\documentclass[12pt]{article}
\usepackage[Mickael]{ammaths}

\begin{document}

\module{Basic constructions}{3}{05}{1 period}
\en\nocouleur

%\prereq{}

\object{\begin{itemize}
        \item Discover the rules of ruler and compass geometry.
        \item Study a few basic constructions.
        \end{itemize}}

\mater{\begin{itemize}
	\item Ruler and compass.
\item Task sheet.
	\end{itemize}}

\modpart{The rules of the game}{10 mins}

The teacher explains the rules of ruler and compass geometry. The fact that the straightedge is not marked is
emphasized, as is the difference between the compass and the divider.

\modpart{Challenge : basic constructions}{45 mins}

Students work in groups of 4 or 5. They have to use the ruler and compass to do some simple constructions. Every
construction must be validated by the teacher before the group proceeds to the next construction. At the end of the
hour every students hands out a personnal paper that will be graded by the teacher.

\begin{enumerate}
\item Copy a given length on a line.
\item Bisect a line segment.
\item Construct a perpendicular to a line at a point on the line.
\item Construct a perpendicular to a line from a point not on the line.
\item Construct an angle bisector.
\item Copy an angle.
\item Construct a parallel to a line through a given point (without drawing any perpendicular to the line).
\item Partition a segment into n congruent segments.
\item Divide a segment into a given ratio (for example 3 to 2).
\end{enumerate}



\pagebreak

\moddocdis{Basic constructions}{3}{05}{Task sheet}

\newcounter{task}
\newcommand{\task}[1]{\stepcounter{task}
\sectionblack{\small Task \arabic{task} -- #1}}

\task{Copy a given length on a line.}

\begin{center}
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\begin{pspicture*}(-2.54,-0.5)(9.22,4.52)
\psline(0.06,2.08)(3.24,-0.42)
\psline(-2,4)(7,4)
\psdots(0.06,2.08)(3.24,-0.42)(0,4)
\end{pspicture*}
\end{center}



\task{Bisect a line segment.}


\begin{center}
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\begin{pspicture*}(-2.54,-1.25)(9.22,3.75)
\psline(0.06,2.08)(3.24,-0.42)
\psdots(0.06,2.08)
\psdots(3.24,-0.42)
\end{pspicture*}
\end{center}

\task{Construct a perpendicular to a line through a point on the line.}

\begin{center}
 \psset{xunit=1.0cm,yunit=1.0cm,algebraic=true,dotstyle=*,dotsize=5pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25}
\begin{pspicture*}(-3.87,-0.41)(10.35,6.23)
\psplot{-3.87}{10.35}{(--24-0*x)/8}
\psdots(3,3)
\end{pspicture*}
\end{center}

\pagebreak

\task{Construct a perpendicular to a line though a point not on the line.}

\begin{center}
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\begin{pspicture*}(-4.07,-1.15)(4.87,6.41)
\psplot{-4.07}{4.87}{(--24-0*x)/8}
\psdots(0,0)
\end{pspicture*}
\end{center}


\task{Construct an angular bisector.}

\begin{center}
 \psset{xunit=1.0cm,yunit=1.0cm,algebraic=true,dotstyle=*,dotsize=5pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25}
\begin{pspicture*}(-1.75,1.21)(5.03,5.83)
\psline(3,5)(-1,3)
\psline(-1,3)(4,2)
\end{pspicture*}
\end{center}


\task{Copy an angle.}

\begin{center}
 \psset{xunit=1.0cm,yunit=1.0cm,algebraic=true,dotstyle=*,dotsize=5pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25}
\begin{pspicture*}(-2.35,0.41)(11.29,6.17)
\psline(3,5)(-1,3)
\psline(-1,3)(4,2)
\psline(8,1)(6,6)
\end{pspicture*}
\end{center}

\pagebreak

\task{Construct a parallel to a line through a given point.}

\begin{center}
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\begin{pspicture*}(-3.75,-0.21)(9.01,7.19)
\psline(-3,5)(5,1)
\psdots(5,5)
\end{pspicture*}
\end{center}


\task{Partition a segment into n congruent segments.}

\begin{center}
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\psline(0,4)(8,3)
\psdots(0,4)
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\end{center}


\task{Divide a segment into a given ratio (for example 3 to 2).}

\begin{center}
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\begin{pspicture*}(-1.95,2.03)(9.85,7.33)
\psline(0,4)(8,3)
\psdots(0,4)
\psdots(8,3)
\end{pspicture*}
\end{center}


\end{document}
