verbatimtex
%&latex
\documentclass{article}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage[frenchb]{babel}
\begin{document}
etex;
input geometriesyr12;

beginfig(1);
u:=0.8cm;
z0=(-0.5,0)*u;label.bot(btex$B$etex,z0);
z1=(2.5,0.5)*u;label.lrt(btex$C$etex,z1);
z2=(4,2)*u;label.rt(btex$D$etex,z2);
z3=(-0.5,2.75)*u;label.bot(btex$E$etex,z3);
z4=(-3,1.5)*u;label.lft(btex$A$etex,z4);
z5=(0.5,6)*u;label.top(btex$S$etex,z5);
z6=(0.5,1.5)*u;label.bot(btex$H$etex,z6);
z7=z6 shifted (5u,0);
draw z4--z0--z1--z2;draw z2--z3--z4 dashed evenly;
draw z5--z0; draw z5--z1;draw z5--z2;draw z5--z4;draw z5--z3 dashed evenly;
draw z5--z6 dashed evenly; draw codeperp(z7,z6,z5,8);
drawarrow z5 shifted (1.5u,0)--z5; label.rt(btex$sommet$etex,z5 shifted (1.5u,0));
drawarrow (point 0.4*length(z5--z2)of(z5--z2)) shifted (1.5u,0)--point 0.4*length(z5--z2)of(z5--z2);label.rt(btex$ar\hat{e}te$etex,(point 0.4*length(z5--z2)of (z5--z2)) shifted (1.5u,0));
drawarrow (point 0.25*length(z5--z6)of(z5--z6)) shifted (-3u,0)--point 0.25*length(z5--z6)of(z5--z6);label.lft(btex$hauteur$etex,(point 0.25*length(z5--z6)of (z5--z6)) shifted (-3u,0));
drawarrow (1.5,-0.5)*u--(1.5,1)*u dashed evenly;label.bot(btex$base$etex,(1.5,-0.5)*u);
path s;s=0.5[z5,z4]--0.5[z5,z0];
drawarrow (point 0.2*(length s) of s) shifted (-2u,0)--point 0.2*(length s) of s;
label.lft(btex face latérale triangulaire etex,(point 0.2*(length s) of s) shifted (-2u,0));
endfig;
beginfig(2);
u:=1cm;
z0=(0,0)*u;
z1=(1.5,-1)*u;
z2=(4,0.5)*u;
z3=(2,2.5)*u;
draw z0--z1--z2;draw z2--z0 dashed evenly;
draw z0--z3;draw z3--z1; draw z3--z2;
label.bot(btex Pyramide à base triangulaire etex,(2,-1)*u);
endfig;
beginfig(3);
u:=0.8cm;
z0=(0,0)*u;
z2=(5.5,1.5)*u;z1=(4,0)*u;z3=(1.5,1.5)*u;
z4=(2.75,5)*u;
draw z0--z1--z2;draw z2--z3--z0 dashed evenly;
draw z0--z4;draw z4--z1; draw z4--z2; draw z4--z3 dashed evenly;
label.bot(btex Pyramide à base rectangulaire etex,(2.75,-1)*u);
endfig;
beginfig(4);
u:=0.7cm;
z0=(0,0)*u;
z1=(5,0)*u;
z2=(7,2.75)*u;
z3-z0=z2-z1;
z4=whatever[z0,z2]=whatever[z1,z3];
z5=z4 shifted (0,6u);
draw z2--z3--z0 dashed evenly;
draw z0--z1--z2; draw z5--z0;draw z5--z1;draw z5--z2; draw z5--z3 dashed evenly;
draw z0--z2 dashed evenly; draw z1--z3 dashed evenly;
label.bot(btex$O$etex,z4);label.llft(btex$A$etex,z0);label.lrt(btex$B$etex,z1);
label.rt(btex$C$etex,z2);label.lft(btex$D$etex,z3);label.top(btex$S$etex,z5);
label.bot(btex$ABCD\ est\ un\ carr\acute{e}\ de\ centre\ O$etex,(xpart(0.5[z0,z2]),-1u));
endfig;
beginfig(5);
u:=0.7cm;
z0=(0,0)*u;label.llft(btex$A$etex,z0);
z1=(5,0)*u;label.lrt(btex$B$etex,z1);
z2=z1 rotated 90;label.llft(btex$D$etex,z2);
z3-z2=z1-z0;label.lrt(btex$C$etex,z3);
z4=0.5[z0,z1] shifted (0,12.5u);label.top(btex$S$etex,z4);
draw z0--z1--z3--z2--cycle;draw z2--z4;draw z3--z4;
z5=z2 rotatedaround(z4,180-2angle(z3-z4));label.lft(btex$A_{1}$etex,z5);
z6=z3 rotatedaround(z4,-180+2angle(z3-z4));label.urt(btex$B_{1}$etex,z6);
z7=z6 rotatedaround(z4,-180+2angle(z3-z4));label.rt(btex$A_{2}$etex,z7);
draw z4--z5;draw z2--z5; draw z4--z6;draw z4--z7;draw z3--z6;draw z6--z7;
draw codeperp(z1,z0,z2,8); draw codeperp(z0,z2,z3,8);draw codeperp(z2,z3,z1,8);
draw codeperp(z3,z1,z0,8);draw codemil(z0,z1,45);
draw codemil(z2,z3,45);draw codemil(z0,z2,45);draw codemil(z1,z3,45);
draw codemil(z5,z2,45);draw codemil(z3,z6,45);draw codemil(z6,z7,45);
draw codesegments(z4,z3,z4,z6,2);draw codesegments(z4,z3,z4,z7,2);
draw codesegments(z4,z5,z4,z2,2);
endfig;
beginfig(6);
u:=1cm;
z0=(0,0)*u;
z1=(3.5,-1.5)*u;
z2=(4,0.5)*u;
z3=(2,2.5)*u;z4=(2,-0.5)*u;draw z3--z4 dashed evenly;z5=z4 shifted (u,0);
draw codeperp(z5,z4,z3,8);
draw z0--z1--z2;draw z2--z0 dashed evenly;draw z0--z3;draw z3--z1; draw z3--z2;
drawarrow (point 0.3*length(z3--z4)of(z3--z4)) shifted (2u,0)--point 0.3*length(z3--z4)of(z3--z4);
label.rt(btex$hauteur$etex,(point 0.3*length(z3--z4)of (z3--z4)) shifted (2u,0));
label.lft(btex$h$etex,point 0.5*length(z3--z4)of (z3--z4));
label.lrt(btex$\mathcal{B}$etex,z4 shifted (1.1u,0.5u));
drawarrow z1 shifted(u,0)--z1 shifted (0,0.7u);
label.rt(btex aire de base etex,z1 shifted(u,0));
path p;p=z0--z1--z2--cycle;
endfig;
beginfig(7);
u:=1cm;
z0=(0,0)*u;
path c;
c=(fullcircle scaled 4cm)yscaled 0.3;draw  (subpath (0,0.5*(length c)) of c)dashed evenly;
draw (subpath(0.5*(length c),length c) of c)  ;z6=(0,4u);label.top(btex$S$etex,z6);
draw (point 0.5*(length c) of c)--z6;draw point 0 of c--z6;label.lft(btex$O$etex,z0);
z4=point 0.85*(length c) of c; label.bot(btex$M$etex,z4);
draw z6--z0 dashed evenly;draw z0--z4 dashed evenly; draw codeperp (z4,z0,z6,8);
draw z6--z4;drawarrow (point 0.3*(length (z6--z0)) of (z6--z0) shifted (-2u,u))--point 0.3*(length (z6--z0)) of (z6--z0);
label.lft(btex$ hauteur$etex,(point 0.3*(length (z6--z0)) of (z6--z0)) shifted (-2u,u));
drawarrow (point 0.3*(length (z6--z4)) of (z6--z4)) shifted (2u,u)--point 0.3*(length (z6--z4)) of (z6--z4);
label.rt(btex$ g\acute{e}n\acute{e}ratrice\ \left[SM\right]$etex,(point 0.3*(length (z6--z4)) of (z6--z4)) shifted (2u,u));
endfig;
u:=1cm;
_nfig:=7;
figure(-10u,-10u,10u,10u);
z0=(0,0)*u;label.lrt(btex$O$etex,z0);
path c;
c=(fullcircle scaled 3u);draw c withpen pencircle scaled 1.5 bp;
z1= point 0.15*(length c) of c;label.rt(btex$M$etex,z1);
z2= z1 shifted (sqrt(20)*unitvector(z1-z0)*u);
label.urt(btex$S$etex,z2);
draw z0 shifted (-u/20,-u/20)--z0 shifted(u/20,u/20);draw z0 shifted (-u/20,u/20)--z0 shifted(u/20,-u/20);
draw z2 shifted (-u/20,-u/20)--z2 shifted(u/20,u/20);draw z2 shifted (-u/20,u/20)--z2 shifted(u/20,-u/20);
draw (z1 shifted (-u/20,-u/20)--z1 shifted(u/20,u/20)) rotatedaround(z1,45);draw (z1 shifted (-u/20,u/20)--z1 shifted(u/20,-u/20)) rotatedaround (z1,45);
draw z0--z2 dashed evenly;
path d;
d=cercles(z2,(sqrt(20)*u));
numeric q; q=length c/length d;
path v;v= subpath(0, arctime(arclength c) of d) of d;
draw v rotatedaround(z2,180) withpen pencircle scaled 1.5 bp;
z3= point 0 of v;z4=point (arclength v) of v;
draw z2--(z3 rotatedaround(z2,180));draw z2--(z4 rotatedaround(z2,180));
draw codesegments(z3 rotatedaround(z2,180),z2,z4 rotatedaround(z2,180),z2,2);
drawarrow (point 0.7*(length v) of v rotatedaround(z2,180)) shifted (0.9u,-u)--point 0.7*(length v) of v rotatedaround(z2,180);
label.bot(btex arc de cercle de même longueur etex,(point 0.7*(length v) of v rotatedaround(z2,180)) shifted (1.25u,-u));
label.bot(btex que le disque de base etex,(point 0.7*(length v) of v rotatedaround(z2,180)) shifted (0.5u,-1.5u));
draw marqueangle(z3 rotatedaround(z2,180),z2,z4 rotatedaround(z2,180),0);
label.lrt(btex $\alpha$etex,z1 shifted (4*unitvector(z1-z0)*u)); 
fin;
beginfig(9);
u:=1cm;
z0=(0,0)*u;
path c;
c=(fullcircle scaled 4cm)yscaled 0.25;draw  (subpath (0,0.5*(length c)) of c)dashed evenly;
draw (subpath(0.5*(length c),length c) of c)  ;z6=(0,3.4u);label.top(btex$S$etex,z6);
draw (point 0.5*(length c) of c)--z6;draw point 0 of c--z6;label.lft(btex$O$etex,z0);
z4=point 0.85*(length c) of c;
draw z6--z0 dashed evenly;draw z0--z4 dashed evenly; draw codeperp(z4,z0,z6,8);
drawarrow (point 0.3*(length (z6--z0)) of (z6--z0) shifted (-2u,u))--point 0.3*(length (z6--z0)) of (z6--z0);
label.lft(btex$ hauteur$etex,(point 0.3*(length (z6--z0)) of (z6--z0)) shifted (-2u,u));
label.rt(btex$h$etex,0.5[z0,z6]);
label.lft(btex$\mathcal{B}$etex,z0 shifted (-u,0));
drawarrow (u,-1u)--(0,-0.4u);label.bot(btex aire de base etex,(u,-1u));
label.top(btex$r$etex,0.5[z0,z4]);
endfig;
end