}}; \end{scope} } %%%%%%%%%%%%%%%%%%%% % COMMON KITES % %%%%%%%%%%%%%%%%%%%% \def\xkite{-1.5} % x position kites (to shift for bicentric) \def\ykite{2} % y position kites (to shift for bicentric) \def\colkite{white} % contour color for kites \def\commonkites{ % common kites in each picture \message{^^J Common kites} %%%% LEVEL 2 %%%%%%%%%%%%%%%%%%%%%%%%%% % RIGHT KITE % https://en.wikipedia.org/wiki/Right_kite#Metric_formulas \begin{scope}[shift={(\xkite*\W,\H)}] \node[below=-1] at (0,0) {\contour{\colkite}{right kite}}; \def\a{0.8} % length short sides \def\b{1.0} % length long sides \pgfmathsetmacro\ang{atan2(\b,\a)} % acute angle \coordinate (S) at (0,0); \coordinate (E) at (90-\ang:\a); \coordinate (N) at (0,{sqrt(\a^2+\b^2)}); % diagonal \coordinate (W) at (90+\ang:\a); \coordinate (right kite) at (0,\a/2); \draw[myshape] (S) -- (E) -- (N) -- (W) -- cycle; \draw[purple line] (E) -- (N) -- (W); \pic[angcol=myblue] {right angle={(S)-(W)-(N):0.20}}; \pic[angcol=myblue] {right angle={(N)-(E)-(S):0.20}}; \pic[nmarks=2,mypurple] {mark line={(E)-(N):90}}; \pic[nmarks=2,mypurple] {mark line={(N)-(W):90}}; \pic[nmarks=1,myblue] {mark line={(S)-(E):90}}; \pic[nmarks=1,myblue] {mark line={(W)-(S):90}}; \end{scope} %%%% LEVEL 3 %%%%%%%%%%%%%%%%%%%%%%%%%% % KITE \begin{scope}[shift={(\xkite*\W,\ykite*\H)}] \ifdim \xkite pt=-1.5 pt \relax % for reduced version \node[below=-1] at (0,0) {\contour{\colkite}{kite}}; \else \ifdim \xkite pt=-1.7 pt \relax % for reduced version \node[below=-1] at (0,0) {\contour{\colkite}{kite}}; % for extended versions \else \node[below=-1,align=center] at (0,0) { \contour{\colkite}{\footnotesize(convex)}\\[-0.3em] \contour{\colkite}{kite}}; \fi \fi \def\a{0.8} % length short sides \def\h{1.1} % height of northern vertex \def\ang{140} % south vertex angle \coordinate (S) at (0,0); \coordinate (E) at (90-\ang/2:\a); \coordinate (N) at (0,\h); \coordinate (W) at (90+\ang/2:\a); \coordinate (kite) at (0,\h/2); \draw[myshape] (S) -- (E) -- (N) -- (W) -- cycle; \draw[purple line] (E) -- (N) -- (W); \pic[nmarks=1,angcol=myred] {mark angle={(S)-(W)-(N):0.22}}; \pic[nmarks=1,angcol=myred] {mark angle={(N)-(E)-(S):0.22}}; \pic[nmarks=2,mypurple] {mark line={(E)-(N):90}}; \pic[nmarks=2,mypurple] {mark line={(N)-(W):90}}; \pic[nmarks=1,myblue] {mark line={(S)-(E):90}}; \pic[nmarks=1,myblue] {mark line={(W)-(S):90}}; \end{scope} } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % COMMON ANGLED TRAPEZIA % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\commonangtraps{ % OBTUSE-ANGLED TRAPEZIUM \begin{scope}[shift={(-0.5*\W,\yrighttrap*\H)}] \node[below=-1,align=center] at (0,0) { \contour{white}{obtuse-angled}\\[-0.3em] \contour{white}{trapezium}}; \def\h{1.0} % height \def\a{0.9} % length of short horizontal sides \def\b{1.7} % length of long horizontal sides \coordinate (SW) at (-\b/2,0); \coordinate (NW) at (-0.6*\b,\h); \coordinate (NE) at (\a-0.6*\b,\h); \coordinate (SE) at (\b/2,0); \coordinate (obtuse trapezium) at (0,\h/2); \draw[myshape] (SW) -- (SE) -- (NE) -- (NW) -- cycle; \pic[angcol=mygreen] {mark angle={(SE)-(SW)-(NW):0.20}}; \pic[angcol=mygreen] {mark angle={(NW)-(NE)-(SE):0.20}}; \pic[angcol=myred] {mark angle={(SW)-(NW)-(NE):0.20}}; \pic[angcol=myred] {mark angle={(NE)-(SE)-(SW):0.22}}; \end{scope} % ACUTE-ANGLED TRAPEZIUM \begin{scope}[shift={(1.5*\W,\yrighttrap*\H)}] \node[below=-1,align=center] at (0,0) { \contour{white}{acute-angled}\\[-0.3em] \contour{white}{trapezium}}; \def\h{1.0} % height \def\a{0.75} % length of short horizontal sides \def\b{1.7} % length of long horizontal sides \coordinate (SW) at (-\b/2,0); \coordinate (NW) at (-0.8*\a,\h); \coordinate (NE) at ( 0.2*\a,\h); \coordinate (SE) at (\b/2,0); \coordinate (acute trapezium) at (0,\h/2); \draw[myshape] (SW) -- (SE) -- (NE) -- (NW) -- cycle; \pic[angcol=mygreen] {mark angle={(SW)-(NW)-(NE):0.20}}; \pic[angcol=mygreen] {mark angle={(NW)-(NE)-(SE):0.20}}; \pic[angcol=myred] {mark angle={(SE)-(SW)-(NW):0.20}}; \pic[angcol=myred] {mark angle={(NE)-(SE)-(SW):0.21}}; \end{scope} } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % COMMON GENERAL TRAPEZIA % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\xirr{-0.8} % x position irregular trapezium \def\xtrap{0.5} % x position trapezium/trapezoid \def\ytrap{3.2} % y position trapezia \def\commonirreg{ % common irregular in each picture \message{^^J Common irregular/trapezium} % IRREGULAR / TRAPEZIUM % If irregular quadrilateral is defined as having no parallel sides, % then some "non-trapezium" kites, cyclic and tangential quadrilaterals are irregular \begin{scope}[shift={(\xirr*\W,\ytrap*\H)}] \node[below=-1,align=center] at (0,0) { \contour{white}{irregular \scriptsize(Brit.)}\\[-0.3em] \contour{white}{trapezium \scriptsize(Amer.)}}; \def\h{1.0} % height \def\a{0.8} % length of short horizontal sides \def\b{1.7} % length of long horizontal sides \coordinate (SW) at (-\b/2,0); \coordinate (NW) at (-0.7*\a,0.8*\h); \coordinate (NE) at ( 0.3*\a,\h); \coordinate (SE) at (\b/2,0); \coordinate (irregular) at (0,\h/2); \draw[myshape] (SW) -- (SE) -- (NE) -- (NW) -- cycle; \end{scope} } \def\commontrap{ % common trapezium/trapezoid in each picture \message{^^J Common trapezium/trapezoid} % TRAPEZIUM / TRAPEZOID \begin{scope}[shift={(\xtrap*\W,\ytrap*\H)}] \node[below=-1,align=center] at (0,0) { \contour{white}{trapezium \scriptsize(Brit.)}\\[-0.3em] \contour{white}{trapezoid \scriptsize(Amer.)}}; \def\h{1.0} % height \def\a{0.75} % length of short horizontal sides \def\b{1.7} % length of long horizontal sides \coordinate (SW) at (-\b/2,0); \coordinate (NW) at (-0.8*\a,\h); \coordinate (NE) at ( 0.2*\a,\h); \coordinate (SE) at (\b/2,0); \coordinate (trapezium) at (0,\h/2); \draw[myshape] (SW) -- (SE) -- (NE) -- (NW) -- cycle; \end{scope} } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % COMMON GENERAL QUADRILATERALS % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\xybicent{-1.32,2.35} % xy position bicentric \def\ytangent{3.0} % y position tangential \def\xcyclic{1.5} % x position cyclic \def\ycyclic{2.8} % y position cyclic \def\ydart{3.67} % y position dart \def\yconcave{4.2} % y position concave \def\xconvex{0.0} % x position convex \def\yconvex{4.0} % y position convex \def\xysimple{-0.75,4.7} % xy position simple \def\xycomplex{0.7,4.7} % xy position complex \def\xyquad{0,5.4} % xy position complex \def\colcirc{white} % contour color for tangential/cyclic/bicentric \def\commonquads{ % common quadrilaterals in each picture \message{^^J Common (general) quadrilateral} %%%% LEVEL 3.5 %%%%%%%%%%%%%%%%%%%%%%%% % BICENTRIC % Construct bicentric quadrilateral for given incircle, circumcircle and one vertex % https://tikz.net/quadrilaterals_bicentric/ % http://dynamicmathematicslearning.com/new-bicentric-construction.html \def\r{0.46} % inradius = radius of incircle \def\R{0.68} % circumradius = radius of circumcircle \def\angXi{40} % polar angle of incircle center \def\angA{-40} % polar angle of point A \pgfmathsetmacro\x{sqrt(\R^2+\r^2-\r*sqrt(4*\R^2+\r^2))} % Fuss's theorem \begin{scope}[shift={(\R+\W*\xybicent*\H+\R)}] \node[below=-1] at (0.0,0.05-\R) {\contour{\colcirc}{bicentric}}; \coordinate (Oout) at (0,0); \coordinate (Oin) at (\angXi:\x); \coordinate (bicentric) at (-60:0.3*\R); \coordinate (bicentric-N) at (90:0.3*\R); \coordinate (bicentric-W) at (190:0.3*\R); \foreach \P [ remember={\angP as \lastang (initially \angA);}, evaluate={ \d=sqrt(\x^2+\R^2-\r^2-2*\x*\R*cos(\angXi-\lastang)); \D=sqrt(\d^2+\r^2); \tanang=90+atan2(\d,\r)+atan2(\R*sin(\lastang)-\x*sin(\angXi), \R*cos(\lastang)-\x*cos(\angXi)); \angP=2*\tanang-\lastang-180; }] in {NW,NE,SE,SW}{ \coordinate (\P) at (\angP:\R); % corner } \coordinate (SW) at (\angA:\R); % overwrite for precision \draw[mydarkgreen] (Oout) circle(\R); \draw[myshape] (SW) -- (SE) -- (NE) -- (NW) -- cycle; \draw[mydarkorange] (Oin) circle(\r-0.01); \fill[mydarkorange] (Oin) circle(0.02); \fill[mydarkgreen] (Oout) circle(0.02); \end{scope} %%%% LEVEL 4 %%%%%%%%%%%%%%%%%%%%%%%%%% % TANGENTIAL QUADRILATERAL % Construct tangential trapezoid from four points of tangency on the incircle % https://tikz.net/quadrilaterals_bicentric/ \def\R{0.5} % inradius = radius of incircle \def\angW{-110} % polar angle of point W \begin{scope}[shift={(\xkite*\W,\ytangent*\H+\R)}] \node[below=-1] at (0.0,-\R) {\contour{\colcirc}{tangential}}; \coordinate (O) at (0,0); \coordinate (tangential) at (O); \foreach \P/\angQ [ remember={\angQ as \lastang (initially \angW);}, evaluate={ \r=\R/cos((\angQ-\lastang)/2); \angP=(\angQ+\lastang)/2; }] in {W/125,N/52,E/-60,S/\angW}{ \coordinate (\P) at (\angP:\r); % vertex } \draw[myshape] (S) -- (W) -- (N) -- (E) -- cycle; \draw[mydarkorange] (O) circle(\R-0.01); \fill[mydarkorange] (O) circle(0.02); \end{scope} \commontrap %shift={(0.0*\W,\ytrap*\H)}] % CYCLIC QUADRILATERAL % Construct cyclic quadrilateral four points on the circumcircle % https://tikz.net/quadrilaterals_bicentric/ \def\R{0.7} % circumradius = radius of circumcircle \begin{scope}[shift={(\xcyclic*\W,\ycyclic*\H+\R)}] \ifdim \ycyclic pt=2.85 pt % for full version \node[below=-1,align=center] at (0,-\R) { \contour{\colcirc}{convex}\\[-0.3em] \contour{\colcirc}{cyclic}}; \coordinate (convex cyclic) at (0,0); \coordinate (convex cyclic-W) at (0,-0.2*\R); \else % for extended versions \node[below=-1] at (0.0,-\R) {\contour{\colcirc}{cyclic}}; \coordinate (cyclic) at (0,0); \coordinate (cyclic-W) at (0,-0.2*\R); \fi \coordinate (O) at (0,0); \coordinate (SW) at (215:\R); \coordinate (NW) at (120:\R); \coordinate (NE) at ( 45:\R); \coordinate (SE) at (320:\R); \draw[mydarkgreen] (O) circle(\R); \draw[myshape] (SW) -- (NW) -- (NE) -- (SE) -- cycle; \fill[mydarkgreen] (O) circle(0.02); \end{scope} % DART \begin{scope}[shift={(\xkite*\W,\ydart*\H)}] \node[below=-6,align=center] at (0,0) {\contour{white}{dart}}; %\node[below=-3,align=center] at (0,0) { % \contour{white}{dart}\\[-0.3em] % \contour{white}{(concave) kite}}; \def\w{1.7} % width \def\h{0.6} % height \coordinate (E) at (-\w/2,0); \coordinate (S) at (0,0.4*\h); \coordinate (W) at (\w/2,0); \coordinate (N) at (0,\h); \coordinate (dart) at (0,0.8*\h); %\draw[mydashed] (W) -- (E); \draw[myshape] (E) -- (S) -- (W) -- (N) -- cycle; \draw[purple line] (E) -- (N) -- (W); \pic[nmarks=1,angcol=myred] {mark angle={(S)-(E)-(N):0.32}}; \pic[nmarks=1,angcol=myred] {mark angle={(N)-(W)-(S):0.32}}; \pic[nmarks=2,markshift= 0.12,mypurple] {mark line={(E)-(N):90}}; \pic[nmarks=2,markshift=-0.12,mypurple] {mark line={(N)-(W):90}}; \pic[nmarks=1,markshift=-0.10,myblue] {mark line={(S)-(E):90}}; \pic[nmarks=1,markshift= 0.10,myblue] {mark line={(W)-(S):90}}; \end{scope} %%%% LEVEL 5 %%%%%%%%%%%%%%%%%%%%%%%%%% % CONCAVE \begin{scope}[shift={(\xkite*\W,\yconcave*\H)}] \node[below=-1,align=center] at (0,0) {\contour{white}{concave}}; \def\w{1.6} % width \def\h{1.0} % height \coordinate (concave) at (0,0.35*\h); \coordinate (N) at (0.4*\w,\h); \coordinate (S) at (\w/2,0); \draw[mydashed] (N) -- (S); \draw[myshape] (-\w/2,0.1*\h) -- (N) -- (0.25*\w,0.5*\h) -- (S) -- cycle; \end{scope} % CONVEX \begin{scope}[shift={(\xconvex*\W,\yconvex*\H)}] \node[below=-1,align=center] at (0,0) {\contour{white}{convex}}; \def\h{1.0} % height \def\w{1.4} % length of short horizontal sides \coordinate (convex) at (0,\h/2); \draw[myshape] (-\w/2,0.2*\h) -- (-0.4*\w,0.9*\h) -- (0.3*\w,\h) -- (\w/2,0) -- cycle; \end{scope} %%%% LEVEL 6 %%%%%%%%%%%%%%%%%%%%%%%%%% % SIMPLE \begin{scope}[shift={(\W*\xysimple*\H)}] \node[below=-1,align=center] at (0,0) {\contour{white}{simple}}; \def\w{1.6} % width \def\h{1.0} % height \coordinate (simple) at (0,0.35*\h); \draw[myshape] (-\w/2,0.1*\h) -- (0.4*\w,\h) -- (0.25*\w,0.5*\h) -- (\w/2,0) -- cycle; \end{scope} % COMPLEX \begin{scope}[shift={(\W*\xycomplex*\H)}] \node[below=-1,align=center] at (0,0) {\contour{white}{complex}}; \def\w{1.6} % width \def\h{0.8} % height \coordinate (complex-W) at (-0.10*\w,\h/2); \coordinate (complex-E) at ( 0.05*\w,\h/2); \coordinate (complex) at (0.1*\w,\h/2); \draw[myshape] (-\w/2,0.1*\h) -- (\w/2,\h) -- (0.4*\w,0) -- (-0.3*\w,0.9*\h) -- cycle; \end{scope} %%%% LEVEL 6 %%%%%%%%%%%%%%%%%%%%%%%%%% % QUADRILATERAL \begin{scope}[shift={(\W*\xyquad*\H)}] \node[below=-1,align=center] at (0,0) { \contour{white}{quadrilateral}}; \def\w{1.6} % width \def\h{0.8} % height \coordinate (quadrilateral) at (0.11*\w,\h/2); \coordinate (quadrilateral-W) at (-0.11*\w,\h/2); \coordinate (quadrilateral-E) at (0.11*\w,\h/2); \draw[myshape] (-\w/2,0.1*\h) -- (\w/2,\h) -- (0.4*\w,0) -- (-0.3*\w,0.9*\h) -- cycle; \end{scope} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % QUADRILATERAL HASSE DIAGRAM (trapezia only) % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tikzpicture} \message{^^JTrapezia only} \def\H{2.2} % height of each row \def\W{2.4} % width of column \def\ytrap{3.0} % y position of general trapezia % QUADRILATERALS \commontraps \commonirreg \commontrap \node[below=-1,align=center,inner sep=1] (quadrilateral) at (-0.2*\W,3.9*\H) {\contour{white}{quadrilateral}}; % CONNECTIONS \begin{pgfonlayer}{back} % draw on back \draw[black] (square) -- (rhombus) -- (parallelogram) -- (trapezium) (square) -- (rectangle) -- (right trapezium) -- (trapezium) (square) -- (3 trapezium) -- (2 trapezium) (parallelogram) -- (rectangle) -- (2 trapezium) -- (trapezium) (irregular) -- (quadrilateral) -- (trapezium); \end{pgfonlayer} \end{tikzpicture} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % QUADRILATERAL HASSE DIAGRAM (trapezia only, incl. obtuse & acute) % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tikzpicture} \message{^^JTrapezia only, incl. obtuse & acute} \def\H{2.2} % height of each row \def\W{2.4} % width of column \def\ysquare{0.2} % y position square \def\yrectangle{1.2} % y position rectangle \def\yrighttrap{3} % y position right-angled trapezium \def\ytrap{4.0} % y position of general trapezia \def\colpara{white} % contour color for parallelograms \def\coltrap{white} % contour color for isosceles trapezia % QUADRILATERALS \commontraps \commonangtraps \commonirreg \commontrap \node[below=-1,align=center,inner sep=1] (quadrilateral) at (-0.2*\W,4.9*\H) {\contour{white}{quadrilateral}}; % CONNECTIONS \begin{pgfonlayer}{back} % draw on back \draw[black] (square) -- (rhombus) -- (parallelogram) -- (obtuse trapezium) -- (trapezium) (square) -- (rectangle) -- (right trapezium) -- (trapezium) (square) -- (3 trapezium) -- (2 trapezium) (parallelogram) -- (rectangle) -- (2 trapezium) -- (acute trapezium) -- (trapezium) (irregular) -- (quadrilateral) -- (trapezium); \end{pgfonlayer} \end{tikzpicture} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % QUADRILATERAL HASSE DIAGRAM (trapezia only, incl. obtuse & acute) % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tikzpicture} \message{^^JTrapezia only, incl. obtuse & acute with grouping} \def\H{2.2} % height of each row \def\W{2.4} % width of column \def\ysquare{0.2} % y position square \def\yrectangle{1.2} % y position rectangle \def\yrighttrap{3} % y position right-angled trapezium \def\ytrap{4.0} % y position of general trapezia \def\colpara{mydarkgreen!3} % contour color for parallelograms \def\coltrap{mydarkred!3} % contour color for isosceles trapezia % QUADRILATERALS \commontraps \commonangtraps \commonirreg \commontrap \node[below=-1,align=center,inner sep=1] (quadrilateral) at (-0.2*\W,4.9*\H) {\contour{white}{quadrilateral}}; % CONNECTIONS \begin{pgfonlayer}{back} % draw on back \draw[mygreenset] (parallelogram) -- (obtuse trapezium); \draw[mygreenset] (parallelogram)++(-1.2,0.7) rectangle++ (2.4,-1.8*\H); \draw[myset] (2 trapezium) -- (acute trapezium); \draw[myset] (2 trapezium)++(-1.2,0.7) rectangle++ (2.4,-1.95*\H); \draw[black] (square) -- (rhombus) -- (parallelogram) %-- (obtuse trapezium) -- (trapezium) (square) -- (rectangle) -- (right trapezium) -- (trapezium) (square) -- (3 trapezium) -- (2 trapezium) (parallelogram) -- (rectangle) -- (2 trapezium) %-- (acute trapezium) -- (trapezium) (irregular) -- (quadrilateral) -- (trapezium); \end{pgfonlayer} \end{tikzpicture} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % QUADRILATERAL HASSE DIAGRAM (incl. kites) % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tikzpicture} \message{^^JTrapezia only, incl. kites} \def\H{2.5} % height of each row \def\W{2.5} % width of column \def\xsquare{0} % x position square \def\ytrap{3.0} % y position trapezia % QUADRILATERALS \commontraps \commonkites \commontrap % CONNECTIONS \begin{pgfonlayer}{back} % draw on back \draw[black] (square) -- (right kite) -- (kite) (square) -- (rhombus) -- (parallelogram) -- (trapezium) (square) -- (rectangle) -- (right trapezium) -- (trapezium) (square) -- (3 trapezium) -- (2 trapezium) (kite) -- (rhombus) (parallelogram) -- (rectangle) -- (2 trapezium) -- (trapezium); \end{pgfonlayer} \end{tikzpicture} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % QUADRILATERAL HASSE DIAGRAM (incl. kites, irr.) % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tikzpicture} \message{^^JTrapezia only, incl. kites & irregular} \def\H{2.5} % height of each row \def\W{2.5} % width of column \def\xsquare{0} % x position square \def\ytrap{3.2} % y position of general trapezia \def\colkite{mydarkred!3} % contour color for kites % QUADRILATERALS \commontraps \commonkites \commonirreg \commontrap \node[below=-1,align=center,inner sep=1] (quadrilateral) at (-0.2*\W,\ytrap*\H+0.8*\H) {\contour{white}{quadrilateral}}; % CONNECTIONS \begin{pgfonlayer}{back} % draw on back \draw[myset] (kite) -- (irregular); \draw[myset] (kite)++(-0.95,0.8) rectangle++ (1.9,-1.78*\H); \draw[black] (square) -- (right kite) -- (kite) (square) -- (rhombus) -- (parallelogram) -- (trapezium) (square) -- (rectangle) -- (right trapezium) -- (trapezium) (square) -- (3 trapezium) -- (2 trapezium) (kite) -- (rhombus) (parallelogram) -- (rectangle) -- (2 trapezium) -- (trapezium) (irregular) -- (quadrilateral) -- (trapezium); \end{pgfonlayer} \end{tikzpicture} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % QUADRILATERAL HASSE DIAGRAM (trapezia only, incl. kites, obtuse acute) % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tikzpicture} \message{^^JTrapezia only, incl. kites, obtuse & acute} \def\H{2.2} % height of each row \def\W{2.4} % width of column \def\xsquare{-0.1} % x position square \def\ysquare{0.0} % y position square \def\yrectangle{1.0} % y position rectangle \def\xkite{-1.7} % x position of kites \def\yrighttrap{3} % y position right-angled trapezium \def\ytrap{4.0} % y position of general trapezia \def\xirr{-1.7} % x position irregular trapezium \def\colpara{mydarkgreen!3} % contour color for parallelograms \def\coltrap{mydarkred!3} % contour color for isosceles trapezia \def\colkite{mydarkorange!3} % contour color for kites % QUADRILATERALS \commontraps \commonkites \commonangtraps \commonirreg \commontrap \node[below=-1,align=center,inner sep=1] (quadrilateral) at (-0.7*\W,4.9*\H) {\contour{white}{quadrilateral}}; % CONNECTIONS \begin{pgfonlayer}{back} % draw on back \draw[myorangeset] (kite) -- (irregular); \draw[myorangeset] (kite)++(-0.95,0.7) rectangle++ (1.9,-1.85*\H); \draw[mygreenset] (parallelogram) -- (obtuse trapezium); \draw[mygreenset] (parallelogram)++(-1.2,0.7) rectangle++ (2.4,-1.8*\H); \draw[myset] (2 trapezium) -- (acute trapezium); \draw[myset] (2 trapezium)++(-1.2,0.7) rectangle++ (2.4,-1.95*\H); \draw[black] (square) -- ($(right kite)-(0,0.2)$) -- (kite) (square) -- (rhombus) -- (parallelogram) %-- (obtuse trapezium) -- (trapezium) (square) -- (rectangle) -- (right trapezium) -- (trapezium) (square) -- (3 trapezium) -- (2 trapezium) (kite) -- (rhombus) (parallelogram) -- (rectangle) -- (2 trapezium) %-- (acute trapezium) -- (trapezium) (irregular) -- (quadrilateral) -- (trapezium); \end{pgfonlayer} \end{tikzpicture} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % QUADRILATERAL HASSE DIAGRAM (full) % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Inspiration: % https://en.wikipedia.org/wiki/Quadrilateral#Taxonomy % https://commons.wikimedia.org/wiki/File:Quadrilateral_hierarchy_svg.svg \begin{tikzpicture} \message{^^JFull Hasse diagram} \def\H{2.5} % height of each row \def\W{2.6} % width of column \def\xsquare{0} % x position square \def\xkite{-1.6} % x position kites \def\xtrap{0.0} % x position trapezia \def\ytrap{3.2} % y position trapezia \def\ycyclic{2.75} % y position cyclic \def\xycomplex{1.0,4.7} % xy position complex \def\xyquad{0.2,5.3} % xy position complex % QUADRILATERALS \commontraps \commonkites \commonquads % CONNECTIONS \begin{pgfonlayer}{back} % draw on back \draw[black] (square) -- (right kite) -- (kite) -- (tangential) (square) -- (rhombus) -- (parallelogram) -- (trapezium) (square) -- (rectangle) -- (right trapezium) -- (trapezium) (square) -- (3 trapezium) -- (2 trapezium) -- (cyclic) (parallelogram) -- (rectangle) -- (2 trapezium) -- (trapezium) (rhombus) -- (kite) (tangential) -- (convex) -- (simple) -- (concave) -- (dart) (trapezium) -- (convex) -- (cyclic) (simple) -- (quadrilateral-W) (complex-W) -- (quadrilateral-E); \draw[frontline] (cyclic) -- (bicentric) (right kite) -- (bicentric) -- (tangential); \draw[blue!20!black!50,dashed] (dart) to[out=-145,in=135,looseness=1.3] ($(kite)-(0,0.2)$); \end{pgfonlayer} \end{tikzpicture} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % QUADRILATERAL HASSE DIAGRAM (full, incl. obtuse & acute) % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Inspiration: % https://en.wikipedia.org/wiki/Quadrilateral#Taxonomy % https://commons.wikimedia.org/wiki/File:Quadrilateral_hierarchy_svg.svg \begin{tikzpicture} \message{^^JFull Hasse diagram, incl. obtuse & acute} \def\H{2.4} % height of each row \def\W{2.6} % width of column \def\xsquare{0.5} % x position square \def\xkite{-2.4} % x position kites \def\ykite{2.0} % y position kite \def\yrighttrap{2.9} % y position right-angled trapezium \def\xybicent{-1.8,1.1} % xy position bicentric \def\ytangent{2.1} % y position tangential \def\xirr{-1.5} % x position irregular trapezium \def\ytrap{3.15} % y position trapezium \def\ydart{3.4} % y position dart \def\xcyclic{-1.5} % x position cyclic \def\ycyclic{2.0} % y position cyclic \def\yconcave{4.0} % y position concave \def\xconvex{-0.6} % x position convex \def\yconvex{4.0} % y position convex \def\xysimple{-1.5,4.6} % xy position simple \def\xycomplex{0.9,4.6} % xy position complex \def\xyquad{-0.3,5.3} % xy position complex \def\colpara{mydarkgreen!3} % contour color for parallelograms \def\coltrap{mydarkred!3} % contour color for isosceles trapezia \def\colkite{mydarkorange!3} % contour color for kites \def\colcirc{mydarkorange!3} % contour color for tangential/cyclic/bicentric % QUADRILATERALS \commontraps \commonkites \commonangtraps \begin{scope}[shift={(0,0.8*\H)}] \commonirreg \commonquads \end{scope} % CONNECTIONS \begin{pgfonlayer}{back} % draw on back \draw[myorangeset] (kite) -- (irregular); \draw[myorangeset] (tangential)++(-1.25,0.8) rectangle++ (1.7*\W,-2.7*\H); \draw[mygreenset] (parallelogram) -- (obtuse trapezium); \draw[mygreenset] (parallelogram)++(-1.2,0.7) rectangle++ (2.4,-1.7*\H); \draw[myset] (2 trapezium) -- (acute trapezium); \draw[myset] (2 trapezium)++(-1.2,0.7) rectangle++ (2.4,-1.85*\H); \draw[black] (square) -- (right kite) -- (kite) -- (tangential) (square) -- (rhombus) -- (parallelogram) (obtuse trapezium) -- (trapezium) -- (acute trapezium) (square) -- (rectangle) -- (right trapezium) -- (trapezium) (square) -- (3 trapezium) -- (2 trapezium) (parallelogram) -- (rectangle) -- (2 trapezium) (rhombus) -- (kite) (irregular) -- (convex) -- (simple) -- (concave) -- (dart) (trapezium) -- (convex) (simple) -- (quadrilateral-W) (complex-W) -- (quadrilateral-E); \draw[frontline] (2 trapezium) -- (cyclic-W); \draw[frontline,mydarkorange!3] (cyclic) -- (bicentric) (tangential) -- (bicentric-N) (right kite) -- (bicentric-W); \draw[dashed,blue!20!black!50] (dart) to[out=-135,in=140,looseness=1.2] ($(kite)-(0,0.5)$); \end{pgfonlayer} \end{tikzpicture} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % QUADRILATERAL HASSE DIAGRAM (extended) % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % https://en.wikipedia.org/wiki/Quadrilateral#Complex_quadrilaterals \begin{tikzpicture} \message{^^JExtended Hasse diagram} \def\H{2.5} % height of each row \def\W{2.5} % width of column \def\xsquare{0} % x position square \def\xkite{-1.6} % shift kite column \def\xcyclic{1.5} % x position cyclic \def\ycyclic{2.85} % y position cyclic \def\ydart{3.67} % y position dart \def\xtrap{0.0} % y position trapezia \def\ytrap{3.2} % y position trapezia \def\yconcave{4.2} % y position concave \def\yconvex{4.0} % y position convex \def\xysimple{0.0,4.8} % xy position simple \def\xycomplex{3.5,4.8} % xy position complex \def\xyquad{1.9,5.5} % xy position complex %%%% LEVEL 1 %%%%%%%%%%%%%%%%%%%%%%%%%% \commontraps \commonkites % CROSSED SQUARE \begin{scope}[shift={(3.1*\W,0)}] \node[below=-1,align=center] at (0,0) { \contour{white}{crossed square}}; \def\a{1.0} % length of each side \coordinate (O) at (0,\a/2); \coordinate (SW) at (-\a/2, 0); \coordinate (NW) at (-\a/2,\a); \coordinate (NE) at ( \a/2,\a); \coordinate (SE) at ( \a/2, 0); \coordinate (crossed square) at (O); \draw[mydashed] (SW) -- (SE) (NW) -- (NE); \draw[myshape] (SW) -- (NE) -- (SE) -- (NW) -- cycle; \draw[purple line] (SW) -- (NW) (SE) -- (NE); \pic[nmarks=1,angcol=myred] {mark angle={(SW)-(NW)-(O):0.20}}; \pic[nmarks=1,angcol=myred] {mark angle={(O)-(NE)-(SE):0.20}}; \pic[nmarks=1,angcol=myred] {mark angle={(O)-(SW)-(NW):0.20}}; \pic[nmarks=1,angcol=myred] {mark angle={(NE)-(SE)-(O):0.20}}; \pic[angcol=myblue] {right angle={(NW)-(O)-(SW):0.20}}; \pic[angcol=myblue] {right angle={(SE)-(O)-(NE):0.20}}; \pic[nmarks=1,markshift=0.08,myblue] {mark line={(NW)-(SE):90}}; \pic[nmarks=1,markshift=0.08,myblue] {mark line={(SW)-(NE):90}}; \pic[nmarks=2,mypurple] {mark line={(NW)-(SW):90}}; \pic[nmarks=2,mypurple] {mark line={(NE)-(SE):90}}; \end{scope} %%%% LEVEL 2 %%%%%%%%%%%%%%%%%%%%%%%%%% % CROSSED RHOMBUS \def\a{1.0} % length of each sides \def\ang{60} % smaller vertex angle (SW) \pgfmathsetmacro\h{\a*sqrt(2-2*cos(\ang))} % height / diagonal \begin{scope}[shift={(2.6*\W,\H)}] \node[below=-1,align=center] at (0,0) { \contour{white}{crossed}\\[-0.3em] \contour{white}{rhombus}}; \coordinate (O) at ({0.1*\a*cos(\ang)},{\a*sin(\ang)/2}); \coordinate (SW) at ({-\a/2-0.4*\a*cos(\ang)},0); \coordinate (SE) at ($(SW)+(\a,0)$); \coordinate (NW) at ($(SW)+(\ang:\a)$); \coordinate (NE) at ($(SE)+(\ang:\a)$); \coordinate (crossed rhombus) at (0.2*\a,{\a*sin(\ang)/2}); \draw[mydashed] (SW) -- (SE) (NW) -- (NE); \draw[myshape] (SW) -- (NW) -- (SE) -- (NE) -- cycle; \draw[purple line] (SW) -- (NW) (SE) -- (NE); \pic[nmarks=2,angcol=mygreen] {mark angle={(SW)-(NW)-(O):0.20}}; \pic[nmarks=2,angcol=mygreen] {mark angle={(NE)-(SE)-(O):0.20}}; \pic[nmarks=1,angcol=myred] {mark angle={(O)-(SW)-(NW):0.23}}; \pic[nmarks=1,angcol=myred] {mark angle={(O)-(NE)-(SE):0.23}}; \pic[nmarks=1,markshift=0.08,myblue] {mark line={(NW)-(SE):90}}; \pic[nmarks=1,markshift=0.08,myblue] {mark line={(SW)-(NE):90}}; \pic[nmarks=1,myblue] {mark line={(NW)-(SW):90}}; \pic[nmarks=1,myblue] {mark line={(NE)-(SE):90}}; \end{scope} % CROSSED RECTANGLE \begin{scope}[shift={(3.6*\W,\H)}] \node[below=-1,align=center] at (0,0) { \contour{white}{crossed}\\[-0.3em] \contour{white}{rectangle}}; \def\a{1.0} % length of short sides \def\b{1.6} % length of long sides \coordinate (O) at (0,\a/2); \coordinate (SW) at (-\b/2, 0); \coordinate (NW) at (-\b/2,\a); \coordinate (NE) at ( \b/2,\a); \coordinate (SE) at ( \b/2, 0); \coordinate (crossed rectangle) at (O); \draw[mydashed] (SW) -- (SE) (NW) -- (NE); \draw[myshape] (SW) -- (NE) -- (SE) -- (NW) -- cycle; \draw[purple line] (SW) -- (NW) (SE) -- (NE); \pic[nmarks=1,angcol=myred] {mark angle={(SW)-(NW)-(O):0.20}}; \pic[nmarks=1,angcol=myred] {mark angle={(O)-(NE)-(SE):0.20}}; \pic[nmarks=1,angcol=myred] {mark angle={(O)-(SW)-(NW):0.20}}; \pic[nmarks=1,angcol=myred] {mark angle={(NE)-(SE)-(O):0.20}}; %\pic[nmarks=2,angcol=mygreen] {mark angle={(SE)-(O)-(NE):0.20}}; %\pic[nmarks=2,angcol=mygreen] {mark angle={(NW)-(O)-(SW):0.20}}; \pic[nmarks=1,markshift=0.08,myblue] {mark line={(NW)-(SE):90}}; \pic[nmarks=1,markshift=0.08,myblue] {mark line={(SW)-(NE):90}}; \pic[nmarks=2,mypurple] {mark line={(NW)-(SW):90}}; \pic[nmarks=2,mypurple] {mark line={(NE)-(SE):90}}; \end{scope} %%%% LEVEL 3 %%%%%%%%%%%%%%%%%%%%%%%%%% % "CROSSED PARALLELOGRAM" ? \begin{scope}[shift={(2.6*\W,2*\H)}] \node[below=-1,align=center,opacity=0.3] at (0,0) { \contour{white}{crossed}\\[-0.3em] \contour{white}{parallelogram}}; \def\a{1.0} % length short sides \def\b{1.4} % length long sides \def\ang{60} % smaller vertex angle (SW) \coordinate (O) at ({0.1*\a*cos(\ang)},{\a*sin(\ang)/2}); \coordinate (SW) at ({-\b/2-0.4*\a*cos(\ang)},0); \coordinate (SE) at ($(SW)+(\b,0)$); \coordinate (NW) at ($(SW)+(\ang:\a)$); \coordinate (NE) at ($(SE)+(\ang:\a)$); \coordinate (crossed parallelogram) at (0.2*\a,{\a*sin(\ang)/2}); \draw[mydashed] (SW) -- (SE) (NW) -- (NE); \draw[myshape] (SW) -- (NW) -- (SE) -- (NE) -- cycle; \draw[purple line] (SW) -- (NW) (SE) -- (NE); \pic[nmarks=2,angcol=mygreen] {mark angle={(SW)-(NW)-(O):0.20}}; \pic[nmarks=2,angcol=mygreen] {mark angle={(NE)-(SE)-(O):0.20}}; \pic[nmarks=1,angcol=myred] {mark angle={(O)-(SW)-(NW):0.23}}; \pic[nmarks=1,angcol=myred] {mark angle={(O)-(NE)-(SE):0.23}}; \pic[nmarks=1,mypurple] {mark line={(NW)-(SW):90}}; \pic[nmarks=1,mypurple] {mark line={(NE)-(SE):90}}; \end{scope} % CROSSED ISOSCELES TRAPEZIUM % https://en.wikipedia.org/wiki/Isosceles_trapezoid#Self-intersections \begin{scope}[shift={(3.6*\W,2*\H)}] \node[below=-1,align=center] at (0,0) { \contour{white}{crossed}\\[-0.3em] \contour{white}{isosceles}\\[-0.3em] \contour{white}{trapezium}}; \def\h{1.0} % height \def\a{0.9} % length of short horizontal sides \def\b{1.7} % length of long horizontal sides \coordinate (O) at (0,{\b*\h/(\a+\b)}); \coordinate (SW) at (-\b/2,0); \coordinate (NW) at (-\a/2,\h); \coordinate (NE) at ( \a/2,\h); \coordinate (SE) at ( \b/2,0); \coordinate (crossed 2 trapezium) at (0,0.8*\h); \draw[mydashed] (SW) -- (NW) (SE) -- (NE); \draw[myshape] (SW) -- (SE) -- (NW) -- (NE) -- cycle; \draw[purple line] (SW) -- (NE) (SE) -- (NW); \pic[nmarks=2,angcol=mygreen] {mark angle={(SE)-(SW)-(O):0.24}}; \pic[nmarks=2,angcol=mygreen] {mark angle={(O)-(SE)-(SW):0.24}}; \pic[nmarks=1,angcol=myred] {mark angle={(NW)-(NE)-(O):0.23}}; \pic[nmarks=1,angcol=myred] {mark angle={(O)-(NW)-(NE):0.23}}; \pic[nmarks=1,markshift=0.06,mypurple] {mark line={(SE)-(NW):90}}; \pic[nmarks=1,markshift=0.06,mypurple] {mark line={(SW)-(NE):90}}; \end{scope} % ANTIPARALLELOGRAM % https://en.wikipedia.org/wiki/Antiparallelogram \begin{scope}[shift={(4.6*\W,2*\H)}] \node[below=-1,align=center] at (0,0) { \contour{white}{antiparallelogram}}; \def\h{1.0} % height \def\a{0.9} % length of short horizontal sides \def\b{1.7} % length of long horizontal sides \coordinate (O) at (0,{\b*\h/(\a+\b)}); \coordinate (SW) at (-\b/2,0); \coordinate (NW) at (-\a/2,\h); \coordinate (NE) at ( \a/2,\h); \coordinate (SE) at ( \b/2,0); \coordinate (antiparallelogram) at (-0.1*\a,{\b*\h/(\a+\b)}); \draw[mydashed] (SW) -- (SE) (NW) -- (NE); \draw[myshape] (SW) -- (NW) -- (SE) -- (NE) -- cycle; \draw[purple line] (SW) -- (NW) (SE) -- (NE); \pic[nmarks=2,angcol=mygreen] {mark angle={(SW)-(NW)-(O):0.20}}; \pic[nmarks=2,angcol=mygreen] {mark angle={(O)-(NE)-(SE):0.20}}; \pic[nmarks=1,angcol=myred] {mark angle={(NE)-(SE)-(O):0.23}}; \pic[nmarks=1,angcol=myred] {mark angle={(O)-(SW)-(NW):0.23}}; \pic[nmarks=1,markshift=0.06,myblue] {mark line={(SE)-(NW):90}}; \pic[nmarks=1,markshift=0.06,myblue] {mark line={(SW)-(NE):90}}; \pic[nmarks=2,mypurple] {mark line={(NW)-(SW):90}}; \pic[nmarks=2,mypurple] {mark line={(NE)-(SE):90}}; \end{scope} %%%% LEVEL 3.5-7 %%%%%%%%%%%%%%%%%%%%%% \commonquads %%%% LEVEL 4 %%%%%%%%%%%%%%%%%%%%%%%%%% % CROSSED TRAPEZIUM \begin{scope}[shift={(3.0*\W,3*\H)}] \node[below=-1,align=center] at (0,0) { \contour{white}{crossed}\\[-0.3em] \contour{white}{trapezium}\\[-0.3em] \contour{white}{\scriptsize(Brit.)}}; \def\h{1.0} % height \def\a{0.75} % length of short horizontal sides \def\b{1.7} % length of long horizontal sides \coordinate (SW) at (-\b/2,0); \coordinate (NW) at (-0.8*\a,\h); \coordinate (NE) at ( 0.2*\a,\h); \coordinate (SE) at (\b/2,0); \coordinate (crossed trapezium) at (-0.13*\a,0.66*\h); \draw[mydashed] (NW) -- (SW) (NE) -- (SE); \draw[myshape] (SW) -- (SE) -- (NW) -- (NE) -- cycle; \end{scope} % CONCAVE CYCLIC QUADRILATERAL % Construct cyclic quadrilateral four points on the circumcircle \def\R{0.7} % circumradius = radius of circumcircle \begin{scope}[shift={(4.0*\W,3*\H+\R-0.1)}] \node[below=-1,align=center] at (0,-\R) { \contour{white}{concave}\\[-0.3em] \contour{white}{cyclic}}; \coordinate (O) at (0,0); \coordinate (SW) at (210:\R); \coordinate (NW) at (120:\R); \coordinate (NE) at ( 40:\R); \coordinate (SE) at (325:\R); \coordinate (concave cyclic) at (60:0.2*\R); \draw[mydarkgreen] (O) circle(\R); \draw[myshape] (SW) -- (NE) -- (NW) -- (SE) -- cycle; \fill[mydarkgreen] (O) circle(0.02); \end{scope} %%%% LEVEL 5 %%%%%%%%%%%%%%%%%%%%%%%%%% % CYCLIC QUADRILATERAL % Construct cyclic quadrilateral four points on the circumcircle \def\R{0.7} % circumradius = radius of circumcircle \begin{scope}[shift={(2.2*\W,4.0*\H+\R)}] \node[below=-1,align=center] at (0,-\R) {\contour{white}{cyclic}}; \coordinate (O) at (0,0); \coordinate (SW) at (215:\R); \coordinate (NW) at (120:\R); \coordinate (NE) at ( 45:\R); \coordinate (SE) at (320:\R); \coordinate (cyclic) at (O); \draw[mydarkgreen] (O) circle(\R); \draw[myshape] (SW) -- (NW) -- (NE) -- (SE) -- cycle; \fill[mydarkgreen] (O) circle(0.02); \end{scope} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % CONNECTIONS \begin{pgfonlayer}{back} % draw on back \draw[black] % simple quadrilaterals (square) -- (right kite) -- (kite) -- (tangential) (square) -- (rhombus) -- (parallelogram) -- (trapezium) (square) -- (rectangle) -- (right trapezium) -- (trapezium) (square) -- (3 trapezium) -- (2 trapezium) -- (convex cyclic) (parallelogram) -- (rectangle) -- (2 trapezium) -- (trapezium) (rhombus) -- (kite) (tangential) -- (convex) -- (simple) -- (concave) -- (dart) (trapezium) -- (convex) -- (convex cyclic) (quadrilateral-W) -- (simple) (quadrilateral-E) -- (complex-W); \draw[black] % cyclic (convex cyclic) -- (cyclic) -- (quadrilateral); \draw[black] % complex quadrilaterals (crossed square) -- (crossed rhombus) -- (crossed parallelogram) -- (crossed trapezium) -- (complex-W) (crossed square) -- (crossed rectangle) -- (crossed 2 trapezium) -- (crossed trapezium) (crossed rectangle) -- (crossed parallelogram) (crossed rectangle) -- (antiparallelogram) -- (concave cyclic) (crossed 2 trapezium) -- (concave cyclic) -- (complex-E); \draw[frontline] (convex cyclic-W) -- (bicentric) -- (right kite) (bicentric-N) -- (tangential) (cyclic) -- (concave cyclic); \draw[blue!20!black!50,dashed] (dart) to[out=-145,in=135,looseness=1.3] ($(kite)-(0,0.2)$); \end{pgfonlayer} \end{tikzpicture} \end{document}