tkz-euclide
Complements
39 The Show¶
39.1 Show the constructions of some lines \tkzShowLine¶
\tkzShowLine[⟨local options⟩](⟨pt1,pt2⟩) or (⟨pt1,pt2,pt3⟩)¶
These constructions concern mediators (perpendicular bisectors), perpendicular or parallel lines through a given point, and bisectors. The arguments are therefore lists of two or three points. Several options adjust the constructions. The idea of this macro comes from Yves Combe.
| options | default | definition |
|---|---|---|
| mediator | mediator | displays the constructions of a mediator |
| perpendicular | mediator | constructions for a perpendicular |
| orthogonal | mediator | idem |
| bisector | mediator | constructions for a bisector |
| K | 1 | circle within a triangle |
| length | 1 | in cm, length of a arc |
| ratio | .5 | arc length ratio |
| gap | 2 | placing the point of construction |
| size | 1 | radius of an arc (see bisector) |
Of course, you can add all the TikZ styles.
39.1.1 Example of \tkzShowLine and parallel¶
\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}
39.1.2 Example of \tkzShowLine and perpendicular¶
\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}
39.1.3 Example of \tkzShowLine and bisector¶
\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[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}
39.1.4 Example of \tkzShowLine and mediator¶
\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}
39.2 Constructions of certain transformations \tkzShowTransformation¶
\tkzShowTransformation[⟨local options⟩](⟨pt1,pt2⟩) or (⟨pt1,pt2,pt3⟩)¶
These constructions concern orthogonal symmetries, central symmetries, orthogonal projections and translations. Several options adjust the constructions. The idea of this macro comes from Yves Combe.
| options | default | definition |
|---|---|---|
| reflection= over pt1–pt2 | reflection | constructions of orthogonal symmetry |
| symmetry=center pt | reflection | constructions of central symmetry |
| projection=onto pt1–pt2 | reflection | constructions of a projection |
| translation=from pt1 to pt2 | reflection | constructions of a translation |
| K | 1 | circle within a triangle |
| length | 1 | arc length |
| ratio | .5 | arc length ratio |
| gap | 2 | placing the point of construction |
| size | 1 | radius of an arc (see bisector) |
39.2.1 Example of the use of \tkzShowTransformation¶
\begin{tikzpicture}[scale=.5]
\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}
39.2.2 Another example of the use of \tkzShowTransformation¶
You will find this figure again later, without the construction lines.
\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'}
\tkzDefMidPoint(A,B) \tkzGetPoint{M}
\tkzDrawSemiCircle(M,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,M)
\tkzLabelPoints(O)
\tkzLabelPoints[above right](N,I)
\tkzLabelPoints[below left](M,A)
\end{tikzpicture}