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\section{The Show}
\subsection{Show the constructions of some lines \tkzcname{tkzShowLine}}
\begin{NewMacroBox}{tkzShowLine}{\oarg{local options}\parg{pt1,pt2} or \parg{pt1,pt2,pt3}}%
These constructions concern mediatrices, perpendicular or parallel lines passing through a given point and bisectors. The arguments are therefore lists of two or three points. Several options allow the adjustment of the constructions. The idea of this macro comes from \tkzimp{Yves Combe}.
\medskip
\begin{tabular}{lll}%
\toprule
options & default & definition \\
\midrule
\TOline{mediator}{mediator}{displays the constructions of a mediator}
\TOline{perpendicular}{mediator}{constructions for a perpendicular}
\TOline{orthogonal}{mediator}{idem}
\TOline{bisector}{mediator}{constructions for a bisector}
\TOline{K}{1}{circle within a triangle }
\TOline{length}{1}{in cm, length of a arc}
\TOline{ratio} {.5}{arc length ratio}
\TOline{gap}{2}{placing the point of construction}
\TOline{size}{1}{radius of an arc (see bisector)}
\bottomrule
\end{tabular}
You have to add, of course, all the styles of \TIKZ\ for tracings\dots
\end{NewMacroBox}
\subsubsection{Example of \tkzcname{tkzShowLine} and \tkzname{parallel}}
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}
\tkzDefPoints{-1.5/-0.25/A,1/-0.75/B,-1.5/2/C}
\tkzDrawLine(A,B)
\tkzDefLine[parallel=through C](A,B) \tkzGetPoint{c}
\tkzShowLine[parallel=through C](A,B)
\tkzDrawLine(C,c) \tkzDrawPoints(A,B,C,c)
\end{tikzpicture}
\end{tkzexample}
\subsubsection{Example of \tkzcname{tkzShowLine} and \tkzname{perpendicular}}
\begin{tkzexample}[latex=5cm,small]
\begin{tikzpicture}
\tkzDefPoints{0/0/A, 3/2/B, 2/2/C}
\tkzDefLine[perpendicular=through C,K=-.5](A,B) \tkzGetPoint{c}
\tkzShowLine[perpendicular=through C,K=-.5,gap=3](A,B)
\tkzDefPointBy[projection=onto A--B](c)\tkzGetPoint{h}
\tkzMarkRightAngle[fill=lightgray](A,h,C)
\tkzDrawLines[add=.5 and .5](A,B C,c)
\tkzDrawPoints(A,B,C,h,c)
\end{tikzpicture}
\end{tkzexample}
\subsubsection{Example of \tkzcname{tkzShowLine} and \tkzname{bisector}}
\begin{tkzexample}[latex=7 cm,small]
\begin{tikzpicture}[scale=1.25]
\tkzDefPoints{0/0/A, 4/2/B, 1/4/C}
\tkzDrawPolygon(A,B,C)
\tkzSetUpCompass[color=brown,line width=.1 pt]
\tkzDefLine[bisector](B,A,C) \tkzGetPoint{a}
\tkzDefLine[bisector](C,B,A) \tkzGetPoint{b}
\tkzInterLL(A,a)(B,b) \tkzGetPoint{I}
\tkzDefPointBy[projection = onto A--B](I)
\tkzGetPoint{H}
\tkzShowLine[bisector,size=2,gap=3,blue](B,A,C)
\tkzShowLine[bisector,size=2,gap=3,blue](C,B,A)
\tkzDrawCircle[radius,color=blue,%
line width=.2pt](I,H)
\tkzDrawSegments[color=red!50](I,tkzPointResult)
\tkzDrawLines[add=0 and -0.3,color=red!50](A,a B,b)
\end{tikzpicture}
\end{tkzexample}
\subsubsection{Example of \tkzcname{tkzShowLine} and \tkzname{mediator}}
\begin{tkzexample}[latex=7 cm,small]
\begin{tikzpicture}
\tkzDefPoint(2,2){A}
\tkzDefPoint(5,4){B}
\tkzDrawPoints(A,B)
\tkzShowLine[mediator,color=orange,length=1](A,B)
\tkzGetPoints{i}{j}
\tkzDrawLines[add=-0.1 and -0.1](i,j)
\tkzDrawLines(A,B)
\tkzLabelPoints[below =3pt](A,B)
\end{tikzpicture}
\end{tkzexample}
\subsection{Constructions of certain transformations \addbs{tkzShowTransformation}}
\begin{NewMacroBox}{tkzShowTransformation}{\oarg{local options}\parg{pt1,pt2} or \parg{pt1,pt2,pt3}}%
These constructions concern orthogonal symmetries, central symmetries, orthogonal projections and translations. Several options allow the adjustment of the constructions. The idea of this macro comes from \tkzimp{Yves Combe}.
\medskip
\begin{tabular}{lll}%
\toprule
options & default & definition \\
\midrule
\TOline{reflection= over pt1--pt2}{reflection}{constructions of orthogonal symmetry}
\TOline{symmetry=center pt}{reflection}{constructions of central symmetry}
\TOline{projection=onto pt1--pt2}{reflection}{constructions of a projection}
\TOline{translation=from pt1 to pt2}{reflection}{constructions of a translation}
\TOline{K}{1}{circle within a triangle }
\TOline{length}{1}{arc length}
\TOline{ratio} {.5}{arc length ratio}
\TOline{gap}{2}{placing the point of construction}
\TOline{size}{1}{radius of an arc (see bisector)}
\end{tabular}
\end{NewMacroBox}
\subsubsection{Example of the use of \tkzcname{tkzShowTransformation}}
\begin{tkzexample}[latex=6cm,small]
\begin{tikzpicture}[scale=.6]
\tkzDefPoint(0,0){O} \tkzDefPoint(2,-2){A}
\tkzDefPoint(70:4){B} \tkzDrawPoints(A,O,B)
\tkzLabelPoints(A,O,B)
\tkzDrawLine[add= 2 and 2](O,A)
\tkzDefPointBy[translation=from O to A](B)
\tkzGetPoint{C}
\tkzDrawPoint[color=orange](C) \tkzLabelPoints(C)
\tkzShowTransformation[translation=from O to A,%
length=2](B)
\tkzDrawSegments[->,color=orange](O,A B,C)
\tkzDefPointBy[reflection=over O--A](B) \tkzGetPoint{E}
\tkzDrawSegment[blue](B,E)
\tkzDrawPoint[color=blue](E)\tkzLabelPoints(E)
\tkzShowTransformation[reflection=over O--A,size=2](B)
\tkzDefPointBy[symmetry=center O](B) \tkzGetPoint{F}
\tkzDrawSegment[color=green](B,F)
\tkzDrawPoint[color=green](F)\tkzLabelPoints(F)
\tkzShowTransformation[symmetry=center O,%
length=2](B)
\tkzDefPointBy[projection=onto O--A](C)
\tkzGetPoint{H}
\tkzDrawSegments[color=magenta](C,H)
\tkzDrawPoint[color=magenta](H)\tkzLabelPoints(H)
\tkzShowTransformation[projection=onto O--A,%
color=red,size=3,gap=-2](C)
\end{tikzpicture}
\end{tkzexample}
\subsubsection{Another example of the use of \tkzcname{tkzShowTransformation}}
You'll find this figure again, but without the construction features.
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}[scale=.6]
\tkzDefPoints{0/0/A,8/0/B,3.5/10/I}
\tkzDefMidPoint(A,B) \tkzGetPoint{O}
\tkzDefPointBy[projection=onto A--B](I)
\tkzGetPoint{J}
\tkzInterLC(I,A)(O,A) \tkzGetPoints{M'}{M}
\tkzInterLC(I,B)(O,A) \tkzGetPoints{N}{N'}
\tkzDrawSemiCircle[diameter](A,B)
\tkzDrawSegments(I,A I,B A,B B,M A,N)
\tkzMarkRightAngles(A,M,B A,N,B)
\tkzDrawSegment[style=dashed,color=blue](I,J)
\tkzShowTransformation[projection=onto A--B,
color=red,size=3,gap=-3](I)
\tkzDrawPoints[color=red](M,N)
\tkzDrawPoints[color=blue](O,A,B,I)
\tkzLabelPoints(O)
\tkzLabelPoints[above right](N,I)
\tkzLabelPoints[below left](M,A)
\end{tikzpicture}
\end{tkzexample}
%<---------------------------------------------------------------------->
\section{Different points}
%<---------------------------------------------------------------------->
\subsection{\tkzcname{tkzDefEquiPoints}}
This macro makes it possible to obtain two points on a straight line equidistant from a given point.
\begin{NewMacroBox}{tkzDefEquiPoints}{\oarg{local options}\parg{pt1,pt2}}%
\begin{tabular}{lll}%
arguments & default & definition \\
\midrule
\TAline{(pt1,pt2)}{no default}{unordered list of two items}
\bottomrule
\end{tabular}
\medskip
\begin{tabular}{lll}%
\toprule \\
options & default & definition \\
\midrule
\TOline{dist} {2 cm} {half the distance between the two points}
\TOline{from=pt} {no default} {reference point}
\TOline{show} {false} {if true displays compass traces}
\TOline{/compass/delta} {0} {compass trace size }
\end{tabular}
\end{NewMacroBox}
\subsubsection{Using \tkzcname{tkzDefEquiPoints} with options}
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}
\tkzSetUpCompass[color=purple,line width=1pt]
\tkzDefPoint(0,1){A}
\tkzDefPoint(5,2){B}
\tkzDefPoint(3,4){C}
\tkzDefEquiPoints[from=C,dist=1,show,
/tkzcompass/delta=20](A,B)
\tkzGetPoints{E}{H}
\tkzDrawLines[color=blue](C,E C,H A,B)
\tkzDrawPoints[color=blue](A,B,C)
\tkzDrawPoints[color=red](E,H)
\tkzLabelPoints(E,H)
\tkzLabelPoints[color=blue](A,B,C)
\end{tikzpicture}
\end{tkzexample}
\endinput
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