$$$$)(c)1997 Inspiration Software, Inc. 5.0 X=~қHH(؇؇EG(HH(d'`:d:d(   .H6$!$$=*T (BBFFF(ABXBXFFF****8h $$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF26Animals Make Believe,kI`vI;E;E  /  7Crw9 ٟ Ԉ GEOMETRY @$hy>]hZn>UZZnZZ  l ]hZnZZZ] \d  tREAL WORLDD,i@M QM x m+S+S ct  $FHTT9  hɿ tJOBS@k Pf<z P +S +S    $FkEpXX9  l tTHEOREMS٫Dmm K8}m K +\ +S   $NBrZZ@ @   tDIMENSIONSnBq(B+S +S    $F {#^^9  T tSPACE GEOMETRYٯ٫mm4m4+S +S    $F^^9 | tPLANE GEOMETRY٬pp12ee12Ss SR  d MozYY:6 ڳ`  tTRIANGLESHٯkpf}R+V+S t  $IkYY<  ,  tEQUATIONS٬iMjMjx+S+S    $F__9 Թɡ QUADRATIC FORMS   /*c5VUklkUkVx/ p %Jmodels p  9CZzk Ckz CZx `ɏ  %Jis used byԫ   +oz ` P P`x ѯʥ %Jis emphasized byx x 8F ."_km ykm y_x8 X| %Jis generated by,   \/jc[klkk[x\/ Ԁ  %Jconsists of(  8F X[]mkkm][x8 8  %Jconsists ofH  /BcM]k2lk2k]x/ T  %Jhas componentن x  ozH^TIIT^x ي %Jrepresented by ɥ ;9Clzkkz F_  rO++`` +..؟++`+f# fdߥ,  Miscellaneous Thoughts F O+..؟  RW*B <L@<88 @ ~ <9e7@<@5E>0QQߥߥ<Q *** MEDIAN: It is a segment from any vertex to the midpoint of the opposite side. 2     ****)(c)1997 Inspiration Software, Inc. 5.0 X:G؂lHH(؇؇EG(HH(d'`:d:d(   ,H6$!$%Tw(BBFFF(ABXBXFFF****fk١$$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF26Animals Make Believej@40P4+S+S ct  $F5KTT9  , tJOBSڿhSF0c+[o+S tt $MPZZ? (  tARCHITECTSԓj0P +|+S  $i5K^^V   tMATHEMATICIANSdڿls% G% P`+Vp+S c0  $IQ~ZZ<  T  tSCIENTISTS$ԓh`gg0+Y+S ` $KYY= <  tEDUCATORSѡdlP%j%jP+Sb+S 0  $FXX9   tSTUDENTS\$n (_)+S +S    $F *#UXX9  Ɉ tTHEOREMSԳѡi@MvMvx+V+S   $IYY<  Ċԟ  tENGINEERS\mmm +Y+S  $KZZ=  ĈԆ  tPHYSICIANSԳkf +S+S   $FkXX9  (Ó tCHEMISTSګ  ]kD[2]5]25[x] È  %Jhas example( ` M; Ey[[x <ԏ  %Jhas example$ ( q{D[]%5]%5[x   %Jhas exampleٿ d ]<k[2]]2[x]< 0  %Jhas example ѫ <q{[]%]%[x< ɓ  %Jhas example L ; *l[cvcv[x ُl  %Jhas exampleԯ  XJfwXR5mR5mXxXJ H %Jcontains ŏ JwY 5%%5 YxJ Ԋ  %Jcontains F$ ,fb:RN*|T] BD*** Mathematicians used geometry to find out real world problems, to characterize structures.:FɊL`  *** Architects use triangular components to enhance the beauty and stability of their designs. Spaceship world in Disney World illustrates the use of triangular shapes in construction. 2     ****)(c)1997 Inspiration Software, Inc. 5.0 X^ `HH(؇؇EG(HH(d'`:d:d(   hLH6$!$%TT&(BBFFF(ABXBXFFF****8j84$$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF26Animals Make Believek@ fI _+S+S c  $FkS}TT9  5,58 tJOBS2     ****)(c)1997 Inspiration Software, Inc. 5.0 X9 olHH(؇؇EG(HH(d'`:d:d(   tJH6!$#Tw(BBFFF(ABXBXFFF****m $$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF 03Flowchart2<k fI _+S +S    $FkS}XX9  ڿ tTHEOREMS(m0m2m C+l +S   $[%[[J    fPYTHAGOREANѬ<o >I^ (_+S+S   $FCSY}__9 ڳh fRIGHT TRIANGLES<(op$/m$<Ss SR  kd MoMjYY:6 T  tTRIANGLESـѬmm m !+i+S  $Y\\I  ʥ8  fAPPLICATIONS<o >^ (!+e+S  $UCY]]E  ن  fAPPLICATION-1ـmpm!(tm!!+e+S  $U4h]]E    fAPPLICATION-24  =WKlNNlx=W $ )is one of the most important   eZ5  5Zxe  ڏ  )representsl   IS?Xz  zXx  ( ) part of \ | ? /X E  E Xx| ? ԳĊ )has some $  !!~S    Sx  ѡ )HAS ԓ |!!+S!!!!Sx|! d )HAS'RV  R ,f'8ߥߥH *** According to Pythagorean Theorem the sum of the squares of the legs of a triangle equals square of the hypotenuse which is the side opposite of the right angle.   _hh*<(ٓ,گ ـ*** PROBLEM: Mike bought a 6-foot-square sheet of plywood to use as a base model railroad. Will the plywood fit into the back of their van if the opening is 44 inches high and 60 inches wide? ـh ـSolution: x^2=(60)^2+(44)^2 . Then, x=74.4 inches>6 feet so that it would fit into the back of their van ـ FFԙ8ٹt| *** Problem: Mike's family plane to purchase a tv-set with a 20 inch diagonal screen to place in wall unit. Width of the screen is about 15 inches. What is the minimum distantance that must be allowed between two shelves of the wall unit to accomodate that set?  ***Solution: (20)^2=(15)^2+x^2 2     ****)(c)1997 Inspiration Software, Inc. 5.0 X1lHH(؇؇EG(HH(d'`:d:d(   6H6!$%R|K(BBFFF(ABXBXFFF****x$$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF 03Flowchart1ɏj0P +\ +S   $N5KZZ@ Tي  tDIMENSIONS8j40P4+S +S    $F5K^^9 | tSPACE GEOMETRYنɏlA%%P +d +S   $TaaD |  tTHREE DIMENSIONALHl&6c&N(= (0  r %;<]WW- ( tCIRCLES(نm`^v^\Ii IH  Q   De~^^V   tQUADRILATERALS,Hmm6m+S+S   $F,VV9  T` tSOLIDS(mpY2eY2Ss SR  Td MozYY:6   tTRIANGLES ņ To%y]55]x   %Jis process in | Ir]|]&]]&]x ٙ  %Jhas component ʆ  ](_]]_(]x    %Jhas component ɥ W]]m]m]xW xT  %Jhas component    X]]Zl]Zl]x    %Jhas component `  q{[%%[x  ɡ  $has example F$ )RL)ߥߥߥ6   *** Area of a circle=p(r^2)6   *** Perimeter =2pr 2     ****)(c)1997 Inspiration Software, Inc. 5.0 XEp؂lHH(؇؇EG(HH(d'`:d:d(    H6$!$%R`|(BBFFF(ABXBXFFF**** l0$$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF26Animals Make Believe@g/ ?+d +S   $T#__D D tTWO DIMENSIONALhjj0+S +S    $F^^9 x tPLANE GEOMETRY@jj0Pj+S+S   $F5Kaa9 | tANALYTIC GEOMETRYip9 )]9  }Ss SR  -d Mo &HYY:6 h  tTRIANGLES8lP%-l%P+S+S   $F7bUU9   tLINESl% _%P)+S+S   $F*UTT9  X| tRAYSϬ8mm4m4+S+S   $FXX9  Tl tSEGMENTSl%%P +S+S   $FVV9  0 tANGLESϬn` ( !+S+S   $F #UU9   tRIGHTo >d^ ( +S+S   $FCnYUU9   tACUTEpE sQE p m+S+S   $FyHVV9  x tOBTUSEj0%Ps+h+S  $X51Kg[[H    tCOORDINATESl`% % P!E+S+S   $FUU9  Lʳ EDGES  \WjX22Xx\W D %Jknown as  cqp{[%%[x @  thas example  q{D[%%[x    thas example ڙ <[]mm][x< \  thas example  qq;{[%%[x \  thas example, P  JYk7o% D D%oxl %Jis described according to theirx  | # t[;  ;  [x| #  H  %Jhas example,    _[R R [x   d  %Jhas example8 l  I6[RE CRE C[x  8  %Jhas example ( j;uE\jj\x  x|  %Jpresented byϹ  M]]x  h  $is process in,   s YVko D%! D%!ox sp $is described according to their4 ړ XfH\^Rm]Rm]^xX D )combination of x <+J];L;L]x<+    )are two sided F$ LR@ ,fi 4L*ߥT*ߥO *** An angle is the union of two noncolinear rays which have the same endpoint.6[    *** BISECTOR: It is the segment from any vertex to the opposite side on the ray bisecting. IIߥ(ߥęI *** They can be considered as combination of segments or two sided rays.  2     ****)(c)1997 Inspiration Software, Inc. 5.0 X:W؂lHH(؇؇EG(HH(d'`:d:d(   >wH6$!$%Tw(BBFFF(ABXBXFFF****9o$$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF26Animals Make Believepl%9%P+\ +S   $N/ZZ@ \  tDIMENSIONS8kofo+d+S  $Tk__D d tONE DIMENSIONALpi0M9jM9x+d+S  $Tv__D X tTWO-DIMENSIONALD8mmomo+d+S < $TaaD T THREE DIMENSIONALɓn(6+S +S    $F #,^^9 ɊL tSPACE GEOMETRY4Dop/m5< GSs SR  Pd MoMjYY:6 |È  tTRIANGLESɓiE3 fE;E;E  | 7C3^9 ÓL T@ GEOMETRY $4l%V%P+S +S    $F`^^9 Æ tPLANE GEOMETRYmm P<zm P +S+S H  $FEpUU9   fSPACEɟ 8 p:_;o;o_x `ɥ %Jis separated as@ 4 UW&a_z%j%zj_x ɿ| %Jis separated asɆ d Xfp:_RmRm_xX \ )is separated as H /'c2]  ]x/ x  %Jhas componentɹ ( n8]oo]x  t  $is process in   ~Yc_%%_x ɡp $is generated by $ Y3c[%%[x  l  $consists of( ɬ pXc.]h;;;h;]xp  h  $is process in  | N:X P PXx| l  )known as F$ RI,fZ''H' p*** LINES ARE ONE DIMENSIONAL SUBJECTS. p((0`ť( 8*** CIRCLES are two dimensional subjects 82     ****)(c)1997 Inspiration Software, Inc. 5.0 X(؂lHH(؇؇EG(HH(d'`:d:d(   [q&H6$!$&Tw(BBFFF(ABXBXFFF****B"i$$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF26Animals Make BelievexiAMMxC+S +S    $F^^9 T@ SPACE GEOMETRYip9$)9$Ss SR  {d Mo &YY:6 Ŀ  tTRIANGLEStxl%~%PQ+S+S   $FVV9  , tANGLESiMBqMBx+S+S   $F{UU9   tEDGES  \j$~]cEd@cEc@]x\    $has component $ Zlo:'^^':ox` $is described according to their  VnSobzcBbzbBoxVX $is described according to their F% .(.. ~ ---;(- 1 ~ 8H48A%2     ****)(c)1997 Inspiration Software, Inc. 5.0 X,؂lHH(؇؇EG(HH(d'`:d:d(    H6$!$(Tw(BBFFF(ABXBXFFF****9j0H$$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF26Animals Make Believe@j0P6+S+S   $F5K,VV9  (, tANGLESL(j`0P +S+S   $F5KUU9    tRIGHT@mmm +S+S   $FUU9  P tACUTELmm6m+S+S   $F,VV9  ` tOBTUSE( @ ;PE[[x     %Jhas example \ O[mm[x    %Jhas example x D[mm[x  D  %Jhas example F' R` ,fbհ@zy|: *** These are the angles which are grater than 90 degrees. ''|8 *** These are the angles which are less than 90 degrees. L!!ʫij! @*** Angles that equal 90 degrees. @2     ****)(c)1997 Inspiration Software, Inc. 5.0 X4n؂lHH(؇؇EG(HH(d'`:d:d(   <H6$!$(Tw(BBFFF(ABXBXFFF****hmj$$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF26Animals Make Believemm4m4+S+S   $FUU9  4T tEDGESkBfqB+S+S Y  $Fk{YY9    tISOSCELESm m9jm9+d+S  $Tv[[D    tEQUILATERALo>B>q^B(+S}+S   $FC{YWW9   tSCALANEjp!r_aSs SR  Rd Mo?\YY:6 ʥ  tTRIANGLES x |V_99_x|  %Jis described as   X_]k]k_x į %Jis described as  5C X_ ]mkm] k_x5  %Jis described as  '~(m](m] F' @zy{ ~ p,fbRML pl( O *** ISOSCELES TRIANGLES are consists of two equal edges and two equal angles.  ( *** Their median and bisector are same.   p%%8|ĈD& X X*** In this kind of triangles, all the edges and all the interior angles are equal. To find out their area we use the following formula, A={(a^2)(3^(1/2))} / 4.  XF X*** To find their height we use h={a*3^(1/2)} / 2 X/ X*** Their height, median and bisector are same. XZZϹ* 0 Tq T*** These triangles has no property in common. They have different angles, different sides and different heights.2     ****)(c)1997 Inspiration Software, Inc. 5.0 XH=؂lHH(؇؇EG(HH(d'`:d:d(   .H6!!$.Tw (BBFFF(ABXBXFFF****+i0t$$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF23Starsj0P) 7+S+S    $F5KTT9  ԙ tBEES4s ;< ; P;E;E  F 7C"99 Ɉ ѡԟ GEOMETRY Ɋpy-0]hZb-0ZZnZZ  Al ]hZZZZ] $  tREAL WORLDtnQ(!+_+S  $P ]#``A ` tRIGID STRUCTURES`Ɋn@(6+S+S   $F #,VV9  LT tNATUREԆtl%4%4P+S+S   $FVV9  ɫ tPLANTSx`l%x%xP+S +S   $FWW9  $Ϲ tANIMALS8Ԇi29cnI829`I`I  bYp cnI08YYIc  ʹ  fPINETREESљxl%\C%\P+S]+S   $F9aa9 ګ SATELITE ANTENNASd8o>c^(+S+S   $FCmY__9 ` QUADRATIC FORMSљq"+h+S  $X[[H    PARABOLOIDS,dj 0-Pl+S+S   $F57KbXX9   fPYRAMIDSj s8isunnr  C  f{7XTzaa./+!ړ fFIVE-POINTED STAR\  !V] ^ ]]Vx! $ %Jmodels|  cApK^-]-]^x  %Jhas example in  WAK^]--]^xW ɓ %Jhas example in8  }WZR]R]Zx}W H  %Jconsist of h }q;ZRRZx} l  %Jconsist ofԿ  !eo[]%^%]][x!   %Jhas example , 2@Me pySR R Sx2  )useԯ   q{ [% % [x    $has exampleD  }y^RR^x} P $has example of   ..8<`RNRN`x. Ԋ $is an example of  D Uc3[*B*B[xU  @  $has example   5C3[[x5  ϡ  )has examplex  | N\e [[xN  D  )are kind of x 0sd~[6%%6[x0     )has example FgD-  RN ~@zw RMߥH *** Bees show eachother the place where they find their food by using geometry. For example, a bee measures the angle between the line segments that connect the bee itself to its home and its home to sunand then he turned to his friends with this angle and finally begins to dance that determines the kind of food. Then his friends see that angle and come to the same place by using this angle. ~Tߥ(ߥ *** There is a design in the body of black-pinetrees. When we count the number of pinecones carefully, we see that there are 8 cones in the right side and 5 cones in the left side. Also all the pine cones are ordered as a mathematical shape, spiral.  ??ߥߥD? *** They are a good example for how geometry models real world. 2     ****)(c)1997 Inspiration Software, Inc. 5.0 X)؂lHH(؇؇EG(HH(d'`:d:d(    H6$!$&Tw (BBFFF(ABXBXFFF****p$$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF26Animals Make Believekpf7+V+S t  $Ik-YY<  d   tEQUATIONS$kf-l+S +S t  $Fk7bVV9   tBEAUTYk`$ 0;E;E  Z 7Cr9  \D GEOMETRY   ~q{aax P %Jis represented by  5ogzaax5 $ $is represented by F%  R 8(8ʡ ?*** There is a rate which is called golden-rate that helps to formulize beauty. Let's say the distance between your belly and your toe-fingers y. And say x for your height.   ?x/y=y/(x-y) ?Here the rational x/y is known as golden-rate. If measurements of a body satisfy this equation it means that that person is really beautiful. This rate is approximately 1,6666... 2     ****)(c)1997 Inspiration Software, Inc. 5.0 X)olHH(؇؇EG(HH(d'`:d:d(   &H6$!$$Tw(BBFFF(ABXBXFFF****i$$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF26Animals Make BelieveHk fI _+S+S   $FkS}__9 ( QUADRATIC FORMS| lh%4%4P+S+S   $FXX9  ĥ ELIPSOID HmpmDme+_+S H $PPZZA  \h  PARABOLOID|l%/%P ?+d5+S  $T#[[D  <  HIPERBOLOIDѥ iM~MxQ+S+S H  $FXX9  `< ANTENNASiM)Mx 7+S +S   $FXX9   fPYRAMIDSD  D ]%5 5%]H ګ 4Bq; 5m6 5m5,  d 5%  5% ѫ  rq{/`z'm5z'm5`xr L $is an example of 8 e<Fz5 5z 2     ****)(c)1997 Inspiration Software, Inc. 5.0 X#olHH(؇؇EG(HH(d'`:d:d(    H6"!$.Tw (BBFFF(ABXBXFFF**** n$$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF24PlantskcnIQM0Z`I`I  %Yp cnIMYYIc  ŀ  fPINETREESnop{IK omImI  w[ p{ICK ZZIp  4   fBLACK TYPEn }p{IK}mImI  &Od p{ICKZZIp  $  fOTHER TYPET  [i X0505 å [/ic05052     ****)(c)1997 Inspiration Software, Inc. 5.0 XCo؂lHH(؇؇EG(HH(d'`:d:d(   2O H6$!$0"u(BBFFF(ABXBXFFF****@'j05,$$$$cccc  >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF26Animals Make Believeh P<z P0 +S+S    $FEpTT9   tBEESPny]hZD8ZZnZZ  Ml ]hZ;C8ZZZ]   tREAL WORLDxl%.%.P+_+S  $P``A  tRIGID STRUCTUREShl@% I% P_+S+S   $FS}VV9  ` tNATUREXxj0P6+S+S   $F5K,VV9  h tPLANTSHhj0P) 7+S +S   $F5KWW9  P tANIMALS$XgcnIy2`I`I  LYp cnI2YYIc    fPINETREESHj0VP+S]+S   $F5`Kaa9 x SATELITE ANTENNASd$lp%\C%\P+S+S   $F9WW9  h fBRIDGESj0PM+h+S  $X5K[[H  x  fPARABOLOIDSD \ qW^R]R]^xqW  %Jhas example in(  q;l^R5R5^xq  %Jhas example in@  ;r|lZ%5%5Zx $  %Jconsist ofX 4 er|Z5% %5 Zxe ,<  %Jconsist of  LZD[[xL   %Jhas example  \ j z[[1  o 1 o[x\     $has example  crp|^%]%]^x  $has example of  4B,G[;<.;.;[x4    )has example L P;EVaOOaxP  )have the shape of F /   ~T <=L  *** Bees show eachother the place where they find their food by using geometry. For example, a bee measures the angle between the line segments that connect the bee itself to its home and its home to sunand then he turned to his friends with this angle and finally begins to dance that determines the kind of food. Then his friends see that angle and come to the same place by using this angle. ~T40,( *** There is a design in the body of black-pinetrees. When we count the number of pinecones carefully, we see that there are 8 cones in the right side and 5 cones in the left side. Also all the pine cones are ordered as a mathematical shape, spiral.  THP< $*** Satelite antennas have the shape of paraboloids which have the below formula. The reason for using parabolas to construct satelite antennas is that only the parabolic shapes can take the largest quantity of frequencies. $  $z^2=x^2+y^2 $tt*lu *** All bridges that are planned by architects are designed by using geometric shapes, especially triangular shapes.  2     ****)(c)1997 Inspiration Software, Inc. 5.0 X=olHH(؇؇EG(HH(d'`:d:d(   XaH6!$%9a(BBFFF(ABXBXFFF****@6l $$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF 03Flowchart1j 0IP _+S+S   $F5SK}VV9  , tSOLIDSPlff_I[IH  N3  DX [[J  ğ  fPOLYHEDRONSTl%%P +Sg+S   $FVV9   fPRISMSPl b FtRdCl `Tkk5 G;pRdCP k k89Rd@`m ę`k  k 4  F87"Rd@_ft (lp   2 _ CA3"Rd@;ft ęlD D_"Rd@2Pflt (l0 #"Rd@ft n K$["L"7  w  I NZZD   $  fPENTAGONALHn( +Z+S  (ġ (W &[[H  p  fRECTANGULARlno :+6 : RRR  btl L{BrZZ?  T  fTRIANGULARHmf < -ef < =KRd@C4 ,lm@g  g  <B"Rd@Jzfdt mf  evf  <"Rd@^PfXt ,mj  wj  8T"Rd@"ft  m`g  eg h h"Rd@-ft n x Z5w x O'"Rd@\ft ( mqP|qP"7"7  w  5~m0s K |sPHARd@w@ (mUt[  t[G-Rd@Z4 n0\ \E+"Rd@,^ft hn6 h&6kH5"Rd@f$t n  L N"Rd@ft hnP J{OFA"Rd@ fʓt  0 !lvY55H 4 Jqw{5%5% $ ~JwSR5R5Sx~J L )hast $ | SRRSx|  )has Ĺ r cJSR xR xSxr  )hasRN ,fʿ lee*īe *** These are figure formed by four or more noncoplanar polygon regions that enclose a part of space. ]d p<s P*** A prism is a polyhedron with 2 congruent faces contained in parallel planes. All other faces are parallelogram. P# P*** In general, area of a prism is:A P Total Area=h*(perimeter of right section)+2*(Area of base) # P Volume = (Area of base)*h 2     ****)(c)1997 Inspiration Software, Inc. 5.0 X$olHH(؇؇EG(HH(d'`:d:d(   H6!$%Rt|(BBFFF(ABXBXFFF****0m$$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF 03Flowchart1k`f8t+~ +S   $jkG^^V  tQUADRILATERALS\mm4m4+S+S   $FXX9  hĥ fPOLYGONSmm-m =+_g+S  $P"[[A    fEQUILITERAL p 4BD[ ]m4 4m][x4  (  )is known as ʹ 4dB[ 4m  4m [x4d    )is known as2     ****)(c)1997 Inspiration Software, Inc. 5.0 X)GolHH(؇؇EG(HH(d'`:d:d(   pFH6!$%R`|(BBFFF(ABXBXFFF****tkp$$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF 04ISO90008k fI _+S+S   $FkS}XX9   fPOLYGONS(k W]  }Ss~SR   d MouHYY:6  ($  fTRIANGLES  q{Za &a &Zx    )consist ofR d,fk~0@zv~P x*ϯ\*tx8 xxd *** They are the union of 3 or more coplanar segments such that each segment intersects exactly 2 other segments, one at each endpoint, and no two intersecting segments are colinear.  *** They are known as convex and concave. If each line that contains the side of the polygon contains no points in the interior of the polygon, it is convex. Otherwise it is said to be concave.  *** The sum of measures of the intertior angles of a covex polygon is (n-2)*180. For exterior angles it is 360. Here, n is the number of sides and (n-2) is the number of triangles in the polygon. Hence we can say that polygons are consist of triangles. 2     ****)(c)1997 Inspiration Software, Inc. 5.0 X4olHH(؇؇EG(HH(d'`:d:d(   .H6!$%R|(BBFFF(ABXBXFFF****wk$$$$cccc >+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF 03Flowchart1kf9s+|g+S  $ikG]]V    fPARALLELOGRAM@8meaea:d:d  5* 6`WW8 ʳ fRHOMBUStn I( _+S+S  )P K&ZZM  TT  fRECTANGLES@mZZ QQgQQ  K KNVVI# < fSQUAREtipM<mM<x+_+S  $Px[[A  h$  fEQUILITERALk cT  q0[0S  Gt -XeHYY9    fTRAPEZOID@  0> X[ e4 4e[x0   P  )HAS EXAMPLE  +I9v[ 4Z 4Z[x+I    )has exampleP  Xfp: 45 44  <UF^zEkzkE^x d )represented as   q{[u u [x  x\  )has exampleR?i~,fk ~@zxaRNeT112 *** They are parallelograms with four equal sides.38p<3 *** They are parallelograms with four right angles. ~--@. *** They are rectangles with four equal sides.80 8*** They are quadrilaterals in which both pairs of opposite sides are parallel and equal. Also angles in opposite sides are equal. 8MMH4M *** They are parallelograms with exactly one pair of opposite sides parallel. 2      ITMP163.TMPtemsiverrnetnett610)TEMPCER3hGI |{This document is an Inspiration 5.0 document. 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