\documentclass[10pt,french,leqno]{article}
\usepackage[latin1]{inputenc}
\usepackage[francais]{babel}
\usepackage[T1]{fontenc}
\usepackage{asymptote}
\usepackage{fancyhdr,geometry}
\geometry{left=1cm,top=1.3cm,bottom=1.3cm,right=1cm,headsep=0.1cm}
\pagestyle{empty}
\begin{document}
\begin{asydef}
// Global Asymptote definitions can be put here.
usepackage("bm");
usepackage("babel","french");
usepackage("fontenc","T1");
usepackage("inputenc","utf8");
defaultpen(fontsize(10));
\end{asydef}
\begin{asy}
import geoplane;
//dessin à main levée
mainlevee=true;
pair A=(0,0);
path tt=rectangle(A,7,5,angle=-15);
draw(tt);
nomme("$A$",sommet(tt,0),sud);
nomme("$B$",sommet(tt,1),sud);
nomme("$C$",sommet(tt,2),nord);
nomme("$D$",sommet(tt,3),nord);
draw(segment(sommet(tt,0),sommet(tt,2)));
etiquette(sommet(tt,0),sommet(tt,2),"8,6 cm");
etiquette(sommet(tt,0),sommet(tt,3),"5 cm");
etiquette(sommet(tt,0),sommet(tt,1),"7 cm",dessus=false);
angledroit(sommet(tt,0),sommet(tt,1),sommet(tt,2));
\end{asy}
\begin{asy}
import geoplane;
pair A,B,C,D,I,L,J;
figure((-0.5,-0.5),(6.5,6.5));
A=(0,0);
B=(0,6);
C=(6,6);
D=C-B+A;
I=milieu(A,D);
L=A+4/6*(B-A);
draw(A--B--C--D--cycle);
draw(L--I);
draw(L--D);
cote(B,C,"6 cm",2mm,0.5*green);
hachurage(I--L--D--cycle,2mm,45,blue);
filldraw(L--D--C--B--cycle,0.8*white);
angledroit(A,D,C,red);
cotemilieu(A,L,"4 cm",2mm);
nomme("$A$",A,p=blue,sud);
nomme("$B$",B,nord);
nomme("$C$",C,nord);
nomme("$D$",D,sud);
nomme("$I$",I,sud);
nomme("$L$",L,ouest);
pointe(milieu(L,I));
codemilieu(L,I,5);
draw(droite(A,milieu(L,I)),dashed);
J=intersectionpoint(droite(A,milieu(L,I)),B--C);
nomme("$J$",J,nord);
codemilieu(A,D,2);
path d;
d=perpendiculaire(A,D,J);
draw(d,0.6*red+dashed);
draw(arc(A,L,2,-92),orange);
codeangle(I,A,J,0,2,green*0.5+1.5bp);
\end{asy}
\end{document}