TBMathM1co

lts^5[ !D grnjvlhk’I6[lujc90hk’0t|ko ABCD g,njvI6hlk,g,af A, B, C F gryoj 0ufmjvo-nj AB c]t BCF 9kdoAogryoj 0ufmjvodq’j mu,j u.9dk’ C c]t ]aflt\\ugmqkj  AB c]h;0ufmjvo dqj’mulv’muj,u.9dk’ A c]t ]aflt\\ugmqkj BCD lv’mvj odq’j 8afdao16gj ,af DD gryoj 0uf mvj o-nj [AD] c]t [CD] c]h;wfhI6[lujc90hk’0t|ko ABCD D @D grnjvlhk’glAo-nj|b’j zjkog,af A mu.j shdjvo 0t|koda[glAo-nj d gryoj ;k’lv’g,af8kj ’ dao B c]t C 16gj lAo-nj dD c]h;0ufmjvodqj’mu,j u.9dk’ C c]t ]aflt\\ugmqjk AB 9kd oAo0ufmjvodqj’mu,j u.9dk’ A c]t ]aflt\\ugmqkj BC lv’mvj odqj’8afdao16gj ,af DD l5fmhkpgryjo0ufglAo-nj AD muj0t|koda[ dD dyf9tdemu & X dkooe.-h;q’;Po c]t [aomafgrnvj lhk’glAo-nj8A’lkddao? !D 9qj’;k’g,af M 16jovdglAo-nj dD c]h;.-h[aomaf c]t ;q’;Pogrnjv0ufglAo-njzjko M c]t 8A’lkdda[ d 3fpxt8y[af8k,0Ao8vo8+wxoUG dD ສະຫງສ.ວວນ.ລິສຂະສິດ       d   M    M 0D d 97 

7D M d @ D9qj’0ufglAo-n8j A’lkdda[ d  zkj o A 1j6I6[]5j,oU.        d  A   lts^5[ ສະຫງສ.ວວນ.ລິສຂະສິດ grnjvc8h,glAo-n|j bj’zkj og,af M muj.shdvj o8A’lkdda[glAo-nj d muj.shdvj oD gryoj c8h, mjvodq’j mu,j u.9dk’c,oj g,af M muj.shdjvooAoD mjvodq’j wx8af d 16lj v’g,af A c]t BD c]h;gryoj c8h,lv’mjvodqj’mu,u.9dk’c,oj A c]t  B c]t ,u]aflt\\ufP;daoD lv’mjvodq’j 8afdao16gj ,af M c]t vudg,af|bj’167j qo]tg[Nv’mP[da[ d c]h;0ufglAo -njzkj o M c]t zjkog,af8afdao0v’lv’mjvodq’j oAo -bj’gxaoglAo-nj8A’lkdda[ d D \\kpgsfG glAo-nmj uwj fhoAowx8A’lkdda[ d 16gj ,afg7y’j dk’0v’ A c]t BD dyf9tde * Xdkolhk’glAo-n8j A’lkdfh;p;ymuvnoj ? 16sj hv’ ,!/d 76wfh.shoadIPoc8h,glAo-n8j A’lkdda[glAo-nj d zjkog,af C .o0v[g9hpmuj .shfaj’I6[]5j,oUD [a’gvuo mhk; 7e,u ]n,[aomaflkd ,uc8j[aomaf c]t ;q’;PoD                                                                              C                                                                                                                                                                                                                                                        B   A d dD mhk; 7e,u ]k;.-h;ymu0hk’gmy’wfh[+L 4hk;kj [+wfh]v’7yfg[yj’;kj ]k;9tgIaf;ymu.f L 98 

ສະຫງສ.ວວນ.ລິສຂະສິດ0D 9q’j c8h,glAo-nj8A’lkdda[glAo-nj d zkj og,af C 3fpxt8y[af8k,7ecotoe]5j,oUG { ;k’g,af A c]t B 16jglAo-nj d c]h;0ufmvj odqj’ muj,u.9dk’ A c]t ]aflt\\u AC.                        { 0ufmjvodqj’ mulv’muj,u.9dk’ B c]t ]aflt\\u BCD lv’mjvodqj’8afdao16gj ,af C c]t  D.  l5fmhkp]k;0ufgloA -njj (CD). D 7D 9qj’.-h[aomaflkd,kd;fg[yj’;jkglAo-nj (CD) 8A’lkdda[ d s^n [+ L @D [qfg/ydsaf !D 9qj’c8h,I6[lk,c9 ABC lkd16j A, I6h;jk AB = 3 cm c]t BC = 4 cm. c]h;;af cmd];’pk; AC.   @D9qj’c8h,I6[7k’\\6lkd ABCD (lkd16j A c]t D?F I6h;jk AB = 3cm, CD = 4,5cm  c]t AD = 3,8 cm. 99 

#D9q’j \\kpg,af A, B c]t C [+]Po-nj16jglAo-nj dD .shlhk’glAo-nj8A’lkdda[ d  zkj o A, B         c]t C. la’gdfgsaoco;.fL $D9q’j lhk’I6[lucj 9lkd ABCD mu,j u0hk’gmqjk 4 cm c]t glAogoa’j 9v,gmqkj   5 cm. &D9q’j lhk’I6[lucj 90hk’0t|komu,j uglAogoa’j 9v,gmqkj 6cm c]t ];’pk;gmqkj lv’lj;o lk,0v’glAogoaj’9v,D *D9q’j \\kpg,af A c]t B .lgj lAo-n|j bj’3fp;kj AB = 4 cmD ,uma’\\qf9adg,afmu1j 6jsjk’ 3cm 9kd  A c]t 7cm 9kd B L (D9q’j la’gdflv’glAo-nj d c]t d’ mu1j 6.j o0v[I6[D r;d,ao9twx8afdao16sj kj ’9kd0v[ I6[s^kpxko.f X[+.sh0uf8+vvdwx9kd0v[I6[?L d  d’  ສະຫງສ.ວວນ.ລິສຂະສິດ le]a[0=h ( vkf9t.-h7;k,lk,kf g]njvoglAo-nj ,kdE-hkp s^n mq[l;j o mu1j 6oj vd0v[.sh,k16dj E -hkp c]h; ;afcmd s^n 7yfw]jvkfg\\ktda[zj6gdaj’                                     )D9qj’la’gdfI6[]5,j oU c]h;9af]Po0Ao8vodkoc8h,I6[8k,]efa[.sh4nd8hv’D dD 0ufglAo-nzj jko K c]t 8A’lkdda[ (DC).  B 0D;k’lujg,af A, B, C, D.   T 7D glAo-njoAo8af XBC) 1j6 T.  A C ’D 0ufglAo-nzj kj o L c]t 0t|koda[ (DB).  K 9D mjvo-nj AC c]t BD 8afdao1j6g,af k  L lD glAo-njoAo8af (DC) 16j L.  -D 0ufmvj o-nj AC c]t BD.  D 100 

ສະຫງສ.ວວນ.ລິສຂະສິດ[qfmu !$ dko[;d];’pk;mvj o-nj c]t dko76o9eo;o.f|bj’ da[];’pk;0v’mvj o-nj !D dyf9tde dyf9tdemu ! Xdko[;d];’pk;mvj o-nj? mjvo-nj AB g-y’j gIqklaopt]ad DDDDDDDDDD c,joDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !D 9q’j xP[mP[];’pk;lv’mjvo-nXj I6[ !? c]t XI6[ @? ]5,j oUfh;plkp8k c]h;d;f g[yj’fh;pdko;afcmdD XI6[!? XI6[ @? @D 9q’j xP[mP[];’pk;0v’mjvo-nj ! c]t @ fh;plkp8k c]h;d;f7nofh;pdko ;afcmdD 1  2  #D .shg,af A c]t B 16jglAo-nj dF c]h;;k’g,af M .l]j ts;jk’g,af A c]t B faj’I6[ ]5j,oUD d  B  M  A  gIqkwfh @ mvj o-nj.\\j DDDDDDDDDDDDc]t DDDDDDDDDDDDDDDDD gIqklk,kf0Po];’pk;  AB 8k, ];’pk;0v’ @ mvj o-njmuwj fhoAo1kj ’.f L       AB = ……….. + ……….  101

4hk;jk M  1j6g7yj’dk’0v’ [AB] lv’mvj o-njoAo9tgxaoco;.fL         ………. = …………         AB = …. ×  AM = … ×………    $D 9q’j c8h,mjvo-nj [CD] 16oj vd dF c]h;;k’g,af E 16jlj;o0uf8+[AB] gmy’glAo-nj d      3fp;jkG BE = CD. .shgvqk [CD] ,k;k’g8a’ [BE]D gIqklk,kfdeoqf     AE = ……..   …  ………            D  ສະຫງສ.ວວນ.ລິສຂະສິດ   C                     A  B  E  dyf9tdemu @ Xdko76o];’pk;mvj o-jnda[9eo;o.f|bj’? !D 9q’j .-h;q’;Poc8h,mjvo-nj AE 7no3fpcmdgvqk];’pk;mvj o-nj [CD] c]h;,k\\kp .ljg7yj’glAo-nj [Ax) .shwfh AE = 3CD.                   D   C     A  102

@D 9q’j c8h,mjvo-nj MN = 4,5 AB 7no3fpoe.-h;q’;PoD               M    M xa[0k;q’;Pog0Qk.sh4nd8hv’ N    H      A  B   #D 9qj’c8h,mjvo-nj EF =  3 AB 7no3fpoe.-h;q’;PoD     4     A  B         ສະຫງສ.ວວນ.ລິສຂະສິດ     E  F  $D 9q’j c8h,mvj o-nj GH = 3× 3 PQ 7no3fpoe.-h;q’;Po.  4   P  Q         3 4 PQ  G  3 3 × 4 PQ  103

ສະຫງສ.ວວນ.ລິສຂະສິດ@D .97;k, { 4hk;kj lk,g,af A, B c]t C 16gj lAo-njfP;dao8k,]efa[F gryoj lk,kfdeoqf zqo[;d];’pk;0v’lv’mvj o-nj [AB] c]t [BC] fa’j oUG AC = AB + BC { gryjo76o];’pk;mvj o-nj AB da[ k fh;pdkooe.-h;q’;Pogrjnvgvqk];’pk; faj’dkj ;,k8+.ldj ao8k,glAo-nj k  gmnjvD 8q;1jk’G !D .sh  AB = 6,7 cm, BC = 4,6 cm. 9q’j 7yfw]]j ;’pk; AC I6h;kj  A, B c]t C 16jglAo-nj fP;daoD [qfcdhG gIqk,u AC = AB + BC Xgrkt A, B  c]t C 16jglAo-njfP;dao8k,]efa[?F gIqkcmo7jkwfhG                   AC = 6,7 cm  + 4,6 cm = 11,3 cm.  @D .o]t[q[dko;afcmdvkg,]ydk gryoj .-h 25fgxaosq;|j;p;afcmd];’pk;D         ! 25f(foot) = !@ oU;X inches)F 4hk;kj AB = 18 oU;F  CD = 1,5  25f X]kp]tvPf9tltg|u.o[qf8+wx?D 9q’j xP[mP[];’pk; AB c]t CD.  [qfcdhG gIqkxjPo CD =  1,5 25f gxaooU; wfh CD = 1,5  25f ×!@ = 18 oU; gIqklts^5[wfh;kj AB = CD.  #D .shg,af M 16j mvj o-n j AB. 9qj’-vdsk];’pk; MB Ih6;kj AM = 5 sq;|;j p c]t AB = 8 sq;|;j pD & sq;|;j p                                                                                 A                              M                      B  ) sq;|j;p [qfcdhG phvo;kj A, M c]t B 16jglAo-nfj P;dao 8k,]efa[ gIqk,uG AB = AM + MB,   ltoAo  MB = AB – AM   gIqkcmo7kj wfhG MB = ) sq;|;j p – & sq;|j;p = # sq;|;j pD 104

#D [qfg/ydsaf !D 9q’j ;k’g,af K 16jmjvo-nj MNF c]h;-vdsk];’pk; KN I6h;kj G MN =  9,35 cm c]t  MK = 5,6 cm.     N    M @D .shg,af A, B, C, D, E c]t F 16jglAo-nj d 3fp;jk AB = CD = DE = 2,8 cm, AF = 10,2 cm; BC = EF.  9q’j -vdsk];’pk; BC.  d #D 9q’j -vdsk];’pk; NP 8k,I6[mu,j u0=h,6o]5j,oU G ສະຫງສ.ວວນ.ລິສຂະສິດ                  MN = PQ = QR 9cm                       M                  N               P                    Q                   R                                      2,6cm  $D 9qj’xP[mP[];’pk;0v’glAomk’ AEFGHIJB c]t  AMB fh;plkp8k X3fp[+.sh7yfw]?j     G H F I                       E J     M    A B c]h;.sh7yfw]zj qo[;d0v’];’pk;mjvo-nj [AE], [EF], [FG], [GH], [HI], [IJ] c]t  [JB]F c]t zqo[;d];’pk;0v’ [AM] c]t [MB]. c]h;d;fg[y’j 7e8v[ 0hk’gmy’D 105

&D 9q’j la’gdfI6[]5,j oU c]h;[vd;kj glAomk’.flAod;kj F glAomk’ A  s^n glAomk’ B?      A  B                       *D 9q’j 7kf7tgofh;plkp8k ;jk];’pk;0v’glAosad16]j 5j,oU |hvpd;jk s^n s^kpd;jk 15 cm.   (D9qj’xP[mP[];’pk;glAosad I6[ ! c]t ];’Iv[0v’I6[ @ fh;plkp8k F c]h; d;f7nofh;pdko;afcmdD 7,2 sq;|j;p I6[ @ ສະຫງສ.ວວນ.ລິສຂະສິດ I6[! )D 9qj’-vdsk];’Iv[0v’c8j]tI6[]5j,oU 8k,0=h,6omu.j sh.                                      10,3 sq;|j;p 7 sq;|j;p 6 sq;|;j p 106

_D 9qj’-vdsk];’Iv[0v’I6[fyol;o]5j,oUX.shsq;|;jp8q;9y’gxao hm)        2,5 1,5   3,5   4,5 7,5 !WD 9q’j c8h,mvj o-nj AB c]h;c8h,G { mvj o-nj muj,u];’pk;gmqjk 5 AB { mjvo-nj mu,j u];’pk;gmqkj 3 5 AB { mvj o-njmuj,u];’pk;gmqkj 5 3 ABX5 3 3 4 4 = 5 + 4 ).  !!D dD 9q’j c8h,mjvo-nj AB muj ,u];’pk;gmqjk 6 cm.  ສະຫງສ.ວວນ.ລິສຂະສິດ 0D c8h,mvj o-nj mu,j u];’pk;gmqkj 4 3 AB;         7D c8h,mvj o-nj muj,u];’pk;gmqkj 3 2 AB.  !@D9q’j c8h,mjvo-nj MP muj,u];’pk;gmqjk 7,6  cm.  c]h;\\kpg,afg7yj’dk’ N 0v’ mjvo-nfj aj’dkj ;D 9q’j [vd];’pk;0v’ NP. c]h;8nj,.l[j jvo9Eg,afgrnjv.shgxaoxt3spd3fpoe.-h 7e;jk “ gxaog7y’j |b’j ” s^n “gxaolv’gmnjv” G          MN……………. 0v’ MP ; MP…………………..0v’  NP           MP…………….. 0v’ MN ;                             NP…………………...0v’ MP.    !#D 9qj’c8h,mjvo-n j AB c]h;oe.-h[aomaf c]t ;q’;Pogrnjvc8h,mvj o-nj BC XA, B c]t C         [+]Po-n?j muj,u];’pk;gmqkj lv’gmnjv];’pk;0v’ ABD 9kdoAo.shc8h,mvj o-nj CD mu,j u];’pk;gmqjklk,gmnjv];’pk;0v’AB (B, C c]t D [+]Po-nj?  107

ສະຫງສ.ວວນ.ລິສຂະສິດ[qfmu !& dko;afcmd];’pk;0v’mjvo-nj !D dyf9tde dyf9edemu !D dko;afcmd];’pk;c,jodkoxP[mP[];’pk;oAo.ljsq;\\;j p;afcmdmujg]nvdw;hD sq;|j;p.odko;afcmd];’pk;c,oj G c,af (rklk/^aj’G mètre; rklkva’dyfG metre  s^n  meter) g-yj’gmqkj da[|bj’lj;oly[]hko0v’|bj’lj;oluj0v’glAoc;’X!W WWW km? g-yj’gxaoglAoIv[|;j p3]dmujzjkoma’lv’0;Ao3]d Xg[yj’I6[?D dD grnjv;afcmd];’pk;muj|hvpd;kj c,af gryoj gIafco;.fL gryoj .-hc,af;afcmdlyj’mu,j u];’pk; |hvpd;kj ! c,afwfh s^n [+L 4hk;jk[+gryoj cdhw01jk’.f L DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD gryjo[+lk,kf.-h c,afgrnjv;afcmd];’pk;muj|hvpd;kj ! c,afwfhD ltoAogryoj 9b’j c[’j ! c,afvvdgxao !W l;j ogmqkj daoD c8j]tl;j ogvUo;kj 108

! gf-uc,af Xdm sp=h,k9kd decimeter).       0 1 2 3  4  5 6 7 8 9  10      I6[0v’w,hc,afsp=h];’pk;]q’ !W gmnvj X,kf8kl;j o ! G !W? w]ptskj ’]ts;jk’lv’0ufltcf’g4y’ ! gf-uc,af g-y’j sp=h ! c,af]q’ !W gmnvj D   ! dm =  1 m = 0,1 m; s^n  1 m = 10 dm  10              0D grnvj ;afcmd];’pk;muj|hvpd;kj ! gf-uc,afgryjogIafco;.fL gryjoc[’j ! gf-uc,afvvdgxao !W lj;ogmqkj daoD c8]j tl;j ogvUo;kj ! -a’8uc,af (cm, sp=h,k9kd centimeter)D                                                              1 cm =  1  dm=0,1 dm   s^n     1 dm = 10 cm ສະຫງສ.ວວນ.ລິສຂະສິດ 10                   1cm          1dm g-ajofP;dao grnvj ;afcmd];’pk;|hvpd;jk ! -a’8uc,af gryjoc[’j -a’8uc,afvvdgxao !W lj;ogmqkj dao c8j]tl;j ogvUo;kj ! ,yo]uc,af (mm, sp=h,k9kd  millimeter)  1cm                             1 mm =   1 cm = 0,1 cm s^n 1cm =10 mm  10   1mm  109

dyf9edemu @ D dD 9qj’;afcmdmjvo-nj]5,j oU c]h;gvqk7jk;afcmd8n,j .l8j k8t]k’D F E  A  C D B H  I  G mjvo-nj ];’pk;16j]ts;jk’ J  …..cm   c]tDDDDDDDDcm  AB  5 cm  c]t 6 cm  ];’pk;cmdgxao mm  CD  3 cm  c]t  4 cm  EF  52 mm  33,3 mm  ສະຫງສ.ວວນ.ລິສຂະສິດ GH  IJ  0D 9q’j c8h,mjvo-ngj -y’j ];’pk;wfhdeoqfw;h16j8k8t]k’]5j,oUG mvj o-nj ];’pk;   mjvo-nj ];’pk;16j]ts;jk’   DDDDDDDDDDDDDDDD c]t DDDDDDD AB  5 cm    KL  0,8 dm  c]t 0,9 dm  CD  145 mm    MN  4,6 cm c]t 5,7 cm  EF  4,5 cm    PQ  0 dm c]t 0,8 dm  GH  0,8 dm  RS  56 mm c]t 57 mm  IJ  38 mm  TU  6 cm c]t 7cm  110

8q;1jk’D B   5 cm  A  0,8 dm < KL<0,9 dm K L  \\kpgsfG le]a[]t[q[vkg,]ydk gryjo.-h25f Xmt;u76o c]t v5xt76o0v’25f? gxaosq;|j;p ;afcmd];’pk;D ! 25f(foot) = 12 oU; Xvyo-% inches)    ! 1kf(yard) = 3 25f = 0,9144 c,af     @D .97;k, dD sq;|j;p;afcmd];’pk; ສະຫງສ.ວວນ.ລິສຂະສິດ sq;|j;p;afcmd];’pk;c,oj G c,afF v5xt76o c]t mt;u76o0v’c,afD gf-uc,af Xdm), -a’8uc,af (cm) c]t ,yo]uc,af (mm)  gxao v5xt76o0v’c,af (m)D gfdkc,af (dam), gIad38c,af(hm) c]t dy3]c,af(km) gxao mt;u76o0v’ c,af(m)D    1 dam = 10 m;         1 hm = 10 dam;            1 km = 10 hm     8hv’9nGj     1 km =   10 hm  1 m  =   10 dm  1 hm =   10 dam  1 dm =  10 cm  1dam = 10 m 1 cm =  10 mm      1 km  = 1 000 m  1 m = 100 cm  1 hm  =   100  m  1 m = 1 000 mm      1 m    = 0,001 km  1 mm = 0,001 m  1 m    = 0, 01 hm  1 cm  = 0,01m  1 m    = 0,1 dam  1 dm  = 0,1 m  111

0D dkoxPj osq;|;j p;afcmd dkoxjPosq;|;j p,ulv’;ymuG  ;ymumu ! dkooe.-h8k8t]k’ grnvj 7;k,ltf;d.odkoxjPosq;|;j pgryjogvqksq;|;j pfa’j dkj ;.l.j o8k8t]k’fa’j oUG ×1000 ×100 ×10  km  hm  dam  m  dm  cm   mm    ÷10 8q;1jk’G ÷100 xjPo 74,5703 dam gxao  cm:    ÷1 000  gIqkla’gdfgsao;jk 4 gxao8q;g]dsq;|j;p0v’ 74,5703 dam. gIqk;k’,ao.l4j ao  dam  ສະຫງສ.ວວນ.ລິສຂະສິດ 9kdoAo gIqkgvqk  8q;g]dc8]j t8q;]q’.l8j k,c8j]tsq;|;j pmujdq’daoD gIqkphkp95fwx.lj4ao cm:    74,5703 dam = 745 7,03 cm    km  hm  dam  m  dm  cm  mm    7  4  5  7  0  3  1  0  0  0            1  0  0         1  0  0  0       0  0  1         0  0  0  1  le]a[8q;1jk’]5,j oU gryjod=xt8y8k,;y[af;ymufP;daoG xjPo 1km gxao m;                           xPj o 1m gxao km,   xPj o m gxao cm; xPj o 1cm gxao m;  xjPo m gxao mm;                           xjPo 1 mm gxao m D     7e8v[G                         1 km   = 1 000 m                                       1 m    =  0,001 km          1 m    = 100 cm                                        1 cm  =  0,01 m          1m    = 1 000  mm                                 1 mm   =  0,001 m  112

;ymumu @ gryjo76o s^n sko.sh !WF !WWF !WWWF D D D 8q;1kj ’ D 9qj’xjPo 3,4 km gxao m, c]h;xjPo 250 m gxao hm. × 1 000       ÷100    km =              3,4 km = 3 400 m  m  m  =  hm           250 m = 2,5 hm    #D [qfg/ydsaf !D 9qj’\\k[g,af A, B, C, c]t D 8k,]efa[.lgj lAo-nj d 3fp;jk AB = 7,4 cm:             CD = 0,3 dm; AD =  125 dmF c]h;-vdsk BC gxao dam.  100 ສະຫງສ.ວວນ.ລິສຂະສິດ @D 9q’j xjPo9e8+wxoUgxao c,af (m), gf-uc,af(dm), -a’8uc,af(cm) c]t ,yo]uc,af(mm)G    dD 5 hm 40 dam 3 m;                                 0D    25 m12 cm 7 mm;     7D 1,2 km 5 dam 13 m;                   ’D  139,5 hm;    9D 2 dm 13 cm;                           lD     28,016 km;    -D 7m 1,3 dm 7 mm;                                   pD   0,07103 dam.  #D 9q’j 8n,j 8q;g]d s^n sq;|j;p;afcmd];’pk;mujg\\ktlq,.l[j vj o9Eg,afG dD 3,7 m = .... cm 0D 52 cm = 0,052…. 7D 12,4  hm 07 dam = …m;   ’. 205 m = 0,205….       9D 712 mm = …….dm                                lD  5,74 dam = 5740…..        -D 3  m = …..mm                                  pD 25 dam 08 cm = … …  m   100 $D 9qj’xP[mP[];’pk;]5j,oUG 0D 10 000 dm c]t  10,1 km  dD 518,03 cm c]t   51,31dm;   ’D  2,01 hm c]t  30,1 m  7D 453,7 dm c]t      4,5 dam ;     113

&D 9q’j xjPo];’pk;8+wxgxao,yo]uc,af Xmm): dD 15 cm; 1 cm; 12,7 cm; 0,35 cm    0D 21 m; 0,27 m; 0,0019 m; 5,0014 m.    7D 4 dm; 1,72 dm; 0,365 m; 0,6501 dm.  *D 9qj’xjPo];’pk;8+wxgxao-a’8uc,af(cm):            dD 1 400 mm; 100 mm; 0,1 mm; 1 219 mm.  0D 9 dm; 0,001 dm; 3,104 dm; 0,00347 dm.  (D 9q’j xjPo];’pk;8+wxoUgxaody3]c,af (km):  dD 26 790 m; 3 087 m; 102 m; 42 m.  0D 420 dam; 32,49 dam; 398,002 dam; 23,1 hm; 0,54 hm.  )D 9q’j 7yfw]fj h;plv’;ymu8jk’daoG dD 875m × 3 S 0D 2943cm×7 S 7D 235,718cm × 7 5 9 11 ສະຫງສ.ວວນ.ລິສຂະສິດ XcotoeG ;ymu ! 0Po 875 = 175x5 c]h;xt8y[afdkoIvo? _D dD grnjvgIaf\\a’lnzjkocfo dt-;’8jk’xtgmfwfhcotoe.shxtdv[7eIhv’7af8yfwx fh;pI6[ 4x6,  gryoj \\kp7;k,;jkgryjo .-hvao.fgxaosq;|;j p 0v’0t|kfI6[ L 0D 16jIhko0kpg7nvj ’o5’j gryjowfh8yfg]d ## .llj ;j ocv;0v’3lh’D gryoj \\kp7;k,;jk ## sq;|j;pvao.f L !WD ’6 @W ;kg0QkI6,N]tlvd vvdI6,N]t7n[D 4k,;jk9ad,N,ao9b’j g0QkI6s;yfL X! ;k = $ lvdS ! lvd = @F& 7n[? !!D ok’ ok]u ,uvkp5gmqkj @ gmnjvvkp50v’ok’ ]yofkD mhk; mv’ ,uvkp5]jon ok’ ok]u !& xu c]t ]njo mhk; 7e @W xuD ma’ $ 7qo,uvkp5];,dao !(W xuD dD 9q’j c8h,mjvo-nlj tcf’g4y’vkp5c8]j t7qoX gvqk0=h,6oc8j]t7qo]q’.lIj 6[?D 0D -vdskvkp50v’]yofk c]h;-vdskvkp5zh6vnoj MD vkp50v’ ok]u vkp50v’ ]yofk DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD 114

ສະຫງສ.ວວນ.ລິສຂະສິດ!@D mhk; lad ,uvkp5gmqjklv’gmnvj vkp50v’mhk; [5o g-yj’gxaorujohv’fP;daoD mhk; [5o vjvo d;jk ok’ [q;lu mugj xaogvNvp0v’]k; * xuD r;dg0qkma’lk,,uvkp5];,daogmqkj da[ vkp5c,8j h60v’ r;dg0qkG )@ xuD dD 9qj’c8h,mjvo-njltcf’g4y’vkp50v’ma’lk,7qoS 0D 9q’j -vdskvkp50v’mhk;ladS 7D 9q’j -vdskvkp50v’ok’ [q;lu c]t mhk;[5oD !#D dD 9q’j c8h,I6[|hk8+wxoU7noS 0D 9q’j ;afcmd0hk’ c]t glAogoa’j 9v,D !$D 16gj 9hpmu,j u8kdk3iG dD 9qj’c8h,mvj o-nj AB muj,u];’pk;gmqjk ) 8kdk3iS c]h;c8h, mvj o-nj mu,j u];’pk; gmqkj $ 8kdk3ig7yj’ c]tmvj o-nj muj,u];’pk;gmqjk * dk3iS 0D 9q’j ;afcmd];’pk; AB, CD c]t EF gxao,yo]uc,af(mm )S 7D 9qj’;afcmd];’pk;8kdk3ivao|bj’ c]h;7yfw]sj k];’pk; AB, CD c]t EF. XxP[mP[zqomujwfhIa[da[zqo0v’0=h 0?D !&D 9qj’c8h,I6[lk,c9 ABC lkd16j A I6h;jk AB = 3 cm c]t BC = 4 cm  c]h;afcmd ];’pk; AC.    16.     9q’j c8h,I6[7k’\\6lkd ABCD(lkd16j A c]t D ?,  I6h;jk AB = 3 cm, CD = 4,5 cm  c]t AD = 3,8 cm. !(D .shg,af A, B c]t C [+]Po-n1j 6jglAo-nj dD 9qj’lhk’glAo-nj 8A’lkdda[ d  zkj o A, B c]t  C. la’gdfgsaoco;.fL !)D 9qj’lhk’I6[lujc9lkd ABCD mu,j u0hk’gmqkj  4 cm c]t glAogoa’j 9v,gmqkj   5 cm. 115

[qfmu !* dko;afcmd];’pk; !D dyf9tde dyf9tdemu !G v5xtdvo;afcmd];’pk; dD v5xtdvomugj ryjo.-hgrnvj ;afcmd];’pk;,uspa’cfjL DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD 0D .oltw\\dvj o s^n 16gj 0fsjk’wdlvds^udmju[+,uv5xtdvo;afcmd];’pk; gryjo.-hspa’ grnjv;afcmdL DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD v5xtdvo;afcmd];’pk; I6[ ! ສະຫງສ.ວວນ.ລິສຂະສິດ I6[ & I6[ @ I6[ * I6[ # I6[ ( I6[ $ I6[ ) 116

7D 9qj’0Po8nj,8k8t]k’]5,j oUG ]}f lyj’mu;j afcmd v5xtdvo.-h;afcmdmujg\\ktlq, ! 0t|kf0v’dtfko w,hc,af @ ];’pk;vk7ko3I’IPo # ];’pk;F ];’d;hk’ 0v’mqj’ok $ ]aflt\\u0v’glAozq, & 0t|kf0v’c[dg8gip * Iv[cv; ( ];’pk;czoj cr ) ];’pk;0v’glAo37h’ _ glAozjko.9dk’]6d7ezkp dyf9tdemu @ D ສະຫງສ.ວວນ.ລິສຂະສິດ 9qj’lhk’I6[lk,c9 ABC;  Ih6;kj AB = 6 cm; AC = 4 cm; BC= 3cm. 3fp.shxt8y[af8k, 0Ao8vo]5,j oUG  { c8h,mjvo-nj AB = 6 cm;                                                            A                                                 B    { 0ufmvj odq’j muj,u.9dk’ A  c]t ]afl\\u gmqjk AC ;                                                                                                                 117

{ 0ufmvj odqj’0v’;q’,qomu,u.9dk’ B c]t ]aflt\\ugmqkj BC.  ສະຫງສ.ວວນ.ລິສຂະສິດ                     c]h;0ufmjvo-nj  AC c]t BC   dyf9tdemu # dD 9q’j la’gdfI6[w,h[aomaf]5,j oU c]h;8v[7e4k,DD     0  1 2  3  4  5  6 7 8 9 10      I6[0v’w,hc,afsp=h]q’ !W gmnvj X,kf8kl;j o ! G !W? { 16j.oI6[w,h[aomaf,uma’\\qf9ad0uf L { ,uma’\\qf9ads;kj ’X[+oa[lv’s;kj ’ohvp1j6lv’lQo?L { 9q’j xP[mP[9eo;os;kj ’da[9eo;o0ufma’\\qf c]h;0Po8nj,.l[j vj o9eg,afD 9eo;o0uf    = DDDDDDDDDD 9eo;os;jk’ = DDDDDDDDDD 9eo;o0uf = 9eo;os;jk’  +  D D D D =   D D D D +  D D D D 118

ສະຫງສ.ວວນ.ລິສຂະສິດ0D 9q’j la’gdfI6[]5,j oU c]h;0Po8n,j .l[j jvo9Eg,afD A  B  16j]ts;kj ’ A c]t B ,uma’\\qf9ad0uf L D D D ,uma’\\qf9ads;kj ’L D D D 7D 9qj’la’gdfI6[]5,j oUD oa[9kd A wxmk’g[Nv’0;k,n ,uma’\\qf9ad0ufL c]t ,uma’\\qf9ads;jk’L 9q’j .sh0=hlts^5[3fp0Po8nj,.l[j vj o9Eg,afD A  DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD ’D 9qj’la’gdfc8j]tI6[]5,j oU ,uma’\\qf9adg,af L c]t ,uma’\\qf9ads;jk’L 9qj’.sh0=h lts^5[3fp0Po8nj,.lj[vj o9Eg,afD I6[ ! I6[ @ 16jI6[ ! ,uma’\\qfDDDDDDDDDDDDDDDDDDg,af c]t ,uma’\\qfDDDDDDDDDDDDDDDDDDDs;jk’D 16jI6[ @ ,uma’\\qfDDDDDDDDDDDDDDDDDDg,af c]t ,uma’\\qfDDDDDDDDDDDDDDDDDDDs;kj ’D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD dyf9tdemu $ !D 9q’j xP[mP[];’Iv[0v’lv’I6[]5,j oU Xfh;plkp8k c]h;d;ffh;pg7nvj ’,n? 4hkgIqk.shI6[gs^qjkoU8yf.oI6[9t85]af 9tlk,kfxP[mP[wfh]aflt\\u0v’ ;q’,qo c]t mjvodqj’K  I6[ ! I6[ @ 119

@D 9qj’-vdsk];’Iv[0v’I6[8+wxoUD 1cm  5 cm         9 cm cotoeG { g7jy’;q’,qoc8]j tvao,u];’pk;gmqjkdaoD { ];’Iv[0v’;q’,qogmqjk 2π r X r c,jo]aflt\\u? #D 9qj’-vdsk];’Iv[0v’I6[]j5,oUD ສະຫງສ.ວວນ.ລິສຂະສິດ   6,35 cm     3,02 cm      3,65 cm   1 cm 2 cm $D I6[lujc9lkd]5j,oUwfhlhk’0Bo3fpdko0uf8+I6[9t85]af-b’j ,u0hk’gmqjk !W sq;|j;pD 9q’j la’gdfg[y’j ];’d;hk’ c]t ];’pk;0v’I6[ lujc9lkdfa’j dkj ; c]h;-vdsk];’ Iv[0v’,aoD   !W sq;|;j p              120

ສະຫງສ.ວວນ.ລິສຂະສິດ@D .97;k, dD v5xtdvo;afcmd];’pk; 7qoltw\\dvj o s^n -k;[hkomuj[+,uv5xtdvo;afcmd];’pk; gryjo,ad.-Gh ;kF lvdF 8uoF 7n[ s^n oU; XoU;3xh? grnvj ;afcmdD ltw|xt95[aogryjo.-hG w,hc,afF c,afd=h3]F c,afd=hzhkF dhv’95]tmafF c,afra[F [aomafXf6[gf-uc,afX@W cm?F g7nvj ’;afcmdI6[-q’dq,F c]tvnoj MDDDDDDDDDDDDD 0D w]ptsjk’ 4hk;kj ,u0uf16jlv’lQo F 9eo;o0uf = 9eo;os;kj ’ + ! 4hk;jk[+,u0uf16lj v’lQo F 9eo;o0uf   = 9eo;os;jk’ − !           4hk;kj ,u0uf16lj QofP; F 9eo;o0uf = 9eo;os;jk’ d=]touglAo;q’9vovaf F 9eo;o0uf = 9eo;os;jk’ 8q;1kj ’ D 16jc7,4t|qocsj’|b’j Xlq,,5f;kj -nj? gryoj x6d8Qow,h lv’8Qo.fsjk’dao & c,afD ];’pk;0v’4t|qogmqjk @ dy3]c,af. Ih6;kj 16lj v’lQo[+,u8Qow,h?   dD 9q’j xP[mP[9eo;o8Qow,h c]t 9eo;os;kj ’S 0D 9q’j -vdsk9eo;o8Qow,hma’\\qfD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD [qfcdhG xjPo 2 km gxao 2 000 m 9eo;os;jk’G   2 000 m ÷ 5 m = 400 s;kj ’ phvo;kj [+,u8Qow,h16lj v’lQo 9eo;os;kj ’  = 9eo;o8Qow,h + ! s^n 9eo;o8Qow,h = 9eo;os;jk’  – 1 = 400 – 1= 399 8QoD 121

7D dko-vdsk];’Iv[ dko-vdsk];’Iv[,u @ ;ymuG !D le]a[I6[s^kpc9 gryoj [;d];’pk;0v’0hk’D @! sq;|j;p D  8q;1jk’D !WF& sq;|j;p   C  A   AB = 5 sq;|j;pS  B   BC = 11 sq; |;j p    CD = 10,5 sq;|j;p              & sq;|j;p !! sq;|;j p   AD = 21 sq; |j;p ];’Iv[ = ( 5 + 11 + 10,5 +21 )sq;|;j p  = 47,5 sq;|j;p @D le]a[I6[czoj ,qo s^n glAo;q’,qo gryjo.-hl6fD ສະຫງສ.ວວນ.ລິສຂະສິດ C  AB  gxaoglAozjkodk’ gryoj ,adcmofh;p  d.  A                OC gxao ]aflt\\u gryoj ,adcmofh;p r  s^n  R O B  d  ];’Iv[0v’czjo,qo = 2πr s^n πd        8q;1jk’D 9qj’-vdsk];’Iv[0v’czjo,qomuj,uG dD ]aflt\\ugmqjk 8,7 cm; 0D glAozkj odk’gmqkj 104 cm;  [qfcdhG XgIqkgvqk7kj xt,ko0v’ π = 3,14 ? d Doe.-hl6f 2πr = 2 x 3,14 x 8,7 cm = 54,636 cm; π0D oe.-hl6f d  = 3,14 x 104 cm =  326,56 cm 122

ສະຫງສ.ວວນ.ລິສຂະສິດ#D [qfg/ydsaf !D oadIPo shv’,!} d 9eo;o $! 7qo]Poc4;dP,vvdde]a’dkpD I6h;jklv’7qo.f 1nosjk’dao 0,8 m. 4k,;kj w]ptsjk’c8zj 6hmu|bj’wxskz6hl5fmhkp,ugmqjk.f L @D 9eo;o4h;ome,t-kfXoa[ma’g]d W ? muj,u ! 8q;g]d,u9ad9eo;o L @ 8q;g]d,u9ad 9eo;oL # 8q;g]dF $ 8q;g]d ,u9ad9eo;oL #D gryjo.-h8q;g]d WF !F @F #F $F &F *F (F )F _ c8]j t8q;9adgmnvj grnvj 0Po9eo;o G dD c8j ! Ivf __ L 0D c8j !WW sk !__ L c8j @WW sk @__ L $D ,Ng-QkoU,usvp8q;|bj’8qdlhk’-b’j ,u7;k,g]yd !W c,afF 8vodk’g;ao,ao0Bo $ c,afF c8j;jk8vodk’7noraf]q’7no @ c,afD 4k,;kj fqoxko.f,ao9bj’9t0Bos;yfxkdlhk’L &D xB, @! sq; 4nd;k’g8a’daow;hD ];’l6’0v’dv’xB,oU,u 89 cm D Ih6;jkxB,[k’-toyf ,u7;k,|k 5 cm, 9eo;o|b’j ,u7;k,|k 3 cm. 4k,;kj xB,c8]j t-toyf,u9adsq; Xxt8y[af8k,;ymu]5j,oU?L dD lq,,5f;jk .o @! sq;oAo,uxB,c8-j toyfmuj,u7;k,|k 3 cm.  dv’xB,9tl6’GD D D D D D   c]t ,ao9ts^5f];’l6’gfu,G D D D D D D D D 0D 7;k,|k0v’xB,ma’lv’-toyf9ts^5fdaoG D D D D D 7D 4hkgvqk7;k,s^5f]noj daomuwj fh.o0=h d ,ksko.sh7;k,s^5f]njomujwfh.o0=h 0 9twfhG D D D D D D g-yj’c,jo9eo;oxB,-toyfmuj|k 5 cm D ’D lts^5[G D D D D 123

*D wdjxts^kf8q;|bj’;k’w0j !_ |j;p8k,c4;-njF lv’|j;p.fskj ’dao # c,afD 4k,;kj w]ptskj ’c8[j vj o,aovvdw0j|j;pmevyfwxsk|;j pl5fmhkp,ugmqkj .f L (D 9qj’xP[mP[];’pk;0v’lv’glAosad]5,j oU3fp[+.sh.h-hv5xtdvoD c]h;d;f7no fh;pdko;afcmdD    )D .shI6[9t85]af WORK             mu,j u];’Iv[gmqkj 32 m.          W O  R gryoj c[j’I6[fa’j djk;vvd gxao   ສະຫງສ.ວວນ.ລິສຂະສິດ   # I6[lucj 9lkd gmqkj dao XI6[g[Nv’0;k?D 9qj’-vdsk ];’Iv[0v’I6[lulj kd c8j ]tvaoD     K  _D 9q’j 8n,j 8k8t]k’]5,j oUG ];’d;hk’0v’I6[lujc9lkd ];’pk;0v’I6[lucj 9lkd ];’Iv[0v’ I6[lucj 9lkd 15,2 cm  28,4 cm    24,5 cm    8,06 cm    32,8 cm    16,9 cm  25,5 cm  8,07 cm  10,7 cm  27,4 cm    124

!WD 9qj’-vdsk];’Iv[0v’I6[]5j,oU8k, a  c]t b :    1,3 cm       b        a      !!D I6[;q’,qo|bj’,uglAozkj odk’gmqjk 12 cmD9q’j -vdsk];’Iv[0v’I6[9t85]af D   ສະຫງສ.ວວນ.ລິສຂະສິດ !@D I6[lk,c9 TEA ,u];’Iv[ 12 cm D9qj’-vdsk];’Iv[0v’I6[lucj 9lkd TEAK         I6h;kj  AT = 5 cm. T K !#D 9qj’lhk’I6[ ( c9D E A dD ,uglAogoaj’9v,ma’\\qfgmqkj .fL 0D ,uI6[lk,c9ma’\\qf9adI6[L 7D 9q’j xP[mP[9eo;oI6[lk,c9 da[9eo;o0hk’0v’I6[s^kpc9D !$D dD 9qj’lhk’I6[ # c9mPj ’ ABC, Ih6;kj G AB =  BC = 4,5 cm. 0D 9qj’lhk’I6[ # c9ltg\\u ABC muj,u0hk’gmqjk 4,8 cm.                     7D 9q’j lhk’I6[lucj 90hk’0t|ko ABCD 3fp;jk AB = 6,5 cm c]t BC = 4 cm. ’D 9qj’lhk’I6[lucj 90hk’0t|ko MNPQ 3fp;jk NP = 5,8 cm  c]t glAogoa’j 9v,                NQ = 4 cm.    125

ສະຫງສ.ວວນ.ລິສຂະສິດ!&D 8k,czomuj]5,j oU w]ptmk’c8sj ^;’rt[k’wxsk-eg|nvc,oj  1,6 cm. c8oj t7vo s^;’;P’9aowxsk -eg|nvc,oj 2,6 cm. 9qj’oe.-hv5xtdvo mujg\\ktlq,grnjv\\kp mu8j A’0v’-eg|nv.ljczomuj]5j,oUD       !*D l;o8vo|bj’gxaoI6[ $ c9lkd ,u];’pk;cmdwfh 36 m. ];’d;hk’cmdwfh          25 m gryjoxads^adIQ;vhv,l;o sjk’dao]ts;kj ’lv’s^ad 1,5 m. 4k,;kj gryjo8hv’ dkos^adIQ;ma’\\qf9adsa^dL !(D dD 9qj’c8h,;q’,qomu,j u];’Iv[gmqjk 12 cm .shgvqk π =  3 0D 9q’j c8h,I6[lujc9lkdmuj,u];’Iv[gmqkj 12 cm.   7D 9q’j c8h,I6[9t85]afmu,j u];’Iv[gmqkj 12 cm.  !)D 9q’j ;k’g,af  A, B c]t C .lgj lAo-nj8k,]efa[ 3fp;jk AB = 42 cm c]t BC = 58 cm.             .shg,af I gxaog,afg7yj’dk’0v’ mjvo-n j AB c]t J gxaog,afg7yj’dk’0v’ mjvo-n j BC.           9q’j 7yfw]j ];’pk; IJ.        126

!_D svp $ 38wx8k,mk’muxj 6fh;p8kdk3imuj,u0t|kfgmqkj daoD glAomk’gfuoc8j]t 38wfhltcf’fa’j I6[]5,j oUG G 38mu ! wxwfh 36 cm  38mu @ wxwfh 48 cm 38mu # wxwfh gmjkq .dL 38mu $ wxwfhgmqjk.f L X4vf9kd[Aoc0’j 0ao7toyflkf 9y’39h @WW#F Kangaroo 2003)    @WD 9qj’-vdskw]ptmk’c8j A sk B -b’j ltcf’fh;pI6[]5,j oUX\\kpgsfG .oI6[oU[+ c,jo];’pk;8q;9y’?G 100cm A 1 cm ສະຫງສ.ວວນ.ລິສຂະສິດ    100cm DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD B 9kd[qfg]d c0j’0ao7toyflkf 9y’39h @WW# @!D gryoj ra[I6[9t85]af.shgxaolv’I6[lujc9lkdgmqkj daomu,j u];’Iv[gmqkj 25,8 cm.          9q’j -vdsk];’Iv[0v’I6[9t85]afoAoD @@D 9qj’c8h,I6[lk,c9mq;j wx RED 3fp;jk RE <ED c]h;;k’g,af A 16jmvj o-nj ED 3fp;kj I6[lk,c9 REA c]t RAD ,u ];’Iv[gmqjkdaoD 127

@#D 9qj’;k’g,af  O(0), A(4) c]t B(7) 16jgmy’cdo9eo;oD c]h;0ufglAo-nj d 8A’lkdda[ (AB) zkj og,af A. ;k’g,af C 16j d 3fp;kj AC = 4D c]h;0ufglAo-nj (BC) zkj o O wx8af (AC) 16jg,af D.  9q’j [vd];’pk; BC  c]h;-vdsk];’Iv[0v’ I6[lk,c9 ABC c]t OAD.  @$D 9q’j c8h,I6[]5j,oU7no.\\j Ih6;jkI6[9t85]afmujltcf’fh;pglAo0kf,u0hk’gmqjk 2,6 cm           c]h; -vdsk ];’Iv[0v’c8]j tI6[oAoD @&D 9qj’-vdsk];’Iv[0v’I6[lk,c9 ABC g-yj’9v, A wfh4nd8afvvdwxc]h; fa’j I6[]5,j oUD ສະຫງສ.ວວນ.ລິສຂະສິດ     C  3,4 cm           4 cm         ,us^kp;ymuG B   6   cm    vkfg]njvoI6[ # c9    ,kg[Nv’-hkp s^n ra[l;j omu1j 6jovd0v[ ,kg[Nv’-hkp c]h; ;afcmd s^n 7yfw]jD 128

ສະຫງສ.ວວນ.ລິສຂະສິດ [qfmu !( dkog7y’j 7n 7;k,leobddPj ;da[dkog7yj’7nmP[.ljglAo-nj|b’j 9qj’g[y’j I6[8+wxoU muwj fh]vdc[[,k3fp.-hg9Ap8kdk3i c]h;lhk’I6[g7yj’7n0v’ ,aomP[.ljglAo-nj c8pj a’[+c]h;D .o[qfoU 9twfhIPodjP;da[dkog7y’j 7nmP[.ljglAo-n|j bj’F dkoc8h,I6[ 3fp[+.-hg9Ap8k dk3i .shoe.-hc8jg7nvj ’,ng]0k7toyfgmqkj oAoD !D dyf9tde !D dkog7yj’7n c]t dkora[ dD oe.-hg9hpdkogdD { .og9hpdkogd c8h,I6[fvdw,h]5,j oUfh;pl=feD { ra[g9Ap c]h;0uf8k,7v’l=fhkos^a’I6[c8h,D 9kdoAoF c[g9hpdkogdvvd 9twfh ma’lv’I6[oAo c,oj I6[g7y’j 7ndaomP[.ljglAo-nj d mujgxao0v’Ivpra[D lk,kfg;Qkwfhvud;jk I6[muj @ gxaoI6[g7y’j 7nda[I6[mu ! mP[.ljcdog7y’j 7n dD 129

0D I6[8afda[cdog7y’j 7nD .-hg9hpdkogdF l=fe c8h,I6[8k,.9D ra[g9hpdkogd8k,glAo-jn d c]t 8afda[I6[muj gIqkc8h,D I6[mujgIqkc8h,4ndra[gxaolv’l;j o .-hl=fe0uf 8k,7v’mk’xUo0v’c8j]t2kd0v’I6[0v’ lv’l;j oD c[g9hpvvd c]h;;k’gr.shrP’D [vj o.fgxao[jvo8afdao0v’I6[da[cdog7yj’7n L @D I6[g7yj’7n0v’g,af|b’j d  dD I6[8+wxoU c,joI6[mujwfh9kddkoc8h,oqd|b’j 8q; c]t wfh]vdc[[7nfaj’wfhvtmy[kp 16j0=h !D dD oqd c]t I6[mujwfh]vdc[[ g7yj’7ndaomP[.lgj 9Ap-nj d. g,af A c]t g,af B g8a’dao mP[.ljglAo-nj d gIqkg;qkwfhvud;jk g,af B c,jog,afg7y’j 7n0v’g,af A mP[ .ljglAo-nj dD d  ສະຫງສ.ວວນ.ລິສຂະສິດ A  B  { 9qj’.-h[aomaflkdgrnjvd;fg[yj’;jkglAo-nj d 8af c]t 8A’lkdda[mvj o-nj [AB] c]t .-h;q’;Po s^n [aomaf,u0uf\\kp d;fg[y’j ;jkglAo-nj d 8afmvj o-nj [AB] 16jg,afg7yj’dk’D { 9q’j \\kplv’g,afg7yj’7ndaoD 9kdoAo d;fg[yj’;jkm5dM g,afmu1j 6jglAo-nj d 8af c]t 8A’ lkd16gj ,afg7y’j dk’0v’mjvo-nDj 0D .-hg9hp0k; 0ufglAo-nj d c]t \\kpg,af A 1j6ovdglAo-nj d. 9kdoAo .-h[aomafF [ao maflkd c]t ;q’;Po lhk’g,af B g7yj’7nda[g,af A mP[.ljglAo-nj dD 130

@D .97;k, !D dkora[ c]t dkog7y’j 7nmP[.lgj lAo-nj|bj’ d  d  1 2 I6[ X!? c]t I6[ X@? g8a’daor=fu g,njvgIqkra[g9Apwx8k,7v’glAo-nj dDສະຫງສ.ວວນ.ລິສຂະສິດ \\kp7;k,;jk I6[ X!? c]t I6[ X@? g7yj’7ndaomP[.ljglAo-nj dD @D g,afg7yj’7n0v’g,af|b’j mP[.lgj lAo-n|j bj’ d  d  A  B  C  lv’g,afc8d8jk’dao A c]t B g7y’j 7ndaomP[.ljglAo-nj d g,nvj glAo-nj d 8af c]t 8A’ lkdda[mjvo-nj [AB] 1j6g,afg7yj’dk’0v’,aoD { lk,kfg;Qkwfhvud;jk g,af B gxaog,afg7yj’7n0v’g,af A mP[.lgj lAo-nj dD { g,af C ovo16jglAo-nj dF g,afg7y’j 0v’g,af C mP[.lgj lAo-nj d c,jo8q;g,af C oAogv’D 8q;1jk’G dD c8h,8q;g7yj’7n0v’I6[|bj’fh;pg9Aple]a[dkogdD .-hg9Ap0k;F c8h,I6[ F c]t 0ufglAo-nj d. oe.-hg9Aple]a[dkogdF c8h, I6[g7y’j 7n 0v’ F mP[.ljglAo-nj dD 131

ສະຫງສ.ວວນ.ລິສຂະສິດ{ c8h,I6[ F F 0ufglAo-nj d c]h;\\kpg,af A c]t B .lgj lAo-nj dD { ;k’g9hple]a[dkogd1v’I6[c8h, c]h;]vdc[[I6[F glAo-nj d g,af A c]t BD { xUog9hp]vdc[[ c]h;;k’g9hp]vdc[[3fp.shg,af A c]t g,af B 0v’8q;dkogd g8a’da[g,af A c]t g,af B 0v’I6[c8h,D .omkj oUF .-hl=fe0uf8+Ivp0v’ F grnjv 9tgvqkI6[ F wx]vd.lgj 9hpc8h,I6[D 0D lhk’c8h,I6[g7y’j 7n0v’g,affh;p[aomaflkdF [aomaf c]t ;q’;PoD c8h,glAo-nj d c]t ;k’g,af M 16oj vdglAo-nj dD .-h[aomaflkdF [aomaf c]t ;q’;Po lhk’c8h,g,af M’ g7y’j 7nda[g,af M mP[.lgj lAo-nj dD !D { .-h[aomaflkd c]t [aomaf0ufglAo-nj8A’lkdda[glAo-nj d zkj og,af MD { .-h;q’;Po lhk’g,af M’ .lgj 7y’j glAo-nj [MH) 3fp;jk HM’=HMD 132

ສະຫງສ.ວວນ.ລິສຂະສິດ#D [qfg/ydsaf !D oe.-hg9hpdkoD dD 0ufmvj o-nj dF ;k’g,af A 16jglAo-nj d 9kdoAo c8h,glAodq’j L mu8j afglAo-nj d 16jg,af ID ;k’g,af B .ljglAodqj’ L D 0D oe.-hg9hpdkogd c8h,glAodqj’ L ′ g7yj’7ndaoglAodq’j L mP[.lgj lAo-nj dD ;k’g,af B′ g7y’j 7nda[g,af BD 7D glAodq’j L c]t glAodqj’ L ′ 8afdao16j.l L ’D oe.-h[aomaf,u0uf\\kp c]t [aomaflkd d;f7nog[y’j ;jkglAo-nj d 8af c]t 8A’lkd da[mvj o-nj [BB’] 16jg,afg7yj’dk’D cotoeG le]a[0h= 0D .shg[y’j 8q;1jk’D @D dko-vdskI6[g7y’j 7nD d D oe.-hg9hpdkogd d;fg[y’j ;jkI6[ F c]t I6[ F ′ g7y’j 7ndaomP[.lgj lAo-nj d [+L 0D 7nda[7e4k,0h= dD oe.-hI6[F c]t I6[F ′ 0v’I6[8+wxoUD cotoeG 9q’j ]vdc[[ma’\\qfI6[ X F ′F F’’ c]t d? fh;pg9Apw0,aoF 9kdoAo d;f g[yj’;jk F c]t F ′ g8a’dao g,njvra[8k,glAo-nj dD #D 16j3I’]t7vo lv’I6[8+wxoUF c8]j t76j8q;8t]qd I6[.fg7y’j 7ndaomP[.ljglAo-nj d D dd 133

$D dD 9qj’]vdc[[I6[0hk’oUfh;pg9Apw0,ao 1v’g9hpdkogdD 0D ra[I6[mudj kogdD 9kdoAo d;f7nog[y’j ;jkrkdlj;o0hk’-hkp c]t 0hk’0;k g7y’j 7ndao[= mP[.ljglAo0kf dD 7D 9q’j -vdskI6[g7y’j 7nvnjo8n,j muj,u.o I6[0hk’0;koUD d &D dD 9qj’]vdc[[I6[0hk’-hkpoU c]t glAo-nj d .ljg9hpmuj,u8kdk3iD 0D lh’c8h,I6[g7y’j 7nda[I6[oUmP[.lgj lAo-nj dD *D oe.-hg9hp,u8kdk3i grnjvc8h,I6[0hk’ ສະຫງສ.ວວນ.ລິສຂະສິດ 0;koU7noD 9kdoAo \\kpg,af A’, B’, A C’ g-y’j c,jog,afg7yj’7n0v’g,af A, B, C mP[.lgj lAo-nj dD B C (D 9q’j c8h,I6[0hk’0;koU7no c]h;\\kp d A1; B1; C1; O1 g-yj’gxaog,afg7yj’7n0v’ g,af A, B, C c]t O mP[.ljglAo-nj dD d2 A 9kdoAo\\kpc8h, A2; B2; C2; O2 B g-yj’gxaog,afg7yj’7n0v’g,af A; B; C; O c]t O mP[.ljglAo-nj d@D d1 C 134

)D .oc8j]td=]tou]j5,oUD 9q’j d;fg[y’j ;kj B gxaogxaog7yj’7n0v’g,af A mP[.ljglAo-nj d s^n [=L phvospa’ L _D oe.-h[aomaflkd c]t [aomaf,u0uf\\kpG dD 0ufglAo-nj d c]h; \\kpg,af A c]t g,af B A d 16jlv’2kd0v’glAo-jn dD { oe.-h[aomaflkd c]t [aomaf,u0uf\\kp ສະຫງສ.ວວນ.ລິສຂະສິດ B lhk’g,af C c]t g,af D g7yj’7nda[g,af A c]t g,af B mP[.ljglAo-nj d 8k,]efa[D 0D 0ufmjvo-nj [AB] c]t [CD]. g,af8afdao0v’r;d,ao1j6.l L 7D d;f7no g[y’j ;kj [AB] c]t [CD] g7y’j 7ndaomP[.lgj lAo-nj d fh;pdko.-hg9hpdkogdD !WD dD c8h,glAodqj’ C c]h; \\kplujg,af A, B, C c]t D .ljglAodq’j faj’dkj ;D 0D oe.-h[aomaflkd c]t [aomaflhk’ c8h,g,af A’,B’,C’, D’ g7y’j 7nda[ A,B,C, D mP[.lgj lAo-nj dD 7D zjkog,af A’,B’,C’, D’ 0ufglAodq’j C ′fh;p,n g7yj’7ndao C mP[.ljglAo-nj dD d;f7nofh;p dko.-hg9ApdkogdD 135

[qfmu !) ,5,F dko;afcmd,5, !D dyf9tde !D 7;k,leobddjP;da[,5, dD 9q’j oe.-hc8j;q’;Po c]t [aomaf X[+,u0uf\\kp? grnjvc8h,I6[lk,c9mu1j 6jmk’0hk’oU7no.lgj 9hp C 0k;3fp.sh,u0t|kfgmqkj daoda[I6[lk,c9gfu,D AB ສະຫງສ.ວວນ.ລິສຂະສິດ cotoe { c8h,mjvo-nj AB; { 0ufmvj odq’j muj,u.9dk’ A c]t ]aflt\\u AC { 0ufmjvodqj’0v’;q’,qomuj,u.9dk’DDDDDDDDDDDDDc]t ]aflt\\uDDDDDD l5fmhkp ,u9ad[vj omugj xaowxwfh0v’g,afDDDDDDDDDL 0D dko]vdc[[0v’,5, A  E  C  B  G  F  I6[lk,c9lkd EFG c,joI6[]vdc[[I6[0v’I6[lk,c9 ABC. 4k,;kj c,oj 9v,.f0v’I6[lk,c9 ABC dq’da[g,af E, F c]t G ? { 9qj’8n,j ,5,.lj[vj o,u9Eg,af8+wxoU .sh4nd8hv’G BnAC = ... , CnBA = ... , AnCB = ... 7D \\kpg,af A c]t B sjk’dao * cm.  { c8h,d5,j 0v’g,afmuj16sj jk’9kdg,af A $ cmF 9kdoAoc8h,d5j,0v’g,afmuj16j skj ’9kdg,af B & cmD { ,u9adg,afmuj16Ij ;j ,dao sjk’9kd A $ cm c]t sjk’9kd B & cmD { c8h,I6[lk,c9mu,j u0hk’ & cm, * cm c]t _ cm. 136 

’D mkj 8jk’M0v’I6[;uD { .o9er;dI6[;u8+wxoUF 9q’j -vdskd5j,I6[;umu,j u,5,gmqkj daoD Xmevyfg[y’j fh;p8kgxqjkF 9kdoAo.-hg9hpdkogd?D 14 5 8 2 67 9 3 { 9q’j dkj p7no8k8t]k’]5,j oUc]h;8nj,oEg[u.ljshv’mujdq’da[,5,8kj ’MD ສະຫງສ.ວວນ.ລິສຂະສິດ ,5, ,5,lkd ,5,cs^, ,5,s;k ,5,rP’ ,5,g8a, ,5,l6o ;uoEg[u @D dko;afcmd,5, B dD [aomafcmd,5, Xg7yj’;q’,qo? A I6[0hk’oU 16lj Qo0v’glAo,u0uf\\kp c,oj g,af16jsjk’lt\\jeltg\\udao0v’ ( )mvj odqj’ ApS . ApB = BpC = ... { gvUo,5, AnOB , BnOC , CnOD , ... ;kj co;.f L { 9q’j .-hg9hpw0,ao ]vdc[[ g7y’j ;q’,qomuj,u .9dk’ O, ]aflt\\u $ cm c]t 0ufmjvo-nj [AS]. ;k’g9hpw0,aoma[I6[8Qoc[[0hk’gmy’ c]t ]vdc[[0uf\\kp c]h; \\kpfh;p8q;g]dD { g7y’j ;q’,qomu,j u0uf\\kplk,kfoe.-h;afcmd ,5,wfhD 137 

8q;1kj ’G 9q’j la’gdfdko;afcmd,5,fh;pg9hpw0,aomujwfh]vdc[[,koUG { ;k’g,af.9dk’ O 0v’g7y’j ;q’,qo.lj9v,0v’,5, a mu8j hv’dkocmd 3fp.sh 0uf\\kp 0 g8a’da[0hk’|b’j 0v’,5, a D ,5, u c,jo,5,sq;|j;pD 7kj ;af cmd0v’ a c,oj #u D { 9qj’;afcmd[aofk,5,0v’I6[]5j,oUfh;pg7y’j ;q’,qomuj,u0uf\\kp muzj t]yffh;pg9hpw0,ao 0k’gmy’F 9kdoU.sh.-hg7nvj ’;afcmd,5,cmdD { 7jk;afcmd,5, u ,u9advq’lk L ສະຫງສ.ວວນ.ລິສຂະສິດ 0D oe.-h[aomafcmd,5,grnjvlhk’c8h,I6[lk,c9D 8q;1jk’G lhk’I6[lk,c9 ABC 3fp;jkG BC= & cm, AnBC = 35D , AnBC = 70D { 0ufmvj o-nj [BC] muj,u];’pk; & cm x  { I6[ltcf’dkoc8h,wfh9afw;h0hk’oUF A  0ufg7yj’glAo-nj [Bx) zjko0uf\\kp 35D 0v’g7y’j ;q’,qo.  C  { fa’j fP;daoF 0ufg7yj’glAo-nj [Cy) zjko0uf\\kp,5, 70D 0v’g7y’j ;q’,qoD { [Bx) 8afda[ [Cy) 16gj ,af A. gIqkwfh I6[lk,c9 ABC mu8j hv’dkolhk’D 138 

7D dkovkj o,5, Â cotoeG { g0a,.sp{j lAoc,oj g0a,-U[vd3,’ Xg0a,3,’? { g0a,.spj{pk;c,oj g0a,-U[vdokmu Xg0a,okmu? { g0a,ohvpc,jog0a,-U[vd;yokmu Xg0a,;yokmu? Â 9q’j xP[mP[,5,muwj fh9kdG { g0a,.spj{lAo c]t g0a,ohvpF { g0a,.spj{lAo c]t g0a,.sp{j pk;S { g0a,.sp{j pk; c]t g0a,ohvpD Â 9q’j vkj o8k8k]k’]5j,oUc]h;8nj,7kj 0v’,5,.lGj ,5, ,5,DDDDDDDDDDDD ,5,DDDDDDDDDDDD ,5,DDDDDDDDDDDD ,5,DDDDDDDDDDDD w]ptg;]k ]ts;jk’ W sk !& ;yokmu ]ts;kj ’ !W sk ]ts;kj ’ !W @W ;yokmu $W ;yokmu sk !& ;yokmu ສະຫງສ.ວວນ.ລິສຂະສິດ @D .97;k, !D ,5, x dD 7ela[ XdkogvUo-n?j ,5,s;E O ,5,l;f I6[0hk’0;koU xtdv[fh;p ,5,l;f c]t ,5,s;ES y rkdl;j omu1j 6jmk’.ogvUo;jk ,5,l;fF rkdl;j omuj16jmk’ovdgvUo;jk ,5,s;ED { gryjolaopt]ad,5,l;ffh;p xnOy s^n ynOx c]t vjko;jk ,5, xOy s^n yOx. { gryjolaopt]ad,5,s;Efh;p xOy s^n yOx c]t vkj o;kj ,5, xOy s^n yOx. { g7yj’glAo-nj [Ox) c]t [Oy) c,jo0hk’0v’,5, xnOy . { g,af O c,jo9v,0v’,5,D 139 

0D ,5,ltgrkt y y O x y x Ox O ,5,lkd ,5,l6o ,5,rP’ 0hk’ [Ox) c]t [Oy) [Ox) c]t [Oy) [Ox) c]t [Oy) ma[-hvoXg8a’dao? 8A’lkddao xtdv[oedaogxaoglAo-nj @D ,5,-toyf8jk’MD dD sq;|;j p;afcmd,5, sq;\\;j p;afcmd,5,c,oj vq’lk gryoj laopt]adfh;p ( D )D { ,5, l6o ,u7kj ;afcmdc,jo 0D 90D   { ,5, lkd ,u7jk;afcmdc,jo 90D ສະຫງສ.ວວນ.ລິສຂະສິດ { ,5, rP’ ,u7jk;afcmdc,jo 180D 180D   0D   0D ,5,cs^,F ,5,s;k c]t ,5,g8a, O  { ,5,cs^,,u7kj ;afcmdohvpd;kj 90D c8sj ^kpd;jk 0D ,5,rP’ { ,5,s;k,u7kj ;afcmds]kpd;kj 90D c8|j hvpd;kj 180D { ,5,g8a,,u7jk;afcmdwfh 360D 8q;1jk’G 25D   140D   360D   ,5,cs^, ,5,s;k ,5,g8a, 140 

8q;1jk’ !D oe.-h[aomaf c]t ;q’;Po lhk’,5, xn'O'y' gmqjkda[,5, xnOy . ;ymuc8h,G B y 16j,5, xnOy G { 0ufmjvodq’j 0v’;q’,qo.9dk’ O 8af [Ox) 16j g,af O A A c]t 8af [Oy) 16jg,af B. X!? 1x 5 y' B' 4 lhk’,5, xn'O'y'G { 0ufg7y’j glAo-nj [O'x') ... X@? O' A' 2 x' { 0ufmjvodq’j mu,j ug,af.9dk’16j O' c]t ]aflt\\u 3 OA 8af [O'x') 16jg,af A' ... (3) { 0ufmjvodqj’0v’muj,ug,af.9dk’16j A' c]t ]aflt\\u AB . ສະຫງສ.ວວນ.ລິສຂະສິດ { lv’mjvodqj’8afdao16jg,af B'D { 0ufg7y’j glAo-nj [O'y') zkj o B' gIqkwfh,5, xn'O'y' mu8j hv’dkolhk’D 8q;1jk’ @D ;afcmd,5, xnOy fh;p[aomafcmd,5,D x O y ;k’[aomafcmd,5,3fp.shG { .9dk’0v’,aog8a’da[9v,0v’,5,S { 0hk’|b’j 0v’,5,g8a’da[0uf\\kp 0D 0v’[aomafcmd,5,S { vjko7kj 0v’,5,16j[aomafcmd,5, g-yj’g8a’da[0hk’mulj v’0v’,5,D .od=]touoU gIqkwfh xnOy = 33D D 141 

#D [qfg/ydsaf A !D I6[fhko0hk’oU,5, NnCI lk,kf0Pofh;ps^kp;ymu N M g-ajoG AnCM s^n NnCM s^n AnCI I dD 9qj’0Po,5,8kj ’M]j5,oUfh;ps^kp;ymuG BP C BnAC , AnBN , BnNC , AnPN , MnCB 0D ,u9ad;ymu.odkoltcf’,5, BnIC fh;p[aofkg,afvnoj mu,j u.oI6[L @D .oI6[0v’[qfg/ydsaf 0=h !F 9q’j [vd-n0j v’,5,mu,j u9v, I ,k.shwfh !W ,5,D 8q;1kj ’G AnIN , AnIC ,.... #D ,5,lkdF ,5,rP’D dD 9qj’0uflv’glAo-nj (xy) c]t (zt) 8A’lkddao c]t 8afdao16jg,af A. 0D 9qj’[vd-n0j v’,5,lkdF -n0j v’,5,rP’D $D 9qj’;afcmd,5,muj16j0hk’oU 9kdoAo9af]Po ,5,muj,u7jkc8j|hvpsks^kpD ສະຫງສ.ວວນ.ລິສຂະສິດ &D ,5,0hk,9v,D dD 0uflv’glAo-nj (xy) c]t (zt) 8afdao16jg,af O, ,5, xnOz c]t ynOt ,u9v, O vaofP;daoD gryjogvUo ,5, xnOz c]t ynOt ;jk ,5,0hk,9v,D 9q’j xP[mP[7kj 0v’ 0v’r;d,aoD 0D 9qj’xP[mP[,5, xnOt c]t ynOz . 6D dD 9q’j c8h,I6[mu1j 6j0hk’0;koU7noD 0D 9qj’xP[mP[,5, AnPB , AnQB c]t AnRB fh;pg9hpdkogdD 142 

(D 9q’j oe.-h[aomaflkdF -vdI6h,5,cs^, c]t A  B  ,5,s;k0v’I6[0hk’0;koUD C  E  D  7ecotoeG .sh0Po7e8v[.lj8k8k]k’gxaolv’[ao-ufaj’oUG ,5,cs^, ,5,s;k DnAC DAB DDDDDDDDDD DDDDDDDDDD )D c8h,I6[lk,c9 ABC mjP’16jg,af A (AB = AC) . 9qj’xP[mP[,5, AnBC da[ AnCB fh;pg9hpdkogdD A ສະຫງສ.ວວນ.ລິສຂະສິດ { oe.-h;q’;Po c]t [aomaf[+,u0uf\\kp a lhk’I6[lk,c9mu,j u0t|kfgmqkj daoda[ BC I6[lk,c9 ABC 0hk’0;koUD _D B mvj odqj’ CpE ,ug,af.9dk’ B. 9q’j oe.-h [aomaf E mu[j +,u0uf\\kp c]t ;q’;Po ]vdc[[mvj odq’j x fa’j djk;8k,0t |kf8q;9y’.lgj 9hp0k;D C !WD 9q’j c8h,,5, umsv = vnsw = wnsx = xmsy !!D                { 9q’j ;afcmd,5,  al,b, cl,d,e  D   { ,u,5,.fcfmj ujgxao,5,cs^,S ,5,s;k ?  143 

!@D ,5,0v’I6[lk,c9D A dD 9q’j ]vdc[[I6[lk,c9 ABC muj16j0hk’0;koU7noD 0D 9q’j ;afcmd,5,0v’I6[lk,c9faj’ B C y djk;fh;p[aomafcmd,5,D !#D 9q’j 7yfw]7j jk;afcmd,5,s;E xOy 0v’I6[0hk’oUD O !$D .oc8j]td=]touF .sh7yfw]j7jk;afcmd0v’,5, xnoz x xy zy 78° 34° z O x 120° 43° zy O ສະຫງສ.ວວນ.ລິສຂະສິດ 15D .oI6[fhko0hk’oU O c,oj g,af|bj’0v’glAo-nj (xy), (Oz) c,jog7y’j glAo-njmuj ,ug,afg7Qk O. { 9q’j 7yfw]j7kj ;afcmd,5, b .oc8j]td=]tou8+wxoUG a = 15D ; a = 63D; a = 98D ; a = 124D . z  .od=]tou.f { 7jk0v’ b 9b’j dq’da[,5,cs^,L x y { 7kj 0v’ b 9b’j dq’da[,5,s;kL O !*D 9q’j [vd7jk0v’,5, a, b,c,d 0v’ I6[0hk’0;koUD ,u,5,.f,aogxao,5,s;k L 144 

!(D 9q’j c8h,lk,,5, xnAy, znBt, unCv 3fp;jkG xnAy = 50D , zmBt = 90D , unCv = 144D D !)D 9q’j c8h,I6[lk,c9 ABC 3fp;kj G BnAC = 65D , AB= 7 cm, AC= 5 cm, cotoeG c8h,,5, BnAC = 65D dvj oD !_D 9qj’c8h,I6[lk,c9 ABC 3fp;kj AB= 8 cm, CnAB = 48°, CnBA = 84° @WD u dD 0ufglAo-nj ( xy) , \\kpg,af B v .ljglAo-njfa’j dkj ; c]t 0ufg7y’j glAo-nj [Bu) c]t [Bv) fa’j .oI6[]5j,oU 64° 26 ° B x y 0D .sh7yfw]j7jk;afcmd0v’,5, unBv , xnBv c]t unBy . ສະຫງສ.ວວນ.ລິສຂະສິດ @!D dD c8h,I6[lujc9 ABCD 7no 8k,0t|kfmuj\\kpw;h.oI6[D 0D 9qj’;afcmd7jk0v’,5, a c]t b @@D A dD 9qj’[vdxtgrf0v’I6[lk,c9 ABC c]t BCD rhv,ma’-Uc9’D B 20 mm C 0D 9qj’[vdxtgrf0v’I6[lucj 9 ABCD rhv,ma’-Uc9’D D 145 

ສະຫງສ.ວວນ.ລິສຂະສິດ@#D dD 9q’j c8h,I6[lk,c9 ABC 3fp;jkG AB= 7 cm, BC= 6 cm, CA= 5 cm 0D 16j0hk’ovd0v’I6[lk,c9 ABC, 9q’j lhk’c8h,I6[lk,c9ltg\\u ABE, BCF, CAG. 7D 9q’j 0ufmjvo-nj [EC], [FA], [GB]. la’gdfgsaoco;.f L xP[mP[];’pk;0v’ mvj o-njfaj’djk;fh;p;q’;PoD @$D .oc8j]tou8+wxoUF 9q’j 7yfw]j7jk;afcmd0v’,5, xnOy D @&D la’gdfI6[8+wxoU y dD 7yfw]7j jk;afcmd0v’,5, a c]t unAv D 0D c8h,I6[7n8k,7jk0v’,5,muj7yfw]wj fh.o0=h dD @*D 9q’j lhk’I6[lk,c9lkd ABC lkd16j9v, B 3fp;kj AB = 5 cm , BnAC = 35D. 146