ປຶ້ມແບບຮຽນ ປ.5

& c[[IPo 7toyflkf -Aoxt4q,lbdlkxumu &

ry,mu3j I’ry, Pitambra Books Pvt.Ltd., B-95, Bijoli Industrial Area,

PIN-284001, Jhansi, Uttar Pradesh, INDIA

8k, ]m[ #&*r9@#!!@WW_
ry,7A’mu ! 9eo;ory, !$@ WWW sq;

0t|kf !) V @& -,
lts’;o]y0tlyf

& c[[IPo
-Aoxt4q,lbdlk
7toyflkf &

1 = 2 1 < 2
3 6 3 3

G B C
G
B C H C BF
A
1dm3 1 D D AE H
1dm F G
E
H

I6[dhvolkd AD

I6[c[0v’I6[dhvolkd

1dm A D

1dm B CAB CD A
AD B
FG

EH EF GH

I6[da[lkd I6[Ec[0v’I6[dHa[lkd
I6[c[0v’I6[da[lkd

shk,0kp



c[[IPo

7toyflkf
-Aoxt4q,xumu &

IP[IP’3fp G v5myf my[,tou XlD;Dl?
s5,rao xD lts;affu XlD;Dl?
mv’0k; cl’l5]y9ao XlD;Dl?
lu,5’75o ;q’9exk Xdq,lhk’76?
oD mv’lts;ao grafs^;’lu X,Dl grp;af?
oD 76o;yw] g7ody8ylad X3I’IPoxt4q,lq,[6o mq’j dk’?
oD 7elyiyr6w- fkik Xlbdlkg,nv’w-g-f4k?

d;fcdh3fp G cv39h vkfzkl5d XlD;Dl?
9ao r6olts;af Xmujxbdlk?

c8h,I6[3fp G mv’fe mv’lyo XlD;Dl?

g0Qk|hk3fp G 0aodk[ rq’v5fq, XlD;Dl?

d;f c]t .sh7egsao3fp G 7totde,tdkoIa[Iv’s^adl6f

dt-;’lbdlkmydko
lt4k[ao7Qo7;hk;ymtpklkfdkolbdlk

;P’9ao @WW_



lk]t[ko |hk
rkdmu !G dkovkj o c]t dko0Po9eo;o
[qfmu !G dkovjko c]t dko0Po9eo;o.orNo4koly[D DDDDDDDDDDDDDDDDDDDDDDDDDDDDD *
[qfmu @G dko9af]Po9eo;oD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD )
[qfmu #G I6[c[[dko0Po9eo;oD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !W
[qfmu $G 9eo;os^kpd;jk ! WWW WWWD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !@
rkdmu @G dko7eo;o
[qfmu &G dko[;d{dko]q[9eo;o4h;o c]t 9eo;omqfltoypq,D DDDDDDDDDDDD !*
[qfmu *G dko76o9eo;o4h;o c]t 9eo;omqfltoypq,D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD @W
[qfmu (G dkosko9eo;o4h;oD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD @$
[qfmu )G dko7eo;og]dmuj,u;q’g]a[D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD @)
rkdmu #G g]0k7toyf
[qfmu _G dkog]nvdv5xtdvoD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD #W
[qfmu !WG dkoc8h,I6[7noD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD #@
ສະຫງສ.ວວນ.ລິສຂະສິດ
[qfmu !!G I6[s^kpc9D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD #$
[qfmu !@G I6[lujc9D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD #*
[qfmu !#G I6[lucj 9lkd{I6[9t85]afD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD #)
[qfmu !$G I6[lk,c9D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD $W
[qfmu !&G dkolhk’I6[D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD $@
rkdmu $G dko7eo;o
[qfmu !*G 75o]adltotdkosko0kfD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD $$
[qfmu !(G mt;u76o c]t v5xt75o0v’|b’j 9eo;oD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD $*
[qfmu !)G m;o7nog8adoyddkosko9eo;o4h;oD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD $)
rkdmu &G dkocdh39f[aosk
[qfmu !_G ;ymudkocdh39f[afskD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD &W
[qfmu @WG ;ymudkocdh39f[aosk X8+?D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD &$
rkdmu *G 9eo;omqfltoypq, c]t g]dl;j o
[qfmu @!G zqoskogxao9eo;omqfltoypq,D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD &*
[qfmu @@G zqoskogxao9eo;omqfltoypq, X8+?D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD &)

[qfmu @#G g]dl;j o{dkoc[’j lj;oD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD *W ສະຫງສ.ວວນ.ລິສຂະສິດ
[qfmu @$G dko[;d c]t dko]q[g]dl;j oD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD *$
[qfmu @&G dko[;d c]t dko]q[g]dl;j o X8+?D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD **
[qfmu @*G I6[c[[dko0Pog]dl;j o c]t mqfltoypq,D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD *)
[qfmu @(G ]efa[9eo;omqfltoypq, c]t g]dlj;oD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD (W
[qfmu @)G ]efa[9eo;omqfltoypq, c]t g]dl;j o X8+?D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD (@

rkdmu (G g]0k7toyf c]t dko;afcmd

[qfmu @_G dko;afcmd];’pk;D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD (*
[qfmu #WG dkooe.-h9eo;omqfltoypq, c]t g]dl;j og0Qk.odko;af
cmd];’pk;D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD ()
[qfmu #!G dko-aj’,;olkoD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD )W
[qfmu #@G dkooe.-h9eo;omqfltoypq, c]t g]dlj;og0Qk.odko-a’j
,;olkoD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD )@
[qfmu ##G dko;afcmd[=]y,kf[ao95D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD )$
[qfmu #$G sq;|j;p;afcmd[=]y,kf[ao95D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD )*
[qfmu #&G dkooe.-h9eo;omqfltoypq, c]t g]dlj;og0Qk.odko;afcmd
[=]y,kf[ao95D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD ))

rkdmu )G ];’Iv[ c]t goNvmuj

[qfmu #*G sq;|j;p;afcmdgoNvmuDj DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD _W
[qfmu #(G ];’Iv[ c]t goNvmuj0v’I6[lucj 9lkdD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD _@
[qfmu #)G ];’Iv[ c]t goNvmu0j v’I6[9t85]afD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD _$
[qfmu #_G ];’Iv[ c]t goNvmu0j v’I6[lk,c9D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD _*
[qfmu $WG ];’Iv[ c]t goNvmuj0v’I6[lujc90hk’0t|koD DDDDDDDDDDDDDDDDDDDDDDDDDDDDD _)

rkdmu _G 8e]k9eo;o

[qfmu $!G lt4kotdkogrnvj 7Qo7yfD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !WW
[qfmu $@G lt4kotdkogrnjv7Qo7yf X8+?D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !W@
[qfmu $#G dkogxaovaf8klj;orq;raoD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !W$
[qfmu $$G dkogxaovaf8kl;j orq;raodq’D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !W*
[qfmu $&G dkogxaovaf8kl;j orq;raoxUoD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !W)

rkdmu! WG g]0k7toyf c]t dko;afcmd ສະຫງສ.ວວນ.ລິສຂະສິດ

[qfmu $*G dkophkp0t|koD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !!@
[qfmu $(G dkog7yj’7nmP[.ljcdoD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !!*
[qfmu $)G cdog7y’j 7nD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !!)
[qfmu $_G dkophkp0t|ko c]t dkog7y’j 7nD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !@W
[qfmu &WG dkog7njvophkp c]t dko\6oIv[D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !@@

rkdmu !!G lj;oIhvp c]t ,kf8klj;o

[qfmu &!G dko7yfw]lj ;j oIhvpD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !@$
[qfmu &@G ,kf8kl;j oD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !@)

rkdmu! @G g]0k7toyf c]t dko;afcmd

[qfmu &#G dkosp=h c]t dko0tspkpI6[D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !#W
[qfmu &$G dkozaoxjPoI6[D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !#$

rkdmu !#G dko7eo;o

[qfmu &&G dkosko9eo;omqfltoypq,D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !#*
[qfmu &*G dkosko9eo;omqfltoypq, X8+?D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !#)

rkdmu !$G ];’Iv[ c]t goNvmuj

[qfmu &(G ];’Iv[ c]t goNvmuj0v’I6[7k’\6D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !$W
[qfmu &)G ];’Iv[ c]t goNvmuj0v’I6[;q’,qoD D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !$@

rkdmu! &G g]0k7toyf c]t dko;afcmd

[qfmu &_G I6[dhvoD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !$$
[qfmu *WG I6[da[lkdD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !$*
[qfmu *!G I6[mkf]Pj ,D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !$)
[qfmu *@G 7;k,I6hdjP;da[[=]y,kf c]t sq;|;j p;afcmd[=]y,kfD DDDDDDDDDDDDDDDD !&W
[qfmu *#G dko7yfw][j =]y,kfD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !&@
[qfmu *$G dko7yfw][j =]y,kf X8+? DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !&$

rkdmu !*G dko;afcmdg;]k

[qfmu *&G sq;|;j p;afcmdg;]kD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !&*
[qfmu **G w]ptmk’F 7;k,w;F w]ptg;]kD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD !*W

rkdmu ! dkovjko c]t dko0Po9eo;o

[qf mu ! dkovkj o c]t dko0Po9eo;o.orNo4koly[

I. dyf9tde

gryoj .sh[afmuj0Pogxao9eo;oF leo;o c]t 8q;|a’lnfaj’8+wxoUG
!)*& km !& V !W7km ) lv’raocxfIhvp-k;c,af
!W WWW km T @ WWW km T (WW km T &W km T * km @#* )WW km2

{ 9qj’0Po[k’leo;omju1j6.oc8j]t[af.shgxao9eo;oc]h;9af9eo;omujg\ktlq,
da[xt3spd]j5,oUG
dD 9eo;ofk;g7ktmujgxao[=]y;ko0v’f;’8kg;aoD
0D ];’pk;0v’c,oj E0v’mjuws^zjkoxtgmf]k; Xgxao km?D
7D ];’l6’0v’r6g[hp Xgxao m?D ສະຫງສ.ວວນ.ລິສຂະສິດ
’D glAozjko.9dk’0v’|;j p3]d Xgxao km?D
9D w]ptsjk’c8|j ;j p3]dskf;’8kg;ao Xgxao km?D
lD goNvmuj0v’ lDxDxD ]k; Xgxao km2 ?D

II. .97;k,

dkovjko9eo;oc,oj vkj o9kds^ads^kpsks^ad|hvpD

8q;1jk’G 9eo;o # )&* # 16js^adsq;rao

) 16js^adsq;Ihvp

& 1j6s^adsq;ly[

* 16js^adsq;|j;p

vkj o;kj G lk,raocxfIhvpshkly[sqd

c8j.o9eo;o * &)# # 16js^adsq;|;j p

) 16sj ^adsq;ly[

& 16js^adsq;Ihvp

* 16js^adsq;rao

vkj o;kj G sqdraoshkIhvpcxfly[lk,

6

 sa^dc8]j tsa^d,u7jkgmqjk !W gmnjv0v’sa^dmu1j 6j]5f4afda[,ao V!W
Xpqdg;Aosa^dsq;|;j p?
V!W V!W V!W V!W V!W

1 000 000 100 000 10 000 1 000 100 10 1

106 105 104 103 102 101 1

III. [qfg/ydsaf

!D 9qj’9af9eo;o8+wxoU.lj8k8t]k’D
!@& S #$@ S shkly[lk, S X$ V !WWW? T X& V !WW? T !# S
X@ V !W#? T X( V !W? T $
8q;1jk’G

-Ao0v’sq;]hko -Ao0v’sq;rao -Ao0v’sq;|;j p

I l | I l | I l |
!W) !W( !W* !W& !W$ !W# !W@ !W !
ສະຫງສ.ວວນ.ລິສຂະສິດ@
# $

@D 9q’j vkj o c]t 0Po9eo;o8+wxoUgxao8q;|a’lnD
(@) S $ W#@ S ! (&& S !@ #!( S @ $#* WWW S !# &@) W!# S

! $@* W#@ S )_(D
#D 9q’j la’gdf9eo;o !) ($* c]h;8v[7e4k,]5,j oUG

dD 8q;g]dsa^dsq;|j;pc,jo8q;g]d.fL
0D 8q;g]dsa^dsq;ly[c,oj 8q;g]d.fL
7D 9eo;ooU9txjPogxao9eo;o.f 4hkgIqk8nj,|b’j .ljsa^dsq;raoL
$D 9q’j 0Po9eo;o]5j,oUgxao8q;g]dD
shkraoshkIhvplujly[lk,S gdQkIhvpg9afly[cxfS ly[gvafraoS sqdIhvp-k;shk

raolujIhvp-k;S lv’]hkocxfIhvplk,ly[raoD

7

[qf mu @ dko9af]Po9eo;o

I. dyf9tde

9q’j 8nj,9eo;o]5,j oU.ljglAo37h’8k,]efa[D

@&W !WWW T @WW T &W & V &WW $V!W#

& V !W@ lk,raoshkIhvp X@ V !W#? T X(V!W@? T X&V!W? !W#

g9afIhvpshkly[ @ V !W# X# V !W#?

!WWW ສະຫງສ.ວວນ.ລິສຂະສິດ

#WWW @WWW
$WWW
8

ສະຫງສ.ວວນ.ລິສຂະສິດII. .97;k,

1kdxP[mP[lv’9eo;o4h;ogIqk8hv’xt8y[affa’j oUG
!D 4hk;kj lv’9eo;ooAoskd,u9eo;o8q;g]d[+gmqjkdaoF 9eo;omuj,u8q;g]ds^kp

d;jkc,jo9eo;omjus^kpd;kj D
8q;1jk’G @$&) > &_)
@D 4hk;jklv’9eo;ooAoskd,u8q;g]dgmqjkdaoF 9q’j g]u,j xP[mP[8q;g]dmuj16jg[Nv’
-hkpl5f0v’ma’lv’9eo;ooAodjvoF 8q;g]dg[nhv’-hkpl5f0v’9eo;o.fs^kp
d;kj c,oj 9eo;ooAos^kpd;kj F 4hk8q;g]d1j6g[Nv’-hkpl5foAogmqjkdaod+xP[mP[
lv’8q;g]d4af,k c]t 8+MwxD
8q;1jk’ G dD _ #$* c]t ) _)(

) _)(
_ > ) ltoAo _ #$* > ) _)(
0D ( @*! c]t ( @&_
( @&_
* > & ltoAo ( @*! > ( @&_

III. [qfg/ydsaf

!D 9qj’xP[mP[9eo;o]5j,oU3fp8n,j g7njv’\kp < s^n > .lj[jvo9Eg,afD
_#( D D D )&* S $ #(@ D D D $ #)( S $W) D D D #_$ S !* #)$ D D D !* #)_ S
(W W&# D D D (W W*$D

@D 9q’j 9af]Po9eo;o]5j,oU8k,]efa[c8|j hvpsks^kpD
#) *@& S )* @#& S *) @&# S )* &#@ S @) *&# S &# *@) S *) #&@D

#D 9q’j 9af]Po9eo;o]j5,oU8k,]efa[c8js^kpsk|hvpD
( )$@ S @ )($ S ) (@$ S @ ($) S ) @($ S @ ()$ S ( $@) S $ )@(D

$D 9qj’0Po9eo;o8+wxoUgxao8q;|a’lnD
_)( S !@$ *WW S ! #WW WWW S # WWW S !@ W@$ WWW S !W @(W S #!& (WW W!@D

9

[qf mu # I6[c[[dko0Po9eo;o ສະຫງສ.ວວນ.ລິສຂະສິດ

I. dyf9tde

!D 9q’j 9af]Po9eo;o8+wxoUc8|j hvpsks^kpD
!W !W! S ! W!! S ! WW! S !! WW! S !!! WWW S !! !W! S !W! !!!

@D 9q’j 9af]Po9eo;o8+wxoUc8js^kpsk|hvpD
*W *W* S *W* S *W* W*W S ** WWW S * W** S * **W S *W *WW

#D 9qj’0Po9eo;o8+wxoU rkp.8hI6[c[[dt9kpD
8q;1kj ’G
*@& = *WW T @W T &
= X* V!W@ ? T X@ V !W? T X& V !?
d D ! #$& = D D D T D D D T D D D T D D D

= XD D D V D D D? T XD D D V D D D? T XD D D V D D D? T XD D D V D D D?

0 D ( )W@ = D D D T D D D T D D D

XD D D V D D D? T XD D D V D D D? T XD D D V D D D?

7 D !W# $&)= D D D T D D D T D D D T D D D T D D D

= XD D D V D D D? T XD D D V D D D? T XD D D V D D D? T XD D D V D D D? T XD D D V D D D?

II. .97;k,

9eo;o|b’j lk,kf0Powfhrkp.8hs^kpI6[c[[g-ajo G
!D 0Pogxao8q;g]d

8q;1kj ’ G !$@ *&)
@D 0Pogxao8q;|a’ln

8q;1kj ’G |bj’Ihvplujly[lv’raosqdIhvpshkly[cxf X|b’j cloluj\noj lv’raosqd
Ihvpshkly[cxf?D
#D 0Poc[[dt9kp
8q;1jk’G
!$@ *&) = !WW WWW T $W WWW T @ WWW T *WW T &W T )

10

ສະຫງສ.ວວນ.ລິສຂະສິດ s^n X!V!WW WWW? T X$ V!W WWW? T X@V! WWW? T X*V!WW? T X&V!W? T )
s^n X!V!W&? T X$ V!W$? T X@ V!W#? T X* T !W@? T X&V!W? T )

III. [qfg/ydsaf

!D 9qj’0Po9eo;o.lj[jvo9Eg,afD
8q;1jk’G @W WWW T ( WWW T #WW T $ = @( #W$
dD !W WWW T @ WWW T $W T ) = D D D D D

0D $WW WWW T @W WWW T )WW T @ = D D D D D
7D X@ V! WWW? T X# V!WW? T X$V!W? = D D D D D
’D X* V!WW WWW? T X# V!W WWW? T X$ V!W? T & = D D D D D

9D X( V!W WWW? T X) V!WW? T X( V!W? T _ = D D D D D

@D 9q’j 0Po9eo;o.lj[jvo9Eg,afD
8q;1jk’G $W &#$ = $W WWW T &WW T #W T $
= X$ V !W$ ? T X & V !W@ ? T X # V !W ? T $
dD (W# &WW = X(WW WWW T # WWW T &WW
= X( V D D D? T X# V D D D? T X& V D D D ?
0D _& WW_ = D D D T D D D T _
= X_ V D D D ? T X& V D D D ? T _
7D ( @$) = D D D T D D D T D D D T )
= X( V D D D ? T X@ V D D D ? T X$ V D D D ? T )
’D !@ W$) = D D D T D D D T D D D T D D D
= X! V D D D ? T X @ V D D D ? T X$ V D D D ? T )

11

[qf mu $ 9eo;os^kpd;jk ! WWW WWW ສະຫງສ.ວວນ.ລິສຂະສິດ

I. dyf9tde
!D 9q’j 0Po9eo;o8+wxoU.oI6[c[[dt9kpD

8q;1kj ’G &* (@$ =&W WWW T * WWW T (WW T @W T$
=X&V!W WWW? T X*V! WWW? T X(V!WW? T X@V!W? T X$ V!?
=X&V!W$? T X*V!W#? T X(V!W@? T X@ V!W? T $

@$ *#& = DDD T DDD T DDD T DDD T DDD
= X... V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD?
= X... V DDD? T XDDD V DDD? TXDDD V DDD? T XDDD V DDD? T DDD

$# @() = DDD T DDD T DDD T DDD T DDD
= XDDDV DDD? T XDDD V DDD? T XDDD V DDD? T XDDD VDDD? T XDDD V DDD?
= XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T DDD

*( #$& = DDD T DDD T DDD T DDD T DDD
= XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD?
= XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T DDD

!)_ $*@ = DDD T DDD T DDD T DDD T DDD T DDD
= XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD?
= XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T DDD

@D 9qj’0Po9eo;o8+wxoUgxao8q;|a’ln c]t gxao8q;g]dD
8q;1kj ’G

sq; sq; sq; sq; sq; sq; sq;Ihvp sq;ly[ sq; sq; sq; sq;
Ihvp ly[ |;j p Ihvp ly[ |;j p Xclo? X\noj ? |j;p Ihvp ly[ |j;p

-Ao0v’8N -Ao0v’sq;]hko -Ao0v’sq;rao -Ao0v’sq;|j;p

0Pogxao8q;|a’lnG ly[lv’]hko lujclo lv’\noj lk,rao |b’j Ihvp -k;shkD
0Pogxao8q;g]dG !@ $@# !@&

12

dD

sq; sq; sq; sq; sq; sq; sq;Ihvp sq;ly[ sq; sq; sq; sq;
Ihvp ly[ |j;p Ihvp ly[ |;j p Xclo? X\njo? |j;p Ihvp ly[ |;j p

-Ao0v’8N -Ao0v’sq;]hko -Ao0v’sq;rao -Ao0v’sq;|j;p

00PPooggxxaaoo88qq;;g|]a’dlG nGD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD
0D

sq; sq; sq; sq; sq; sq; sq;Ihvp sq;ly[ sq; sq; sq; sq;
Ihvp ly[ |;j p Ihvp ly[ |j;p Xclo? X\noj ? |j;p Ihvp ly[ |;j p

-Ao0v’8N -Ao0v’sq;]hko -Ao0v’sq;rao -Ao0v’sq;|j;p
ສະຫງສ.ວວນ.ລິສຂະສິດ
00PPooggxxaaoo88qq;;g|]a’dlG nGD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD

7D

sq; sq; sq; sq; sq; sq; sq;Ihvp sq;ly[ sq; sq; sq; sq;
Ihvp ly[ |;j p Ihvp ly[ |;j p Xclo? X\noj ? |j;p Ihvp ly[ |j;p

-Ao0v’8N -Ao0v’sq;]hko -Ao0v’sq;rao -Ao0v’sq;|;j p

00PPooggxxaaoo88qq;;g|]a’dlG nGD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD DD

#D 9qj’0Po9eo;o8+wxoU3fpoe.-hde]a’0v’ !WD
= DVD!W*
8q;1kj ’G $#* WWW DWDWDWD DD $D #D *D ( WWW WWW WWW =DDDDDDDDDD
!$ WWW WWW =
&) WWW WWW = D D D D D D D D D D D @W WWW WWW WWW = D D D D D DD D D D
*_@ WWW WWW = D D D D D D D D D D D *#W WWW WWW WWW = D D D D D D D D D

13

II. .97;k,

8q;g]d.o9eo;o4h;o9tg]uj,c8j-Ao0v’sq;|;j pF -Ao0v’sq;raoF -oA 0v’s;q

]kh oD .od]= to9u eo;omsju k^ pd;kj ! WWW WWW gIqklk,kflhk’-Aogruj,9kd-Ao

0v’sq;]hkofaj’oUG

sq; sq; sq; sq; sq; sq; sq;Ihvp sq;ly[ sq; sq; sq; sq;
Ihvp ly[ |j;p Ihvp ly[ |j;p Xclo? X\noj ? |;j p Ihvp ly[ |j;p

-Ao0v’8N -Ao0v’sq;]hko -Ao0v’sq;rao -Ao0v’sq;|j;p

vkj o;jkG lv’Ihvplujly[gvaf]hko
0Pogxao8q;g]dG @$! WWW WWW

ສະຫງສ.ວວນ.ລິສຂະສິດ
sq; sq; sq; sq; sq; sq; sq;Ihvp sq;ly[ sq; sq; sq; sq;
Ihvp ly[ |;j p Ihvp ly[ |j;p Xclo? X\njo? |j;p Ihvp ly[ |;j p

-Ao0v’8N -Ao0v’sq;]hko -Ao0v’sq;rao -Ao0v’sq;|;j p

vjko;kj G |bj’raolv’Ihvply[lk,]hkolv’Ihvply[lurj aolv’Ihvpshkly[lk, s^n
|bj’8Nlv’Ihvply[lk,]hkolv’clo|b’j \noj lurj aolv’Ihvpshkly[lk,
0Pogxao8q;g]dG ! @!# @!$ @&#

grnvj gIaf.sadko0Po9eo;omu,j ug]dl6o16mj hkps^kp8q;’jkp0Bo7;oxt8y[affaj’oUG
!D oe.-hg]dde]a’0v’ !WD 8q;1jk’G @$* WWW WWW = @$* V !W*

@D oe.-hdkooa[gxaosq;rao s^n sq;]hkoD
8q;1jk’G @$* WWW WWW 0Pogxao @$* ]hko
! WWW WWW WWW 0Pogxao !WWW ]hko s^n X! 8N?

14

III. [qfg/ydsaf
!D 9qj’0Po9eo;o8+wxoU.oI6[c[[dt9kpD
8q;1kj ’G
)* #@& = )W WWW T * WWW T #WW T @W T&
= X)V!W WWW? T X*V! WWW? T X#V!WW? T X@V!W? T X&V!?
@ ) # ( & = = X )V!W$? TX *V!W#? T X#V!W@? T X @V!W? T &
DDD T DDD T DDD T DDD T DDD
= XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD?
= XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T DDD
&$ (!) = DDD T DDD T DDD T DDD T DDD
= XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD?
= XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T DDD
@)# @&* = DDD T DDD T DDD T DDD T DDD T DDD
= XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD?ສະຫງສ.ວວນ.ລິສຂະສິດ
= XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T XDDD V DDD? T DDD

@D 9qj’0Po9eo;o8+wxoUgxao8q;|a’lnD 9D ($* &_@ WWW
dD # *!$ WWW
0D $@) WWW WWW lD )&( !*& WWW
7D *WW WWW WWW -D @ ($) @&! WWW
’D &$@ !#* )WW pD $ *&# (@# &@W
#D 9qj’0Po9eo;o8+wxoUgxao8q;g]dD
|bj’]hkoS lv’8NS sqd8NS lv’]hkocxfcloly[raoS lujIhvply[lk,]hkoshkcloS
g9afIhvpcxfly[]hkogdQkclolk,\njosqdraolujIhvpS shk8Nlk,Ihvplv’]hkoD
$D 9q’j 0Po9eo;o8+wxoU3fpoe.-hde]a’0v’ !WD
dD ! $WW WWW 9D &)$ WWW WWW
0D &* WWW WWW lD # WWW WWW WWW
7D @* #!@ WWW -D !@ WWW WWW WWW
’D #$@ WWW WWW pD $(& WWW WWW WWW

15

rkdmu @ dko7eo;o

[qf mu & dko[;d{ dko]q[9eo;o4h;o c]t 9eo;omqfltoypq,
I. dyf9tde
!D (9*WWq’j WW7WyfT-w(]@WjgW]TWdW_]=5j,=oDDUGDDDDDDDDDDDDD
D D D D S &#W T $W T * = D D D D D D D D D D D S
D D D D S
@D ok’ ok]yo 9tx5’c8j’vkskodyoIj;,da[\6Dj ]k;7yf;kj 9tgIafvksko-toyf
.f|bj’ ]ts;jk’8e\kdsj5’da[g0Qkx5hooEdtmy g-yj’g7nvj ’x5’c8’j vkskofaj’
djk;,u]kpdkofa’j oUG

g0Qkx5hooEdtmyD

g0kQ xoh5 _ WWW d[u dtxy @ WWW d[uສະຫງສ.ວວນ.ລິສຂະສິດ
xk !) WWW d[u zda dt]ej xu @ WWW d[u
\kdrkh ; & WWW d[u \kd4;jq # WWW d[u
\kdgzfa cs’h # WWW d[u sv,]k[ @ WWW d[u
zda [;jq cs’h @ WWW d[u sv,xvh , @ WWW d[u
zda mP,cs’h ! &WW d[u s;q 0kj ! WWW d[u
\kdgzfa f[y ! WWW d[u

8e\kds5j’D
\kds5j’ * WWW du[ xkcfd @ WWW du[
\kdg]ajo @ WWW du[ oE8ko ! WWW du[
\kd0k, ! WWW du[ dtxy @ WWW du[
\kdok; ! WWW du[ d5h’csh’ & WWW du[
\kddvd ! WWW du[ zad[hq’ @ WWW du[
\kdgzaffy[ ! WWW du[ zaddt]ej xu @ WWW du[
zadmP,csh’ ! WWW du[ 0P[\6 $ WWW du[
dD 9qj’7yfw]dj ko.-h9jkp7jkvkskoc8]j t-toyfD
0D ok’ ok]yo 9tg]nvdvksko-toyf.f9bj’9twfh9jkpg’yo|hvpL
]k;9txt1afg’yowfh9addu[L

16

#D w]ptmk’c8jot7vos^;’;P’9aoskmjk]kf,uxt,ko )&F&@ km ok’ ;P’lu
gfuomk’9kdot7vos^;’;P’9aowxmjk]kf g,nvj c]jo]qfwxwfh #@F#& km ]k;
wfhc;j 1k,]5’D 9kdoAo 9bj’gfuomk’8+wxvud !#F!( km c]t wfhc;j 1k,ohklk;
8n,j vudD

dD 9q’j 7yfw]wj ]ptmk’c8;j P’9aoskgInvoohklk;0v’]k;D
0D pa’vud9ad km 9b’j 9tIvfmjk]kfL

ot7vos^;’;P’9ao g7njvow22hkoE’n,j I

II. .97;k, ສະຫງສ.ວວນ.ລິສຂະສິດ
grnvj 1kd[;d s^n ]q[9eo;o4h;o s^n 9eo;omqfltoypq,gIqk8hv’8A’[ah’g]d
3fp.shc8]j ts^ad164j aofP;daoc]h; [;d s^n ]q[ c8j0;ksk-hkpD
8q;1jk’G dD dko[;d 0D dko]q[

T@($@)_ T#**#FF$&&$ -&#*($# - @#&F$)*
!@_F&*

_(( __F__ !_! !W&F_@*
III. [qfg/ydsaf
!D 9q’j -vdskzqo[;d0v’g]d]5,j oUG
dD !$ T * T !@ T ) T # T ( T @( T # T !& T & S 9D $W* T@_ T !#!) S
0D !F& T #F& T @F& T (F& T #F& T $F& T )F& T!F& S lD ($F) T !F) T @&F!# S
7D *$) T @!& T @) S -D _$!F# T !@WF@) T!F$ S
’D !@#& T $( T #!@ S pD (F#* T $#F( T !WWF#) D
@D 9qj’-vdskzqo]q[0v’g]d]5j,oUG
dD )$* { !#( 0D !*)$ { $@! 7D (#) { @!(
’D !#F!$ { )F@! 9D @W#F) { )$F$ lD !@F#!) { )F$#(

17

#D 9qj’-vdsk7e8v[c]h;0Po.l[j jvo9Eg,afD
dD X)$#@F) _ *$F$? T X&*F!) _ !#F@$ T )? = D D D D D D D
0D X@!$F&@ T !_F@#$? T X@$)F!_ _ !@F@!? = D D D D D D D
7D X(W# _ $@F@&? T X@W!$ T !#FW) T #F$!@? = D D D D D D D
’D X@$) _ !$F#$? _ X@WF$!@ _ &F!@&? = D D D D D D D

$D 9qj’7yfw]jg]d]5j,oUG *&$W
dD T (!*@$_ 0D $()_ 7D _ )@W*
T (_@$
D D D D
DDD DDDD

CD T _)F@* 9D T $W&F!_ lD T &(@F$(
$_F#( @#(F&$# $)&F()
D D D D D
D D D D D D D DDDDDD
ສະຫງສ.ວວນ.ລິສຂະສິດ
&D 9qj’8nj,8q;g]d.lj[vj o9Eg,afD
dTD
$ • 0D T * • • @ ! 7D T ( • $ @
• ) • @ # • $ @ • •

( @ _ ! W ! • • & ( !

CD_ $ • @ F W $ 9D _ ) @ • F #
# • F ( W (•#F•

•((F#• •!WF&

*D 9q’j 7yfw]cj ]h;8n,j .l.j o
dD )!@#F$@W _ X&()F&*_ T *)_F&*)? = )!@#F$@W _
=

0D &(_F$&# _ X)_(F$&* _ $&*F&*#?= &(_F$&# _
=

18

(D 9qj’7yfw]cj ]h;8n,j .lj 9kdoAo la’gdfg[y’j zqo[;d16j0=h d c]t 0=h 0
gmqjkdao s^n [+L

dD X!@& T *)? T )_ 0D !@& T X*) T )_?
X!@&T*)? T )_ = T )_ !@&TX*)T)_? = !@& T

= =

la’gdfgsao;jkzqo[;d1j60=h d c]t 0 D D D D D D D D D D D D D D

)D ok’ ok]u ,ug’yo () WWW du[ c]t mhk; g9u ,ug’yo &( &WW du[D
4k,;jkma’lv’,ug’yos^5f]noj dao9addu[L

_D ]5’7e ,ug’yo !*_ &WW du[F ]k;-NglNv|b’j zno]k7k #& WWW du[F 3lh’|bj’zno
]k7k (& WWW du[ c]t dtgxqJk|bj’|;j p]k7k $& WWW du[D
4k,;kj G dD ]5’7e 9jkpg’yoma’\qf9addu[L
0D g’yo0v’]k;pa’gsn^v9addu[L
ສະຫງສ.ວວນ.ລິສຂະສິດ

!WD goNvmujfyol;o0v’]5’[5o7E gmqjkda[ #@$ m@ c]t 0v’xhk[5ogduf gmqjkda[
&@W m@D 9q’j lhk’7e4k, c]t 7yfsk7e8v[0v’[qfg]dfaj’dkj ;D

!!D zqogda[dP;j g0Qk16jlk,mqj’ok0v’-k;okzh6|b’j ,ufaj’oUG
@#&F$* kg S #(!F_@& kg S *(_F)! kg.

9q’j oe.-h0=h,6ogmy’oU lhk’gxao[qf39f c]h;7yfw]jsk7e8v[D

19

[qf mu * dko76o9eo;o4h;o c]t 9eo;omqfltoypq,

I. dyf9tde

!D j jfk;ryfltfko j j zqo[;d0v’m5dM9eo;o.oc8j]tc4;9tgmqkj dao\qf Xmk’

ovoF mk’goU’?D 9q’j la’gdfc]h;xt8y[af8k,7elja’]5j,oUG

X!?D # X@?D

!! ( * @

$_

!@ ! & )

!W ສະຫງສ.ວວນ.ລິສຂະສິດ

dD 9q’j d;f7no7eg;Qk0hk’gmy’oAo4nd8hv’[+L zqo[;d.oc8]j tc4;,ugmqjk.fL
0D .sh76o @ .l9j eo;o.oc8j]t;q’,qo0v’fk; X!? c]h;0PozqowfhIa[.lj;q’

,qo0v’fk; X@? 9kdoAo 7yfw]jzqo[;d.oc8j]tc4;9twfhgmqjk.fL
7D fk; X@? 9tgxaofk;ryfltfko[+L
’D 9q’j d;f7nofh;pdko76o9eo;o.oc8]j t;q’,qo0v’fk; X!? .sh #D
@D 9qj’8A’[A’g]dc]h;7yfw]Dj
@$_ V ( = D D D D D D D S () V ) = D D D D D D D S *@ V #& = D D D D D D D S
$@& V !W = D D D D D D D S &!$ V @W$ = D D D D D D D S @WW V #W& = D D D D D D D

#D 9q’j 76og]d8+wxoUD !#$
V@#F#& !) @$ #F&
V !F@ V WF* V

$D 9q’j 8A’[A’g]dc]h;7yfw]Dj )F$#( V !WWW = D D D S
#*F$ V !W = D D D S WF$#@ V !WW = D D D S #F* V !F) = D D D
*F$@ V & = D D D S #)$ V @F& = D D D S

20

&D 9qj’la’gdf8q;1jk’c]h;0Po9eo;o8n,j .l[j jvo9Eg,afD
8q;1kj ’ G &@ V @F# = X&@ V @? T X&@ V WF# ?=!W$ T !&F* = !!_F*
*$ V #F) = X*$ V #? T X*$ V WF)? = D D D T D D D = D D D D
!FW* V (_ = XD D D V (_? T XD D D V (_?= D D D T D D D = D D D D

II. .97;k,

!D dko76o9eo;o4;hoD
dD ;ymu76omujg7upxt8y[afzkj o,kD

V $#_
&(
#W(# $#_ V (
@!_&W $#_ V &W
@&W@# $#_ V &(

0D lk,kf0Powfhvudfa’j oUG ສະຫງສ.ວວນ.ລິສຂະສິດ
$#_ V &( =
X1$4#@44_!2V_4&&4W4W3? T X1 4$#4#4_W2(V4#44(3 ? @& W@#
T =

@D dko76o9eo;omqfltoypq,D
dko76o9eo;o4h;oda[9eo;omqfltoypq, s^n 9eo;omqfltoypq,da[9eo;o
mqfltoypq,gIqkxt8y[af7nda[dko76o9eo;o4h;oda[9eo;o4h;oD 9kdoAo 9bj’
\kp95f.ljzqo76o3fp.sh9eo;o8q;g]drkdlj;omqfltoypq,0v’zqo76ogmqjk
da[zqo[;d0v’9eo;o8q;g]d rkdlj;omqfltoypq,0v’8q;8A’ c]t 8q;76oD

8q;1kj ’ G V #) V #) V!&$FF@( V!W V!&$@(
@F* @* V!W
V!W
@ @ ) @@) @_$ @_$
(* (* (#& (#&
_ ) F) ' !W _)) (*F$$ '!WW (*$$

21

III. [qfg/ydsaf
!D 9qj’76og]d]5,j oU

V$)& V *$W V #W$_ &*W_
) ( V#

(D $D *D D DDDD DDDD DDDD
V () V !WW = D D D D @) V $@ = D D D D
@& =DDDD _) V !WWW = D D D D !!& V !W) = D D D D
*!# V !W = D D D D
()& V (WW = D D D D @#!) V @WWW= D D D D (W* V )@ = D D D D

@D 9qj’g]nvd7e8v[mu4j nd8hv’16j0hk’]5j,c]h;0Po8nj,.lj[jvo9Eg,afD
dD &W& V &@ = D D D D 0D _) V #( = D D D D
7e8v[G @*@*WS @**@WS @*W@* 7e8v[ #@** S #*@* S #**@

#D 9qj’la’gdf dD ! _ @ !) ສະຫງສ.ວວນ.ລິສຂະສິດ
8q;1kj ’G ! V _ V @ = !) # ) $ _*
& * ( @!W
! V # V & = !&


!& $#@ &*

9qj’8n,j 9eo;omjug\ktlq,.lIj 6[X0? c]t I6[X7?

0D !@ @ @$ 7D @ & $W

( @!W !)_
(@ $)
* ) *

@) !W) !@W $) $& !*)

22

$D 9q’j -vdskzqo76o0v’g]d]5j,oUD !F@& V )*&F@F$# V $W_FFW)#!
V $& V (F_@ #&W
@F# !$ V

&D 9q’j -vdskzqo76oc]h;8nj,.l[j vj o9Eg,afD (F@)& V !WWW = D D D D S
$@F) V !W = D D D D S *F() V !WW = D D D D S &F@& V !) = D D D D D
#@F& V ) = D D D D S *$FW@ V &* = D D D D S

*D 9qj’8nj,\kp95f.ljzqo76o]5j,oU.sh4nd8hv’D
@$* V &F@ = !@(_@ S (FW#! V $@ = @_&#W@ S *!F) V #F& = @!*#WD

(D 9qj’g]nvdgvqk7e8v[mu4j nd8hv’.l[j vj o9Eg,afD
dD &$)V!WF& = D D D D D 0F _&#)VWF_& = D D D D D
8v[ G &(&F$ 8v[ G _W*!F!
&(&$ _W*W!
&(&# _W*F!! ສະຫງສ.ວວນ.ລິສຂະສິດ

)D 9qj’la’gdfc]h;0Po8nj,.lj8k8t]k’]5j,oU
X goNvmuIj 6[lujc9lkd = ];’pk; V ];’d;hk’?

];’pk; #&F& @& $&F@ &)
];’d;hk’ !$ !)F& #* !@F&

goNvmuj $_(

_D 4hkgvqk9eo;o|bj’76oda[ ) 9twfhzqo76ogmqkj da[ _*D 4k,;jk9eo;omujgvqk
,k76oc,jogmqjk.fL

!WD g-nvdglAo|bj’pk; *F(& m , 4hkgvqkg-nvdmupj k;gmqkj daooU ( glAo,k;k’8+dao
9tpk;gmqjk.fL

!!D g0Qk4q’|bj’|ad *F& kg, 4hk,ug0Qk!WW 4q’ 9t,uoE|adgmqkj .fL

23

[qf mu ( dkosko9eo;o4h;o

I. dyf9tde

!D 9qj’8n,j 8k8t]k’8+wxoUD

8q;8A’sko 8q;sko dko0v[0Ao 9eo;o8q;g]d.o
zqosko

*@& @& @& V !W < *@& < @& V !WW @

$W&W @& @&V!WW < $W&W < @&V!WWW #

_!**) )W$

!)!W) #* ສະຫງສ.ວວນ.ລິສຂະສິດ
!W_#* _&

@$@@& $@&

@D 9q’j la’gdf8q;1jk’ c]h;skog]d0=h8+wxD 8q;1jk’ @G _!**) )W$
8q;1kj ’ ! G _ _!**) )W$ !!@*) !!$
)W$WW !!$ W#@@)
WW!@
_ !!@*)
)W$W

_ W#@@)
#@!*

WW!@

d;f7noG X)W$ V !!$?T !@ = _!*&*T!@ = _!**)
_!**) sko.sh )W$ wfh !!$ c]t glf !@

24

dD 9qj’skog]d]5j,oU3fpxt8y[afmeov’fP;daoda[8q;1jk’ !D

(@)$ !$ #*$( #@ @)$ $W

*$!# !) (@#$ &W &@$) @$

0D 9qj’skog]d]5j,oU3fpxt8y[afmeov’fP;daoda[8q;1kj ’ @D

#$* !@ $)( @# *&_ &@

()$ #@ )@&* )* &@$) _!

_&*& $! $(&*& @& _&($ @@

()&* (@ (&*$@ )$ $(&$) *$ສະຫງສ.ວວນ.ລິສຂະສິດ

II. .97;k,

dkosko9eo;o4h;ogIqklk,kfxt8y[afwfhfa’j oUD

dD dkoskoc[[pk; 0D dkoskoc[[lAo

_ @*)_ @$ @*)_ @$
_ @$ !!@ @) !!@
W@) $_
@$ W!
_ W$$)_
W!

d;f7noG X@$ V !!@? T ! = @*)_
\kpgsfG dkod;f7noc,jogvqk8q;sko76oda[zqoskoc]h;[;dda[8q;glfD

25

III. [qfg/ydsaf

!D 9q’j la’gdf 8q;1jk’ c]h;-vdsk9eo;o8q;g]d0v’zqosko
8q;1kj ’G *)( ' )&
0v[0Aofh;p )& V ! < *)( < )& V !W
zqosko,u ! 8q;g]d

$)#@ ' &@ S $#(& ' !@& S (!#$& ' &@) S
$@(&* ' #W_ S &_) ' @* S &(_## ' !@# D

@D 9q’j la’gdf8q;1kj ’c]h;skog]d8+wxoUD

_ )*!@W#( #W&
@(

_ @@!!##(& ສະຫງສ.ວວນ.ລິສຂະສິດ

WWW@

(*WW @& )_(! @_ #$__ @#

_))_ )_ ($#) @! _W! !)

$#(W$ &_ #() #& @@) @W

26

#D 9q’j 8n,j zqo76o.l.j o8k8t]k’D

dD V )WW 0D V !@$W 7D V (@)$
$ # *
&W &W @WW
*WW (W #WW
*&$ _W #@W
(#) &WW #$W
)#@ $&@ $@W
_(* *&( &!W
!W WWW (@W (WW

$D 9q’j gIafg]dsko8+wxoUc[[lAoD

!@#$ ' *() S (!#$& ' !#& S $#(& ' #& S ສະຫງສ.ວວນ.ລິສຂະສິດ
&_) ' @* S &@(W ' !&W S _(@# ' !#W S
&&* ' @# S )_@$ ' !!& S &(*$ ' @$D

&D .odkolv[gla’g0QkIPo,afmtpq,xumu!0v’3I’IPo,afmtpq,csj’|bj’,uzh6lt
\ad $&W 7qoF lt4komujlv[gla’c,oj .-hshv’xt-5, ! shv’ c]t shv’IPoF
I6h;kj shv’xt-5,oaj’wfh !@W 7qo c]t shv’IPooa’j wfhshv’]t #W 7qoD .odko
lv[gla’7A’oU8hv’.-hshv’IPogxaoshv’lv[gla’9adshv’L

*D shv’7q;dyo,u];’d;hk’ $ m c]t ];’pk; * m. 4hk8hv’dkox6fh;pdk3i
mu,j u0t|kf @W cm V @W cm 9t8hv’.-hdk3ima’\qf9adczjoL

(D c,7j hkzh6|bj’0kpxkoyo dy3]dik,]t !@ WWW du[ 9eo;o @) dy3]dik,F
wfhdew]ma’\qf *$ $WW du[D 4k,;kj ]k;-Nxkoyody3]dik,]tgmqkj .fL

)D ]qfg,7ao|b’j oaj’wfh @( 7qoD 4hk1kd0qolqj’oadIPo9eo;o *$( 7qo 9t8hv’dko
]qf9ad7aoL

27

[qf mu ) dko7eo;og]dmuj,u;q’g]a[

I. dyf9tde

!D 9q’j 7yfw]gj ]d]5j,oUG
dD X!#@ T $&? _ X)# _ (@? V @

0D X@$# _ @#@? T X&(@ T @)? V *
7D X@&$# _ !#(& ? V X!@* _ !@W? ' #

’D X(& V $? T X!&& T !&? ' &
9D X#@W V #? _ X&WW T &)? ' _

@D 9q’j la’gdf;ymudkocdh39f0=h Xd? c]h;oe.-h.o0=h8+wxD
Xd?D 7v[7q;0v’]5’;aook ]hP’wdj $@* 38 c]t gxaf !&# 38D .o’;fmevyf
]k;gvqkwdjvvd0kp @*@ 38 c]t gxaf _* 38 l;j omujgsn^v]k;8hv’dko]hP’w;h
.shc8j]t38,uoE|adltg]pj @ kg c]h;9b’j 9t0kpvvd.o’;fmulv’D 4k,;kj
gxaf c]t wdjmju9t0kp.o’;fmulv’,uma’\qf9ad kgL
ສະຫງສ.ວວນ.ລິສຂະສິດ
;ymucdh G XX$@* _ @*@? T X!&# _ _*?? V @

1444442444443 1444442444443

X!*$ T &( ? V@

1 4 4 4 44 2 4 4 4 44 3

@@! V @ = $$@

7e8v[ G $$@ kg
X0?D xhk;aofu ,ug’yoma’\qf !@W WWW du[F ]k;-Nxk $ kg. dy3]dik,]t
!) WWW d[u F -zN da dkf @ kg, d3y ]dik,]t & WWW d[u F -\N kddPh ’ @ kg, dy3]
dik,]t !@ WWW du[F l;j og’yomugj sn^v9tc[j’.sh]6d0v’]k; @ 7qo gmqjkdaoD
4k,;jk]6d0v’]k;9twfhg’yo7qo]tgmqjk.fL

28

II. .97;k,

.odko7eo;og]dmuj,u;q’g]a[ gIqk8hv’7yfw]jg]d.o;q’g]a[dvj oD 9kdoAo 9bj’

7yfw]8j k,sa^ddko0v’dko7eo;oD

8q;1kj ’G XX&$ V @ ? _ X!@ T )? ' &? V @

1444442444443 1444442444443

X!W) _ @W ' &? V @

1444442444443

X!W) _ $? V @
1 4 4 4 44 2 4 4 4 44 3

!W$ V @ = @W)

III. [qfg/ydsaf ສະຫງສ.ວວນ.ລິສຂະສິດ

!D 9q’j 7yfw]jg]d]5j,oU
dD XX&$W T *W? _ X*(W _ &@W?? V *
0D X_$W ' $? T X$&@ _ #W@? V $
7D X*_@ _ !$@? ' & T X#!$ V @? ' $
’D X(&$ _ @$$? T X!#& V $? ' &
9D X#$! V #? _ X*$@ ' #? T X@*@ T #)?

@D mhk; ]u vkj oxB,oymkosq;mu ! wfh $ |hk8+,N ]k;.-hg;]kma’\qf !@ ,NF sq;mu
@ vkj owfh * |hk8+,N ]k;.-hg;]kma’\qf !W ,ND 4k,;kj ]k;vjkooymkoma’\qf
9ad|hkL

#D ,Nmevyf ok’lul5rao 8ej czjowfh !$F& m, ,Nmulv’8jewfh !WF@& m, ,Nmulk,8ej wfh
!&F@& m, ,Nmuluj8ej wfh @ gmvjn 0v’,mN lu v’D ]k;wf7h kj cI’’koc,fa ]t !@WW du[D
4k,;jkrkp.oluj,N]k;9twfh7jkcI’’koma’\qfgmqjk.fL

29

rkdmu # g]0k7toyf

I. dyf9tde [qf mu _ dkog]nvdv5xtdvo

!D 9q’j 7yfw]jzqo[;d]5j,oUD

#& cm T ($ mm = D D D D mm S _WFW! dm T WFW! cm = D D D D cm S
! km T &WW m = D D D D km S @ hm T #W dm = D D D D hm S
WF#& km T WF$ hm = D D D D m S ! km T # hm = D D D D dm D

@D 9qj’[vd-n0j v’v5xtdvoc8]j tvao8+wxoU G

dD 0 5 10 20 30 40 50 60 70 80 90 0D 7D

0 5 10 20

9D -D ສະຫງສ.ວວນ.ລິສຂະສິດ
CD lD

#D 9t.-hv5xtdvovao.fgrnvj .shg\ktlq,.odko;afcmdly’j 0v’]5j,oUG

B

A dD mvj o-nj C 0D 0Aowf

c[[IPo c[[IPo
-Aoxt4q,lbdlk

7toyflkf 3

7toyflkf dd ! @ # $ & * ( )

10 20 30 40 50 60 70 80 90 100110 120

0 1 2 3 4 5 6 7 8 9 10 11 12 13

7D ;q’,qo ry,mu3I’ry,lbdlk -Aoxt4q,lbdlk xumu # dt-;’lbdlkmydko shk,0kp
8k, ]m[ 0v’dt-;’lbdlk lt4k[ao7Qo7;hk;ymtpklkfdkolbdlk
II. .97;k, 9eo;ory, ! WWW WWW sq;
@WW_
0t\kf !) V @& -,
lts’;o]y0tlyf

CD xB,c[[IPo 9D shv’gInvo

dkog]nvdv5xtdvo;afcmd7;og]nvd.shg\ktlq,da[;Pdmu8j hv’dko;afcmd

g-ajoG [aomafG .-hle]a[;afcmd];’pk; ! c,af]q’,kg-aoj ];’pk;0v’l=feF

xB,0PoD

30

w,hc,afG ,u];’pk; ! c,af .-hle]a[;afcmd];’pk; ! c,af 0Bowxg-aoj
];’l6’0v’/kshv’IPoF ];’pk;0v’w,hcxI6[F D D D

c,afd=hG ,u];’pk; #{& c,af .-hle]a[;afcmd];’pk;0v’;af45dq’j c]t -nj
muj7hkp7ndaoda[.-hw,hc,afD

c,afzhkG { mju,u];’pk;c8j !W c,af 0Bowxg4y’ &W c,af lj;os^kp.-h;af
cmd];’d;hk’0v’l;oF wIjF okF ];’pk;0v’glAomk’ c]t vnoj MD

{ mju,u];’pk; !F&W c,af .-hle]a[.odko8afspy[D
[aomaflkdG .-hle]a[;afcmd,5,lkdF gxaov5xtdvorNo4ko.odkoc8h,I6[

g]0k7toyf.o|hkrP’g-oaj lhk’I6[lk,c9F I[6 lcju 9F mvj o-8nj A’lkddaoD
g9hp8kdk3iG .-hle]a[c8h,I6[F 0tspkpF sp=hI6[ s^n c8h,I6[7noD

III. [qfg/ydsaf

!D 9q’j c8h,I6[]5j,oU7noD

dD 0D
ສະຫງສ.ວວນ.ລິສຂະສິດ
@D 9qj’;afcmd c]t [aombd.lj8k8t]k’D

]kpdko;afcmd v5xtdvomuj.-h.o 7jk;afcmd
dko;afcmd
];’Iv[0v’cv;8qogv’
];’pk;0v’dtfko
];’l6’0v’0k38t
];’dh;k’0v’xN,0Po
];’d;hk’ s^n ];’pk;0v’shv’IPo

#D 9qj’;afcmd];’pk;0v’0hk’ s^n c8j]tl;j o0v’I6[]j5,oUD

Xd? X0? X7?

31

[qf mu !W dkogg8h,I6[7no

I. dyf9tde
!D 9qj’xP[mP[9eo;o]5,j oU3fpoe.-hg7nvj ’\kp = S < s^n >
dD !&W cm . . . . !F& cm ’D ( . . . . )
!@ mm !@ mm

0D &$ dm . . . . WF) dm 9D _W dam. . . . _ m

7F !F) cm . . . . @F& cm. . . . lD !WWW m. . . . ! km

@D 9qj’]vdc[[I6[]5j,oUD

ສະຫງສ.ວວນ.ລິສຂະສິດ

#D 9q’j c8h,I6[]5,j oU7noD

dD 0D 7D

II. .97;k,

grnjv1kdc8h,I6[7no.sh7nda[I6[mu.j shdjvo c]t grnvj g]nvdv5xtdvomujg\ktlq,
gIqk8hv’I6h;jkI6[muj.shdvj ooAo,u95fryglfspa’cfLj
8q;1jk’G I6[0hk’oUxtdv[fh;p
• I6[9t85]afg-yj’,u $ 0hk’gmqjkdao c]t gmqkj @ cm ,u $ ,5,lkdD

32

ສະຫງສ.ວວນ.ລິສຂະສິດ• g7y’j I6[;q’,qomuj,uglAozjkdk’gmqkj da[0hk’0v’I6[9t85]afD
ltoAoF grnvj c8h,I6[faj’dkj ;7nogIqk8hv’.-h[aomafF [aomaflkd c]t ;q’;PoD

III. [qfg/ydsaf

!D 9q’j ]vdc[[I6[]5j,oUD

@D 9q’j c8h,I6[]5j,oU7noD

Xd? X0? X7?
#D 9q’j la’gdfI6[]5j,oU c]h;ry9t]tokg[yj’;kj gIqk9tlk,kfc8h,7nowfh[+L

4
3
2
1

$D ok’ ok]u c]t mhk; g1h c0’j daomklu.ljI6[\kd,;j ’F r=\qfg];kma’lv’mklu
c]h; !( I6[F ok’ ok]u mkluwfhs^kpd;kj mhk; g1h # I6[D 4k,;kj c8]j t7qomk
luwfhz6h]t9adI6[L

33

[qf mu !! I6[s^kpc9

I. dyf9tde

9qj’la’gdfI6[]5,j oU c]h;0Po a, b, c, d, e, f, g, h, i, j, k, .l[j voj 9Eg,afD

ab c d

e f. g h

ij k

I6[mju,u # 0hk’7nI6[ D D D c , g , D D D D D DD D D D DD D D D D D D D D D D D D D D D D ສະຫງສ.ວວນ.ລິສຂະສິດ
I6[muj,u $ 0hk’7nI6[ D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D
I6[mju,u & 0hk’7nI6[ D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D
I6[muj,u * 0hk’7nI6[ D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D

IID .97;k,

[aofkI6[g]0k7toyf.o|hkrP’muxj tdv[fh;p0hk’1kj ’|hvplk,0hk’0Bowx
gvUo;jkG I6[s^kpc9D
8q;1jk’G I6[lk,c9 X,ulk,0hk’?F I6[lucj 9 X,uluj0hk’? c]t vnoj MD
I6[s^kpc9];,,uI6[s^kpc9mqj;wx c]t I6[s^kpc9ltg\uD
!D I6[s^kpc9mqj;wx

I6[s^kpc9l;f I6[s^kpc9;EX3do? I6[s^kpc9w0;j

34

@D I6[s^kpc9ltg\uD

I6[lk,c9ltg\u I6[lucj 9ltg\u X9t85]af? I6[sqdc9ltg\u

III. [qfg/ydsaf .l[j jvo9Eg,afD d

!D 9q’j 0Po a, b, c, d, e, f, g, h, i, j, k, c

a b

e f g h

i j k

I6[mu,j u $ 0hk’7nI6[ D D D . . . . D D D D D D D D D D D DD D D D D D D D D D D D D D D D D D ສະຫງສ.ວວນ.ລິສຂະສິດ
I6[muj,u & 0hk’7nI6[ D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D
I6[mu,j u * 0hk’7nI6[ D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D
I6[mu,j u ) 0hk’7nI6[ D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D

@D 9qj’8n,j 8q;g]d\kp0v’c8]j tI6[]q’.o8k8t]k’ .shdq’da[-nj0v’I6[grnjv
[vd;jk[aofk8q;g]dgs^qjkoAoc,jo8q;g]d0v’I6[xtgrffP;daoD

3 11 22
23
4 12 18
25 9 10 13 16 19 24
20
1 15 21
14
17
67 8

xtgrfI6[ 8q;g]d\kp0v’I6[

I6[lk,c9
I6[lujc9

35

[qf mu !@ I6[lucj 9

I. dyf9tde

9q’j 9ecod[aofkI6[]5j,oU8k,75o]adltot0v’0hk’c]h;0Po.l[j jvo9Eg,afD

(1) (2) (3) (4)

I6[X!? ,uluj0hk’ D D D D D D D D D D D D D D D D D D c]t lv’0hk’g-yj’|hk0t|kodaoD
I6[X@? ,ulv’0hk’g-y’j |hk D D D D D D D D D D D D D D D c]t D D D D D D D D D D D D D D D
I6[X#? ,ulv’0hk’ D D D D D D D D D D D D D D D D D D D D D D D
I6[X$? ,ulv’0hk’g-y’j |hk D D D D D D D D D D D D D D D D c]t D D D D D D D D D D D D D D D

IID .97;k, I6[7k’\6,ulv’ສະຫງສ.ວວນ.ລິສຂະສິດ
0hk’0t|koD
I6[s^kpc9muj,uluj0hk’9vfdaogvUo;jkI6[ lucj 9D

8q;1kj ’G

I6[9t85]af,uluj0hk’gmqkj dao

c]t ,ulu,j 5,lkdD

I6[lucj 9lkd,ulv’0hk’g-yj’ I6[fvd9ao,ulu0j hk’
|hkgmqkj dao c]t 0t|ko gmqkj daoD
daoF ,uluj,5,lkdD

I6[lujc90hk’0t|ko,ulv’
0hk’g-yj’|hkgmqkj dao c]t
0t|kodaoD

III. [qfg/ydsaf

!D 9q’j la’gdfI6[]j5,oU c]h;\kp.l8j k8t]k’.sh4nd8k,]adltotmujdeoqfw;hG

dD 0D 7D CD 9D

36

d07C9

lv’glAogoa’j 9v,gmqjkdao c]t 8A’lkddaoD
lv’0hk’0t|kodao c]t [+gmqkj daoF lv’glAogoa’j
9v,[+8A’lkddaoD

luj,5,lkdD
lv’glAogoa’j 9v,8A’lkddao c]t lju0hk’gmqkj daoD
lv’0hk’g-y’j |hk0t|kodao c]t gmqjkdaoF glAogoaj’
9v,8afdao169j 5fg7yj’dk’0v’c8]j tglAoD

@D 9q’j lhk’7noI6[lucj 9 ABCD 4hkI6h0hk’ D
0v’,aogmqkj 2cm, 3cm, 4cm, 5cm
c]t glAogoaj’9v, BD gmqkj 5cm faj’I6[. 4 cm

5 cm 5 cm C

ສະ3cຫງmສ.ວວນ.ລິສຂະສິດ
2 cm
B
A

#D 9qj’la’gdfI6[]j5,oU c]h;8nj,7eg;Qkmjug\ktlq,.l[j jvo9Eg,afD
X!? X@? X#? X$? X&?

dD I6[mu,j u0hk’gmqjkdao c]t luj,5,gmqjkdaoc,joI6[ D D D D D
0D I6[muj,ulv’0hk’0t|kodaoc8pj k;[+gmqkj daoc,joI6[D D D D D
7D I6[mu,j ulu0j hk’gmqkj dao c]t lv’,5,g-y’j |hkgmqjkdaoc,oj I6[ D D D D D
’D I6[muj,ulv’0hk’g-yj’|hk0t|kodaoF pk;gmqjkdao c]t ,ulu,j 5,lkdc,joI6[D D
9D I6[mu,j ulv’0hk’g-yj’|hk0t|kodao c]t pk;gmqkj daoc,joI6[ D D D D D


37

[qf mu !# I6[lucj 9lkd{I6[9t85]af

I. dyf9tde

!D ,uI6[.fcfmj uj,ulv’0hk’g-yj’|hkdaogmqkj dao c]t 0t|kodao8k,c8]j t7j6
c]t ,ulu,j 5,lkdD

a d f
g
b h
c e

@D 9qj’.-hg9hpmujgxaoI6[lucj 9lkdD 9kdohao A ສະຫງສ.ວວນ.ລິສຂະສິດ

.shra[faj’I6[fhko0hk’ c]h;8aflj;omjugs^nv l;j omujgs^nv
vvd g,nvj gIqkc[vvd9tgsaoglAospa’cfLj

c]t 9twfhI6[spa’cfLj B Aj

II. .97;k,

!D I6[lujc9lkd ABCD c,oj I6[lujc9muj,uG

{ lv’0hk’g-y’j |hkdaogmqjkdao (AB = DC, AD= BC).

{ lv’0hk’g-yj’|hk0t|kodao (AB) // (DC), (AD) // (BC).

{ lv’glAogoa’j 9v,gmqjkdao (AC = BD).

{ lv’glAogoaj’9v,8afdao16jg,afg7yj’dk’ O 0v’c8]j t

glAo (OA=OC,OD=OB). DC
{ ,5,ma’lujgxao,5,lkdD O

AB

38

@D I6[9t85]af MNPQ c,oj I6[lujc9mu,j u G { lu0j hk’gmqkj dao MN = NP = PQ = MQ.

Q p { lv’0hk’g-y’j |hk0t|kodao(MN)//(PQ), (MQ)//(NP).

H { lv’glAogoa’j 9v,gmqjkdao MP = NQ.
{ lv’glAogoaj’9v,8afdao c]t 8A’lkddao16jg,afg7y’j

dk’ H 0v’c8j]tglaho(MP) (NQ), HM=HP=HN=HQ.
N { ,5,ma’lugj xao,5,lkdD
M

III. [qfg/ydsaf

!D 9q’j [vd;kj .oI6[]5j,oU,uI6[9t85]af9adI6[ c]t I6[lujc9lkd9adI6[L

@D dkoc8h,I6[9t85]af c]t I6[lujc9lkdD ສະຫງສ.ວວນ.ລິສຂະສິດ
dD 9qj’c8h,7noI6[lucj 9lkd c]t I6[9t85]af]5j,oU3fp.-hg9hp8kdk3iD

0D 9q’j c8h,7noI6[lucj 9lkd c]t I6[9t85]af]5j,oU3fp[+.-hg9hp8kdk3iD

#D 9qj’c8h,I6[mu,j u0hk’gmqjkda[ $ cm .sh7nI6[]5j,oUG

39

[qf mu !$ I6[lk,c9

I. dyf9tde

!D I6[.fhgxaoI6[lk,c9D

X!? X@? X#? X$? X&?

X*? X(? X)? X_?

@D 9q’j .-hfY;w,hmju,u];’pk; #cm, $cm, &cm c]t *cm, -toyf]t # fY;,k

xtdv[.shgxaoI6[lk,c9 9twfhI6[lk,9t-toyf.fcfjL 3 cm ສະຫງສ.ວວນ.ລິສຂະສິດ
4 cm
dD 4hkoe.-hc8fj Y;w,hxtgrffP;daoD 5 cm
0D 4hkoe.-hc8fj Y;w,hlv’xtgrf8kj ’daoD 6 cm
7D 4hk.-hc8jfY;w,h # xtgrf.olujD

#D 9qj’;afcmd];’pk;0v’0hk’ c8]j tI6[c]h;8n,j .l8j k8t]k’.sh7q[4h;oD

B BA B B B

(1) (2) (3) (4) (5)

A CA C CA CA C

I6[mu ];’pk;0v’0hk’ Xcm? -nj0v’I6[lk,c9

AB BC CA

1
2
3
4
5

40

II. .97;k,

I6[s^kpc9mju,ulk,0hk’gvUo;kj I6[lk,c9D

I6[lk,c9ltg\u I6[lk,c9mPj ’ I6[lk,c9mq;j I6[lk,c9lkd I6[lk,c9lkd

,ulk,0hk’ ,ulv’0hk’ wx[+,u0hk’.f ,u,5,|b’j gxao mPj ’,ulv’0hk’

gmqjkdao gmqjkdao gmqjkdao ,5,lkd gmqkj daoc]tlv’

0hk’oAoxtdv[
gxao,5,lkd
III. [qfg/ydsaf

!D 9qj’lhk’lk,c9ltg\uF I6[lk,c9mjP’F I6[lk,c9mqj;wxF I6[lk,c9lkdF

I6[lk,c9lkdmPj ’D ສະຫງສ.ວວນ.ລິສຂະສິດ

@D dD 9qj’[vd-nj0v’I6[lk,c9]j5,oUG
B B AB
B

X!? A X@? A X#? CC X$?
C
CC C

A X&? B
A B A X*?
0D 9q’j cmd7;k,pk;0v’c8Ij 6[gmu’oUc]h;0Po.lj8k8t]k’

I6[mu ];’pk;0v’0hk’ Xcm? ];’Iv[0v’
I6[ Xcm?
AB BC CA
2+3+3=8
!@ # #
@
#
$
&
*

41

[qf mu !& dkolhk’I6[

I. dyf9tde

!D 9q’j lhk’I6[lucj 9lkdg,nvj I6h];’pk; 4 cm c]t ];’d;hk’ 2 cm

4 cm 2 cm

@D 9q’j lhk’I6[9t85]af ABCD I6h;kj G glAogoaj’9v,

AC = BD = 3cm

3cm

#D 9q’j lhk’I6[lk,c9ltg\u ABC, I6h;kj 0hk’

A B = BC = AC = 4,5 cm

4,5 cm ສະຫງສ.ວວນ.ລິສຂະສິດ

$D 9q’j lhk’I6[fvd9ao MNPQ, I6h;jkglAogoaj’9v,

MP = 5 cm NQ = 3 cm

3 cm 5 cm

II. .97;k,

dkolhk’I6[g]0k7toyf.o|hkrP’ gIqk8hv’vu’.lj75o]adltotrNo4komuj9e

gxao0v’I6[oAoD

8q;1jk’ !G lhk’I6[lucj 90hk’0t|ko ABCD g,njvIh6;jk0hk’|b’j pk; 2 cm

vud0hk’|bj’pk; 4 cm c]t ,uglAogoaj’9v,glAo|b’j 0v’,aogmqjk 5 cm.

;ymulhk’G
{ lhk’I6[lk,c9 ABC mu,u0hk’ AB = 4 cm, BC = 2 cm, AC = 5cm
3fpvu’8k,dkolhk’I6[lk,c9g,nvj I6hlk,0hk’D
{ zjkog,af A lhk’glAo-nj0t|koda[ BC.

42

DA { zjkog,af C lhk’glao-nj0t|koda[ AB.

5 4 { lv’glAo-nfj a’j dkj ;9t8afdao1j6g,af D c]h;

C 2 B 9twfhI6[lucj 90hk’0t|ko ABCD.

8q;1kj ’ @G lhk’I6[fvd9ao ABCD g,nvj I6hlv’glAogoaj’9v,,aopk; # cm

c]t & cm.

;ymulhk’G { lhk’mvj o-nj AC = 5 cm, 9kdoAo oe.-h;umuc[j’mjvo-nvj vd

gxaolv’lj;ogmqjkdaoF lhk’ BD = 3 cm 8A’lkdda[ AC 1j6g,af

g7yj’dk’0v’c8j]tglAo XI6[ dD? D

D

A CA C

XI6[ d? B B XI6[ 0?ສະຫງສ.ວວນ.ລິສຂະສິດ

{ 9kdoAo8+g,af A .lj B, B .lj C , C .lj D c]t D .lj A d=9twfhI6[fvd9ao

ABCD mu,j uglAogoa’j 9v, AC = 5 cm c]t BD = 3 cm I6[X0?D

III. [qfg/ydsaf

!D 9q’j lhk’I6[lujc9lkd ABCD mu,j u];’pk; c]t ];’d;hk’gmqjkda[

dD 3,5 cm ; 1,5 cm ; 0D 4 cm; 2 cm.

@D 9qj’lhk’I6[9t85]afF 4hk;jkglAogoa’j 9v,0v’,aogmqkj da[

dD 2,8 cm ; 0D 4,4 cm ; 7D 3 cm.

#D 9qj’lhk’I6[fvd9ao g,nvj lv’glAogoaj’9v,0v’,aogmqjkda[

dD 2 cm ; 3 cm ; 0D 1,4 cm ; 4,6 cm.

$D 9qj’lhk’I6[lk,c9]5j,oU

dD I6[lk,c9ltg\u ABC I6h;jk0hk’ AB = BC = AC = 6,5 cm.

0D I6[lk,c9mPj ’ ABC I6h;jk0hk’ AC = AB = 6 cm c]t BC = 4 cm.

43

rkdmu $ dko7eo;o

[qf mu !* dkosko0kf

I. dyf9tde
!D 9q’j skog]d8+wxoU c]h;0Pozqosko c]t 8q;glf.lj[vj o9Eg,afD
8q;1jk’G _!!@@ * zqoskoc,jo @
WW @ 8q;glfc,jo W

dD ) $ zqoskoc,joDDDDDDDD lD @& & zqoskoc,joDDDDDDDD
8q;glfc,joDDDDDDDDDD 8q;glfc,oj DDDDDDDDDD

0D ( # zqoskoc,oj DDDDDDDD -D #* _ zqoskoc,joDDDDDDDD
8q;glfc,oj DDDDDDDDDD 8q;glfc,joDDDDDDDDDD

7D !& & zqoskoc,oj DDDDDDDD pD $@ ) zqoskoc,oj DDDDDDDD
8q;glfc,joDDDDDDDDDD 8q;glfc,joDDDDDDDDDD
ສະຫງສ.ວວນ.ລິສຂະສິດ
CD @$ ( zqoskoc,joDDDDDDDD fD $& ( zqoskoc,oj DDDDDDDD
8q;glfc,oj DDDDDDDDDD 8q;glfc,oj DDDDDDDDDD

9D @) ) zqoskoc,oj DDDDDDDD 8D *W !@ zqoskoc,oj DDDDDDDD
8q;glfc,joDDDDDDDDDD 8q;glfc,oj DDDDDDDDDD

@D 9q’j 0Po9eo;o]5j,oUmulj k,kfsko0kf.sh ! c]t 8q;,aogv’gmqkj oAo.l[j jvo
9Eg,afD
!F @F #F $F &F *F (F )F _F !WF !!F !@F !#F !$F !&F !*F !(F !)F !_F c]t @W
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

II. .97;k,
!D dkosko0kfD
dkosko0kf8hv’,uzqoskogxao9eo;o4h;o c]t 8q;glfgmqjkl6o XW?
8q;1jk’G _##** $
WW _ zqoskoc,oj _
8q;glfc,jo W

44

@D 9eo;omusj ko0kf.sh ! c]t 8q;,aogv’gmqjkoAogvUo;kj 9eo;o,6o
8q;1kj ’G @ F # F & F ( F !! F !# F !( F !_D DDDD

III. [qfg/ydsaf

!D 9qj’la’gdf
!#! ' ) = X)W T $W T !!? ' )
= X)W ' )? T X$W ' )? T X!! ' )?

1 4 4 4 44 2 4 4 4 44 3

sko.sh0kf )

8q;glf0v’dkosko !#! ' ) c,jovaofP;daoda[ !! ' ) g-y’j c,oj #
9q’j xt8y[af7n0hk’gmy’grnjv-vdsk8q;glf0v’dkosko8+wxoUG
dD !@$ ' # = D D D D 7D !W@ ' _ = D D D D
(_ ' # = D D D D _&W ' _ = D D D D
#*$ ' # = D D D D !W&! ' _ = D D D Dສະຫງສ.ວວນ.ລິສຂະສິດ
0D &*) ' & = D D D D ’D )) ' !@ = D D D D
!*&! ' & = D D D D !$( ' !@ = D D D D
&W** ' & = D D D D !##W ' !@ = D D D D

@D 9q’j .-h8q;g]d &S $ c]t # grnjvxtdv[gxaoD
lv’9eo;omujsko0kf.sh @
lv’9eo;omusj ko0kf.sh #
lv’9eo;omjusko0kf.sh &

#D 9q’j 0Po9eo;o,6o.lj[jvo9Eg,af.o9eo;o]5j,oUD
$ F ( F !W F !# F !* F !_ F @@ F @& F @) F #! F #$ F #( F $W F $# F $*D
9eo;o,6o,u D D D D D D D D D D D D D D D D D D D D

$D 9q’j 0Po9eo;o,6oma’\qfmuj16j]ts;jk’ $W { *W .l[j jvo9Eg,afD
9eo;o,6o,u D D D D D D D D D D D D D D D D D D D D

45

[qf mu !( mt;u76o c]t v5xt76o0v’|b’j 9eo;o

I. dyf9tde

!D 9qj’0Po < 4nd < s^n < zyf < .l[j vj o9Eg,af.oc8j]txt3spd]5,j oUD
DDDDDDDDDDDD zqo[;d0v’8q;g]d9eo;o|bj’sko0kf.sh # 9tc,oj mt;u76o0v’ #D
DDDDDDDDDDDD m5d9eo;omujsko0kf.sh @ 9tsko0kf.sh $D
DDDDDDDDDDDD m5d9eo;omjusko0kf.sh $ 9tsko0kf.sh @D
DDDDDDDDDDDD 9eo;omu]j q’mhkpfh;p $ 9tsko0kf.sh &D
DDDDDDDDDDDD 9eo;omujsko0kf.sh !W 9tsko0kf.sh @ c]t .sh &D

@D 9q’j 0ufvhv,gvqk9eo;omujsko0kf.sh @ c]t .sh $ rhv,daoD
) S !W S !@ S !$ S !* S !) S @W S @@ S @$ S @*D

II. .97;k, ສະຫງສ.ວວນ.ລິສຂະສິດ
dD mt;u76o c]t v5xt76oD
@ V !)= #*
8q;1jk’G 9eo;o #* c,jomt;u76o0v’ @ # V !@= #*
9eo;o #* c,jomt;u76o0v’ #
9eo;o #* c,oj mt;u76o0v’ $ $ V _ = #*
9eo;o #* c,jomt;u76o0v’ * * V * = #*
9eo;o #* d=pa’c,jomt;u76o0v’ ! F _ F !@ F !) c]t #*
9eo;o ! F @ F # F $ F * F _ F !) F #* c,jov5xt76o0v’ #* gIqkg;Qkwfh;kj #*

sko0kf.sh ! F @ F # F $ F * F _ F !@ F !) F #*D

0D 9eo;o4h;omju,u8q;g]d76j XWF @F $F *F )? 1j6mhkp]h;oc8cj ,oj mt;u76o

0v’ @ s^n ]h;oc8sj ko0kf.sh @D

7D m5d9eo;o4h;omuj]q’mhkpfh;p W sn^ & c,oj mt;u76o0v’ & s^n sko0kf.sh &D

'D grnvj 1kdI6h9eo;omujsko0kf.sh # s^n _ gryjo[;d8q;g]d0v’9eo;ooAoD 4hk

zqo[;dgmqkj da[ #S * s^n _ 9eo;ooAo 9tsko0kf.sh #D 4hkzqo[;dgmqjkda[ _

d=sko0kf.sh _D

46

8q;1kj ’G { 9eo;o #$& sko0kf.sh # phvo;jkG
zqo[;d # T $ T & = !@ c]t ! T @ = #
{ 9eo;o #$@ sko0kf.sh _ phvo;kj G
zqo[;d # T $ T @ = _
III. [qfg/ydsaf
!D 9q’j 0Po9eo;omujsko0kf.sh # c]t .sh & rhv,dao.o9eo;o]5,j oUD
@! S #& S $& S &! S (& S _& S !#& S @@& S $*& S &@!D
@D 9qj’8n,j 8q;g]d.lj[vj o,u9Egrnjv.sh9eo;o8+wxoU
dD sko0kf.sh @
@D&D S D $) D
D D *$ S (W$ S
D D0D sko0kf.sh #
*$# D S ) D @$ S D D # D
$@ S )W S
7D sko0kf.sh @ c]t .sh #
D D @D ສະຫງສ.ວວນ.ລິສຂະສິດ
D D D D *$ S ) # S @$ S

#D 9qj’8nj,8q;g]d.l[j vj o,u9E g,njvsko.sh & 9t,u8q;glffa’j ]5j,oU
dD 8q;glfc,jo ! 7D 8q;glfc,jo #
D D DD D D D D D $# S !@$ S (# )@& S $ # S ! #
0D 8q;glfc,jo @ ’D 8q;glfc,jo $
D D D D D D D @$* S !W@! S (* S @$ S (# S @$

$D 9qj’9af9eo;o8+wxoU.lIj 6[mu1j 6j0hk’]5j,
!($_ S #@&W S ()_# S @W@& S !#)& S @WW! S !!@ S

!W@ S $& S @W#W S _#W S @$& S (&W S !*W& D

mt;u76o0v’ & mt;u76o0v’ @

mt;u76o0v’ #

47