គីមីវិទ្យាថ្នាក់ទី៨ summary of chemistry grade 12

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&9

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21 = s

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tiSStuS91S&tjbl5ffiSfll?ltti~HtuSl::l IJ

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-3

,

10, 100 ... Hltiffll::lt

= -0.03

usu s tus 91 s ftj ruffi sm ?J run sl::lm ?J&'ul::l •

!JfnifliM :

4

3=

-

L3

1

-

3 = 0.3

'1

'1


: 2 = 2! 3

3 '

-13 =

l

<j

t2 gu~ 2 n5S&ll2ffitn:fl2 91JB

-2 3 '

0

u28 -3

0

1.!

0.5

4

3

' 8 ' 5

6 '

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3

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1 : nbutnm'1§u22 "'l

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= 8= = 2= 6

tf:ifUHfUS lO

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&ll22ltit'lffl'i§ l...i

1.!

-7

3.5 '

-14

'

'

21

6

-3.5 '

'i

. I

=

-7

2 = -14 = -3.5 0

<j

3 ""~

'

0

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: nMfi' x tw'!§J~u~2n52&ll2 : tr:iH15 7! =

2

15 tSlg 45 X

=

45

x

t

_!2 2

15x = 2 x45 X =

2

X

45

=

2X 3

=

6 'i

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-2

t'lffl'i§thlfil- ' l...i

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y

5- '

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nur]tntsJuu : ussn5s&lls -5 5udlbus2n5S&lls -I mbn:tH15 -5 <-I &'imgG@S 1.1

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7

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!;tlQl s 28

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!;i:tHl5 36 > 28 54

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n. ~ , o.3 4

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3 0.3 = 10

120 ~ - 160 3

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36

03 = 3 .

25 30 5 -0. 25 = -100 = -120 ' 4

5 4 -0.25 < 0.3 < 4 < 3 '1 1

1

7

3 ' 3 '

5

-9

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12

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n.

2. l

3

3

tl.

-

30 120


2.3.

rngn.n:

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5 ' 7

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HHuH

u

-15 ' 20 "'

Gcf!w: ""

n.

-~ 3 = ~~

=

g 6 x 13

x

3)

= 78 9UH!iti~t§Jtifi -

6

u

2. -25 = (-5) X 5 = ~ g'it§~ti'ii:lt§~jjfi ~ -35 (-5)x7 7 Li Liu u 7 5 = ~ ''img 36 X 20 = j;1 -l 5) X . 36 -48 Li

= 720

1vflvff : tirm fim j;111 &scrsu s n1s 9ls:nh tHilt§t Nm uH3 MH n csl:.

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5

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10

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= 35 + 79 lO

~+~

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7 7

5

b

10

= 35

+ 79 =

= a+c "'

b

2 -3 + 5

. 8

til -3 + 4 'I

5


.. - 3 -5 n.

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3-5

7+7 =

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8

5

+ -8

=

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=

+

-2

-5

=

- 3- 5

=

-8

=

-l

z+-7 = 7-7 = 2 = 0

~·· 8

8

= -3 + -4 = -21-20

lli. -3 + 4

=

-41 '1

?i. 437.56 + 127.95 '1

. fi (-3~)

.

5

"' (-1) d. 4

+(3!1 = -18 + 19

4)

+ ?+z = 6

3

1!1. 437.56 + 127.95

fi.

5

=

-72 +95

- 3 + 10 + 28 = 35

=

565.51 '1

(-21) +(-~}

c S ""~ e " "" tl!i'i:.fiS ab' d f thti~Srs.HHflS '1

tjnmn ~+~+~ thusatus9la b

II

2. ~ + ~ 3.

=

d

j

lJ

~ + ~ ( ruQ nn :1Ji9Jli)

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6

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...

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n"(~+!I+~= ~+(2+~) 63)3 6 33

0

(runnn:a) s 1"1 1

= ~ +(7 +5\ = ~ +4 = 5+24 6

3 -)

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"63)

133-72

!!i (~ +~1 +(17 +2)

8J

. 7

7

63)

=

8

-7

29

"l

5+14_12

=

6

=

6

19_ 2 6

61 "l

=

42 = (~ +-5\ +(~ + 17) = 0+20 7 i) 8 8 8

=

~

2

"l

tLf'il'tHf:::IHll 'Llirug nn:~ 1

(~+D +C4~

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9-7

10

=

2

7 10

"l

2•

l

5

= l0 =

2 ~-Z = 1o-1 = ~

. 4

8

8

8

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tJmni :~-~ b b

=

~ b

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n.

=

3 7 5-10

2.

n 9

2

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"l

tJtiw: ""

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2

2 " 12-3 =

9

8

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=

l

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6

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5 7

4-8

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sna ?

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li

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2

4

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2

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4

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3 1--

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5+8+2

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m m tel fil h H n tHU n~ li <a II 1.1 li

~h~n1 ~

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= 20

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=

4-3

1

=-

4

'1

: telMsnt:Hu~nn ~x3.8 ~ 38 8X •

=~

38 8 X 10

=

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: telMsnjjru~nn (-~)

(-~)(-2) 3 15

7

= (-2)(-7) = 14 '1 3 X IS

n. o.25 x 48

2. 245.4 x 5.3

tel. (-3.2)(7.4)(-0.l )(-0.5)

m. (-4)(-~)(~(D

. n. 0.25 X 48 = 2. 245.4 X 5.3

2 ; X 48 = 10 2454

~X 48 =

X~~ =

=

tel. (-3.2)(7.4)(-0.1)(-0.5)

130062

12 =

1300.62

= [(-3.2)(-0.5)]

l)]

= (1.6)(-0.74) = -1.184

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=

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=

(-2)(-D

=

l 'i

'i


c

'

MmflJ:

1~5

n.

0.75 x

1.

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,

= ac

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d b

e

3.

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4.

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5 4

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9


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~

3 3 . --+25 10 '1

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. 5

2.

5

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5

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2130 =

,... 24 6 n. -25 +

3

23

28 -4 2. 27 +

. -

24

n. -25 +

6

24

.., 28 + -4 = 28

X

15

12

4X3

x6

=

51 = 7 X 17 =

119

"'· 27

f:l. -18 + -6

-18 X 25 = 3 X 5 = 15 '1

=

40

2.

+

-10

fi. 154.63 + 4.7 'l

n. snnsgu'h:n1r;tsmHnHU1 "" u l

tSl:: '1

2. d~hdh'i:Hi5tStiribfilrultntHMSh 3.26cm ~

ul

r:1.

l.l

l

...

t1h~hiiiru&gJr; '1 l

f:lMsnt~trl[ltSti~tmnnfnh '1 xcm

3.26cm p = 16.38+2 = 8.l9cm '1

~. ~n'G5t~h~h~ru I

r;


m~ x dlTI5t~~ttl~'\fiD&&lJ 1

x+ 3.26 = p X+ 3.26 = 8.19

al~

x = 8.19-3.26 = 4.93cm

~crtsg ~~'\1IDt9Jntf:lcr~tff1Mtni:!1:f!SLli

4.93cm '1

1 '>

"'

?1. ?JMS"J~~tn!{JHSu~tmM

ffl~ Sdl~~(.!11{JltSu~&Alrultn~ tmgt?JLil2

S = 3.26x4.93 = l6.0718cm

[:jutS& tsn&AlMtn~ffiS:t~'in!m 16.071 II 1 .:; 1..:: iJ'

2

'1

-5 ?

-5

n.

(?.xl0)+4+(2xOJ)+

?1. (8x1000)+(2x

+

-5 '1

~.

xO.Ol)

(4x

+ 4 + (2 X 0.01) +

lli. (7x

xO.OOl)

+

x

X

0.000!)

+4+(2x0.1)+

i:!. 5(100) + 4( 10) + s + 6C/o) + 9C~o) + 3Coloo) '1 3.

MHM~cr~s~i:ittffl't§dlLliin?'i

n.

28.45

?1. l 19

9. 1.378

i:!. 0.347 '1

lli.

4. lli. 5.

17

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t n tHHHl.HHJl S

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.,o "" tntiS!HuS9lS 1.1

1.1

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Jo NL1:j ru 1.1

n. (-~) + (2~)

m.

~.

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G;)

2. (-3~) -(-2~)

l=i.

+ (-2~)

ti . (!+!)+(~-!) 2 3 8 4

3~- 25 5 8 ti. -7 4 -+512 9

3 25 + 2~ 8 8 + 2 '1

2~-(-~

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1D

n. -~5 . (!.! . 1~ 17 1 lli.

11.21+17.~1

22

16 22

um mm 13 + 13 IJl ......,

13. 14.

tictl~rh ""

tl (- !.! + 1~ . 26

ti. - 11 + 21 - 17

ti

. .

13

1

22

(-!.!).~+(-3)·(-!.!) 21 7 7 21

'1

13 x 13 '1

=

tU ~<:: b

2• - (11 13' 16 . 26 51

d

tSlll ~ b

mnti~ti~tsllti~Q)

e

~ d

e '1

trultiton'fsu.nfiLumt2

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Rrul~fiHTTlrulSbSliH3EliDhl

a

~

M

1.

M

~ru~rul 5 2

9

3

8

2

sb

10 000 = 10 X lOX 10 X lO

(~r HlS~132lb

52 Hlsm 5 fiJru?Jnn 2 us nm 4

l

"'-

ID

"' t?lnHltHuHfdH~


axaxax ... xa

!S1:£fi(}]S

'l

=

~-~

nnm "

n. 4 X 4 X 4 X 4 X 4 X 4

~-

axaXaX

•.. X

a 'l

20101iffl

"

.. li. 4x4x4x4x4x4 = 4

6

6 :iJ. a X a X a X

i

•.. X a =

010

2010 '1

nJun n'*i9 2:

.. 8 27

2 X 2 X 2 X 2 X 2 = 32

li.

5

f!'i.

(-3)

3

3nm

"

=

(-3)

X

(-3) X (-3)

= -27

31iffl

"

61iffl

.

"

) = 11

[

1

-1

2. y . y . y . y ..... y '1

li. x·x·x·x·x·x

20131iffl

nn ~~ &Lffll§trr~ 2.

(-~6

"


fJ ETt'ln 1M"' : li. 2

3

X

MHMHH SJl '!§ :11 b

4

2 = (2

X

2 X 2)(2

X

tll

2 X 2 X 2) = 2 X 2 X 2 X 2 X 2 X 2 X 2= 2

3+

~~

3nm

4nffi

"

...

x3x3x3x

x3x3x3x3x3x

s;;m ...

7nm

"

= 3X 3X3X3X3X 3X 3X 3X3X3X 3X 3

= 3

5 7 +

= 3

12

(5+7)n~

111

lli. a ·an

=

(a· a· a· ... ·

·a· a· ... ·

~

~

mnffi

nnffi

=

'1

~

(m+n)l'l~

"

"

+n

a·a·a· ... ·a=

t?.itf~lnJl ~ ntm ru~csi !:l t!:l ru iJ

n

·a =

~-

2

8 2 8 2. (-5y 2 )(7y) = (-5. 7)(y . y )

?.'i. ( -5xy-2 )

-

n. x 9 ·x4

(3 x y

3 8)

5

-2 (3 x 3y 8)

R

?.'i. ( -5xy )

(-5y )(7y )

3)

=

-35. y 2 + 8

= - ( 5 x S (x · x 3 · y -2 · y 8 )

=

-35y lO

=

-3 · x l + 3 · y

?.'i.

5

2+8

'1

= -3x4y 6 '1

+n


---::---::-"':::---::--- = 2 X 2 X 2 '-----y---'

= 27

4

= 23

= 8

3Mfl

"

-..,---::-----,-"-:---:--- =

7 5

3X3 = 3 -

'---y---'

= 32

=

9

'1

2li ff1

"

5 li ff1

"

5

n.

l=i.

'1

---2

-5xy .

. n.

3 8

4x Y

-6

=

106 -

(-2)

6

~- -

100

= (-2)

6-5

= (-2)

1

.

= -2

( -2)5

4

et

?

29l'UlH'Wll=IM21 a

a

a·a·a·a a·a·a·a t'Ul~HS8 l

a0 = 1

m,y- = -2

l

n.

6

ttlru

4

'1

4

a a::f.:O '1 2 .

.,

t'Ul6HS2 a

1 'ij .,..

-2 a

.. l=inflal

2.

runt

11

g

u

(D2 (D4

4

a

-11

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tlnm aiy 'i:flstiq_!14 ~tmgs9NJ~tSHbG~ : '5wttntlnm

a

' X

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3 2

, x y

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, -3az y

'1


Gtr!w: ""

bnm 2 b3 xy

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x, y, b

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a ' b ' c

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H'i~'l.rlannm

I n. -xyz

:&. 8x yz

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2 3 4 u. 3xyz

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s

UHfl M1fi tJ fi iUHHl fi

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tiG <I

.,

~

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1,

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sh

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-

b

b

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1

tidst! ...,

= 6b (tint~?inn u

i

&~?inn i

ttfi

rnl:lnbnm 5x- 2x

5x - 2x = 3x

53


: l=HUlSl

n.

2xy+ 5xy

2.

2 3

2 3

?1. 8x y z- 3x y z-

2

2

+ x y- 5x y '1

lli.

. n.

+ 5xy = (2 + 5)xy

2.

= (3 2 3

=

7xy

+7+ l

2 3

- 3 - 7 )x y z = -2x y z 2

2

+ x y - 5x y = (l 0 + 1 - 5 )x y

lli.

11 2 3

2 3

f.i. 8x y z - 3x y z 2

=

=

2

6x y '1

: f.iMSl

1

2

?

n.

~-

+ (-4ac 2b3 ) + 7ac 2b3

lli.

+ (-3/ c b ) + 8/ c b

5x-y-3xy 2 2

f.i.

+3ax y

b.

+ (-3x 2y)

lfi

2 3

+ ( - 1ac 23) b + 7 ac 23 b '1

2

li 1

..

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2x

tlnm

5x

2x

'1

b sx tlnmshg'9hLYt~b

tf.iU1St~jJ'il{JlLNg9mslldlti

n.n~

2x

(5x)(2x) = '1 2

4

2 : f.iMSl (4x yc )(3x/c) 2

4

3

(4x yc )(3xy c) =

2 3

3 4 5

12 xyc


A

=

(18a)(l2a) = (1

=

(l8)(12)(a)(a)

=2

t sinh m~'itJfltJfl ~ w ~ tfiffi tsfi nn En t t:n ru~w I

II

A = (l8a)(l2a) = 216a

2

L_j

l8a

<J

i:lmsg td'in9ntH:lJi-@~!ig'tfls A II 4W i.J"N II lj

n.

3

=

2

2.

(5xy )(x y) 2 2

fi. Gab 3)(3a b h. ( ./5x

1.6.

2

ill.

)

)Gi7)

'i

lfiitHHHim

'tf!St~liiftll'~sh 16x/

fiMEnm

'1

tS8ttl9'9h'tflS'[Yt~ht~Sh

mrl{Pru

= t~Lnftll

'i

ggh

+

tfiOlStltrl{PWUog ""9nt 16xy

4y

2

=

(16)(x)(y)(y) (4)(y)

"'""' 2 : 2tnf.nfM9

=

'i

"' fiMEnf:lrumn

+(


n.

l8xyi 9. - - 2 9yz

(Sx/) + (xy)

. n.

(Sx/) + (xy) =

=

xy

s/

3

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f:i. l a b + 2ab =

1

2

2ab '1 : i:i1:UHn1lruffin

n.

+X

ill. xyz

211

2.

+

3

b.

---r yz

.1. 3xy

A

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~mag

u1m1JitS'l!itmn.n

ABC t~sb 3y+ 2x + 8 m1lru\JnUtlnmgs~'G~tuli

'1

tlnm

cgm ./)

3x+ l 3abc

2x -:- 3y

9

4x + 3xy

2

"" lJitrl

si -2x+ 7 i + 2ab 2 + b 3a + 2b

2

-

3c

2


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nmm I

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~

tHHH'itl'Ultn I !.1 !.1 <101

3x-8

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l 2 -x -3a +4 2

x,a

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'lJ'i ~

X

5} - 2x + 1 'tfl S~ t1J1 ~ -i

'

l '1

2iy-l 'tfls~ttn~ "'.Q}

fJ !17 tn HUUJ 2 :

n.

2i-4x+3 mnmm~ i

2

3

4

" x '1 rul&S

3

II + 5x - 3x , y + 4y x + 7 + y , 2k -4 +

- k '1


11- 3x +

2 3

:

4

3

3

4y x+y x+y+ 7

7+y+yx+

5

m

n.

+x-3

f-1.

+ 2ab+

3 -x+ 3

2.

4

tHH1 m A= 2i+3a-4 Stl B

-7a+6 '1

=

f.1rulS1A+B 2

tf.10lSA+B=

+3a-4)+(5a -7a+

mtf.1Hi~dn c; Glll II

+

A+ B =

+(3a-7a)+(-4+6)

l

+ (-4a) + (2) (tintlnm!:lmn) U

II

"'

-4a+ 2 '1 mE=

tf-101!:!

E-F =

-2x+

+ 4x + 5)

2

+

-x )+(-2x-

- 6x+ 3 '1

mA=

f.1rulS1 A+B

Sb

- 2x + 7

A-B '1

Stl

F =

i

+ 4x + 5 '1 f-1 rul S1 E- F

-5) (!:lntlnm!:ltHn) II 01


tJCflW :

t:HUl S1 A+ B

""

si- 2x

+

2

!:HUlSlA-B

+ 7x + 4

+7x+4

-6

LfJHuff: n. M

= 2i + 3x +

2. M

=

ti. M =

2

tiMSl M+N

N = - i + 2x + 4

l

I2i+2ab+54 l

M-N tf;Jrn

Sb

N

=

9i-4ab-25

3

2

xy + 2xy- 3

2

N = -xy -

2

2

-16

'j

lfimummm I

I

t~Ln~u'itmnntnb

<:!>

ti xx 3x

t~Ln~u'itmnn&nb

=

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2

<:$;

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t~Ln~u'itm nnfnb drntiM I

x(3x+ l)

tfitJ ttl nlffi S~tJ

X

3x

StJ 3x + 1 ~

I

r--r-1 x(3x+ l)

=

2

3x +x 'i

tnt! tf;JnlffiSlffilJi 3x+2 ttims t~Ln~~udn I

I

Sh

x+ l

=m

J

ttiUlS (3x+2)(x+ l)

X

~ndlt'iยงtJi 'i ru x

2

ggtJ

=

3x +3x+2x+2

=

3i+Sx+2 'i

L_L_1


2

2

2

+3x (xy)-3x (5y) +2+31+3 X y- 1522 X y

=I = 12x

5

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nmm I

rul

1 +x

'1

3x s~ 2x-3 '1

2

: ta~jl=lnn!rl

x

2

3x+ 1

-

X

2x-3 -3x+

+

2

+ 9x-3

)(x -3x+ 1)

S?'i~ 7368 dl

3 : fi5H

+3X

: 7368 = 7000 + 300 + 60 + 8 = 7 X 1

: n nn !r!th15?'irul I

n. 2x2(2x 2+ 3x-l) 5

-25)(a +

lli.

1.1

2.

+2ab+

~.

1 M = ;tY 3xy

2(2

II

7

21 = 3x7

3) S~

3 '1

0 5x 4 - 30x6 ) + 5x 2 '1 4

(15x -

60

?'!.

&!rl8

2 : firul!rl

+6xl0+8 '1

"" mqms

wu~~ rugd ru cfJ

II

SS 21

sg

0

'G.

7

+2ab)(a-b) 2

2

-12xy-16)(x y-7 + y) '1

&?'iffi'Gn5Hn5~

21 +7 =

21 7

= 3 '1


X

1

x-1

------

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-1)

-x+4

-x+l 3

----------+

rJmni : d5Mnn

cfitab MS'i .... iJ u

d5MnnnHs~1H'or;-@::ufitsbMS'i .... iJ u

tj:im

mdsb

m9

mdabnUJm9 I

2 'l

2

5 61


?

+ 4y-- 7) + (2y + 3) 2

: ti='lQiS

+4y -7 3

2y+3

2

2

-(8y + !2y )

4y -

?

0- 8y- -7

+6

....

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....

hllliHli9 2

....

MruHli9 3

0

2

-(-8y -12y) O+l2y-7

0

-(12y + 18) 0 3

2

25

+6

(8y +4y -7)+(2y+3) =

m

2 :

0

25 'i 2y+ 3

- 2) + (x- 1)

x-1

X

2

X X

2

x-1 -1

n.

1=1. ( 6x

62

24

2 3 2

+ 5x-

+

35

2. (5x y + 2x y

(ab +2ab)+ (2x- l)

ill.

+6a-55)+

22

22

l2x y ) + (x y )

-5) '1

,.,

..,


3.

b

a

.A.

~dl t~t,nltll fil t~ ti:l rnffi 2~~ fJ'[EJh ~ ~2h 1

trH fi91l m nJtl t hlS hd ffiUfi ttl~fi91l fiG 'J .:G u· "' u .:G i.J'u 2

2

2

a

a

b -<

ab

ab

?

(a+b) =a +ab+ab+b2 dl9t94 (a+b) lJ

=

2

+ ab + ab + b

(a+b) =

2

(1) 2

2

+b) =a + 2ab + '-y---J (+)

+ 3)2 '1 (x + 3)

2

= =

i+3x+3x+3

2

+ 6x+ 9 '1

riuruit:fJ@2: r1~r~

ornw : ..,

+ + 2ab+

ffl'i:3n5'i:32 u n 2

t?Hn 2 (2m+ 3n) =

+ 2 X 2m X 3n + + !2mn +

2

(2m+ 3n) = 0

0

Grnw .., :

2

'1

?

tt:ll

wun fi !!iJ9 3 (J

+ 12mn + 9n

: ?Hl.ll 21 101 - '1

tf.'lHlGfiJa fij~ 1o1

ffl'i:3n5'i:32 (a+b/ u n

=

2

=

ooo + 1)

2

+2ab+

63


2

+2x IOOx l + 1

10000 + 200 + I 10201

~tHS8 101

2

= 10201 <J

: t1S"JfifHSJl'H2lb 2. (5x + 2y)

:

2

2

ff!i. (6x + 4)

"'

" ff!iM~UHn!ilfltdn~n 0:: W iJ' Oil II

2

ill. (a+5)

2

'1

(m'Hm2lb II

tff!i'l:flS a Sb b 1d'l:f!Stl::lru a> b (.'}

a-b 2

1::.

-ab

-b) =

-ab+ b

2

ab

-ab-ab+

I

I

I

-I )(x-l) L...LJ 2

2

= x -x-x+ 1

-2x+ l <J 2 : nS"Jn Gm-nr

: ffi'HHms tl In ) 1 a ( 2m-n

2

=

i- 2ab +

-mn+ 64

<j

2

= (I2m) -2x 1

><n+

"""' 1::.

a-bl bi

.

b

-mn+

I ~ ,_.

ab

a


ffl1HU'i:H~ (a-b) = II G'l 2

-2ab+b

2

tr:iQl S ( 100- 1/ = =

2

-2 X 100 x I + 1 10000 - 200 +

= 9801 2

99 = 9801 "1

n. (x-2y) 2 e

ri!lfi

2.

-y)

2

r:i.

(a-b)(a+

"'

,

!UJ1tnlnn : r:irulS"H~lJiW

a

nTIHd8

+

m~au9

1

't~lJiWf~n~

8t~fH~

- b

"~

2

IHGgtf!iQlS (a-b)(a+ II

a

01

~GCS8 l<a-b)(a+b) nlumfn1u 1 : n!ln

= a

2

-b

2

1

"1

"~

-2)(x+2)

tr:i'i:nS (x-2)(x+2) =

+2x-2x-2x2 =

nlunlinlu 2 : rl!ln

- 3n)Gm + 3n)

ocflw : "" tr:iQlS

m~m~a II

UP

ocflw: ""

~tHS8

=

Gmr

&r:iffitHuHN~ 101 x99

ooo+ l)(Wo- n lOI

X

"1

-(3n/ =

~m 2 -

: r:innSl 101 x 99 "~ = (IOO+

nooo-o

-b2

+ tr:ims

-4 "1

+

G'l

Gm-3n)Gm+3n)

nlunnnlu 3

+

=(a-

=

99 = 9999 "1

2

- 1 = 10000 - 1 = 9999

"I


( l + l )( - l) = 0

(2 +

1) = 3

(3+2)(3-2) = 5

+

(10 +

-3) = ...

10-

=

...

'1

+

=(a+

U:l"H15 (a+b)

2

=

+2ab+

~Slllt?iOlS (a+

2

+b) (a+ 2

+2ab+b )(a+

+

+

+3x+ l '1

n.

+ 2y)

3

2.

+

?i.

-- 2ab +

66

+

)3

ill. ( 1a + b 5

'1


'l

tr:l'i::n S (x- 1)

n. •

(3x-2y)

r:l~H'l

3

3

= x -

+ 3x

(5)

'i

3

?.1. (2x-y)

3

~

(a-b)(a-+ab+

1:?-'lffitHdHnH (a-b)(i+ab+b

2

) =

a3 +

" fit:i! '" : 1:1 Sl 61 (xf/Jf.ffl II tN 2

tfi'i::DS (x-l)(x +x+ 1) =

-1 'i

l:'fJtifJU : rl~rinbSJl~;nt~ n.

(a-l)(i+a+1)

+3x+

2. (x- 3

fi. (2x-1)(4i+2x+ l)

1:1~&1

2

(a+b)(a -ab+

(;?.'lffitHuHhl~

(a+

-ab +

3

=a -

+

+

+

" '" f/Jf.fflfit:i!: 1:121&1 (x+ II .., tfi'i::n S (x + l)(x

n.

(a

2

3

x + 1) = x + l 'l

+ 1) (a 2 -a + 1)

fi. (2x+ 1)(4i

2. (x + 3

3x+ 9)

2x+ l)

67


=

i-2ab+

+

+ab+

+

+

-ab+

1 I

1 1

+l) =x+l· 2

2

1 2 1

+) =x +2x+l 3

+

4

+ 4i + 6x + 4x + l

+ 1) = + l) =

1 3 3 1 14 6 4 1 1 5 10 1 5 1

+ 3x + l 2

+ wi + 5x+ 1

.. ~tHSll

l'HSJl'i§

t2Jl'i§ 3x+3y+3z 'l

3x+3y+3z

t~

HltHuHNHtl

3x+3y+3z

=

3(x+y+z) '1

3(x + y + - 3) + y(2b-

+

68

-3) = (2b-3)(x+y) '1

t~QlS


0

0

I

W'lf1Ui f!ij

I

: ttl n rH SJI 'iยง

Grim : n&SJI'iยง

(3x

+

+l)

+ l)

+

+l)

+1)=

+1

+ 2y- y)

+I +I)

o

2 t'ltiams (a+b) l.i 11 n

~ U?'lf11

-b)

+1) =

+I

2

n.n"' : ttl n.n t SJI 'iยง :11 t:aun 'iยง

dru~n.nn 2

2. ~-4x+ 16 '1

ttl fin&SJI'Eยงtild rn~ n.n n

n.

?

2

4a + 12a + 9

=

2

4a + !2a + 9a = (2a) + 2 X 2 x a X 3 + 3

i

2

4

=

(x\2 2)

, 4x

2

+ 3) '1

+3

2. ~-4x+ 16 tttlW

2

+

+2ab+ 2

12a=2x2ax3 atl9=3

(2af

=

2x~x4

-2ab+

~.

n. i+ 10x+25

2

= x +2xxx5+5 2

+5) =

tlID tH S 8 2

~. X -

i

+ lOx + 25 =

20x + 100

i - 20x + 100

2

2

+5)(x+5)

+

= X - 2 X X X lO

+ 5) "' +(

-1

I:HHS8 x 1.1

2

-

20x + 100

=

'1

-1 "'

69


+

+ 16/

+

'1

2

(2x) -2 x 2x x 4y +

=

= (2x-

~.

+ Jimn +

(Jim) 2 + 2 X Jim

=

n.

+

- 8x+ 12

(n\

n + 2)

2

2

J2m+~2

= (

+

X

(Jim+ ~2

=

~.

y

2

+

+y

'1

2

~.

- 12n + 32

3

2. 27y -64 '1

n.

t~'i:flS

si + /

+

tt!Hi.HTI5ih51.3ffHl t~Hl'Uih5Hih5~

2.

t~'i:flS

3

(2x/ + (/)

=

3

8x + y

27y -64

=(a+

3

=

=

3

(2x) +

-ab+ = (2x+

3

3

t~Hl'Uih5Hih5~ 27/ 64

+ab+ 3

+ 12y+ 16) '1

= (3y) -

: t:n r'i m SJll:3 21 iH Lffll:3 r:ll d blH] nn nff1

. 2.

3

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4

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(3i-2t

c~ms

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2

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~

0

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2 2

-

morn~n.nnm l

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+ 1)-

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=

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n!:SJl'i:321btru:ifll3hlHhl~ F

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l

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a

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1997 , 2674 ' 20011 ,82470 , 872036 ' 973248, 881722"'

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39

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tueo-

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_ l

X

-

I

l-3

_ I

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3x4_3_4

51 fi.

b '1

a

15.

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2

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n. MHMdHt3n9 1..!

s

2

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502 t'iSflttJ

Y

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u

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turlth

1

rum 89


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0

mmg

t = 45

+ 5)

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2

2

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~

Om=

~~h'i::flht l'l 9

= 3

12

1. ' t~gLhflti5

AI~

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= 45

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6x

30

X=

90

i

+ 6x + 3

5 "!

t9Jnt~ruums&n~~MbJJ! IJ

2m+ 6 = 12 ?

1 :

=

tu-@nutltin'9 1'i::flS1:HiHHTIH1 '1 ~ w ~

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: tsinbtuf:1mal!iHlm

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=

= 45

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6(5)+ 15

J 45

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nu ""

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7

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2 5

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ti

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2x 5

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20 20

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b

= 148

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b=~ 8

a = 3b + 17 =

a

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= 478 = 59.75cm

8

14.25cm

n. 8- 2(x + 1)

= -3x +

114

8

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~..

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l4.25cm 59.75cm '1

1 lli.

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3

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= 2a(a-

tf:iQlS

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=

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=

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\1.1

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01

u

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2a(a-

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= 0

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= 0

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r

j) - 1

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j+ (~~2 = (D2

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2

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r~:uns

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o

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25 = 0

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3

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300

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=

a 0

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OQ

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300

300

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190

T

x= X

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= 23.75

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ru

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1

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=

36

3x

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9

X

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X

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3em

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n

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m

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.,

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100 = 100 22

rl fi

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2n + 5 = 25

~.

= 12

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~-

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t:!.

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= 35

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= -18n

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= 2(z + 3)

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liHuihru

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I 2

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4

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nn. 5.

2

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2

'1

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I

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.

1

2

3

4

5

6

7

8

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37°4

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39°5

39°

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usa 1J

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0

36°8

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=

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120

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2. y-x = H

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ill. 3x +

b.x-3y=-3

G.-3x+l5y=9'1

= 10

121


l.

t.iHiH'l l em ct1

A:x=3 ,y=5

B: x = -3 , y = 4

C:

X=

D:x=O,y=6

E:

X=

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F:

X

H:

X=

3

G:

2 'y = -3

X

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X=-

2

3.

l=1ft5tHHnHUHntl ABCD t£::ibli'i:fl8n!:Hli A(-3 , 8) ; !J l u

5) ;

Q

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D:

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n

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5.

n.

y-3x

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1

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122

2. y

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4

ill. 3x + y = 2

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2) ~i5 C( -6, 3) '1

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4 4 2 0

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5

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{Chapter 1·4) Nome:

afTif17UuJ:

21b &Liii~:H SHtl fi ~ffl M I

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Cla,:_M;L Mork:___il6

Answer the following qu.rnions

l. How did the bobY gof stung?

"[4,

46

58

65

70

75

48

59

66

71

7'15

51

59

I ,l

72

79

52

60

66

72

80

54

62

67

73

82

55

63

68

73

83

55

64

68

73

84

56

65

69

74

89

I!

I

'""f'~ <rowls ·N-!.. .,. ~ £, ?"J''J} {,,. ,J ;.,, {, 1:) 1o;jJ ,;,J ·~,J I.

0~t_;~{f~a::G~ t~t;"&:e~~Y after 1he boby got stung?

fn.nb fun&Ltin~ 1:lu21btrut?11f~ qfim II II

d5nub t{JtitHi s st:H15'J .:::

2.

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'i

nbnHWi&sg 01

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l

<~

l

uuJm{lucrm~H~

ma{]ticrm A-'fs 9s ~ ru1:11 ~nb mnhtHn.nh q

q

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25


rhntl 9 ~

45- 50 ' 50- 55 , 55-60 ' 60- 65 , 65- 70 , 70- 75 ' 75- 80 '

80- 85 s tl 85 - 90 'i 45

50 mmR9 1 fl::lrn45 n.rrlmtmrn&Hn'i:3tsmRstl5o t'ifllmtmrutnHsmR 'i L

c:t;

cs

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s

s

d]cilltl tS 2'i:fl s rum t~L{H~ti1tl'i:39 s ru~tl brum 9 m R tJ Q;l

0 eJ

Liw

eJ

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ttli tlj'i:fl s f.l5fHUl :m tl5 s

I

blintl filHtHn fltltitMtl Wnl:'itifi~ 'i "'l

li

tJ

en llltlUtMtl ~mth3ss1:1tl 1.1

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tH!:fHffiR

1

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2

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3

3

55 - 60

J.Ht I

6

4

60 - 65

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4

5

65 - 70

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9

6

70 - 75

J.Ht If I

8

7

75 - 80

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3

8

80 - 85

If//

4

9

85 - 90

I

1

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40

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s~R~tHnnt218 fil~~m~'i:fl s ru~M :@sEJli!EbtLdl ru 'i I

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90

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a

11

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0.62

0.83

0.78

0.77

0.88

0.79

0.84

1.07

0.81

0.88

1.10

l.Ol

1.03

0.87

!.13

0.94

0.94

0.68

0.97

0.71

0.80

0.73

0.86

0.92

0.65

0.89

0.97

0.92

0.85

.1

1.08

1.14

1.00

1.05

0.95

1.01

0.91

0.75

0.68

1.19

0.73

0.85

0.66

0.87

0.81

0.77

0.83

1.05

l.Ol

0.80

Ltlf~i:lm~·H 0.1 '1 2.

dh~fr:Hli'HISihM~tidli:'l l.i

kg 't:flSGSSUSlS? ll ,...,

~tidli:'l2kg't:flSGSSUSlS? 1.1 1..;

s

n. r:Dtl89 s~ ru fil'a ill ttlti t ttl rud~ mm rt ttl rt ni:'l fll n i:'lu ~ ~ 1

I

i:'l fun '~tlnl:1 G

0.62 2bnssutict61~ Ll9 'i

61t1§61m5ct61ts9s2 GV U

1

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II

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nl:1

0.60 - 0.70

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5

0.70 - 0.80

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0.80 - 0.90

Jill

15

I

0.90 - 1.00

!I

8

1.00 - 1.10

////

9

1.10 - 1.20

f

5 ttyntiMfu

50

27


hl~11dlh 1

""" 2. 110 ~ S1f U:Hli'i:fl

t::»

0

n

11~21f'i:fl2'i:flhls:l11thh lkg ri

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= 36

nq~ntits~~mhHn5

'i dsstsgmd 1.1

'1

ffi'ij

0

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: nUH&hftffi n

n.

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hl~11thb 2kg

f11 n t'[35n ti ii h H

m

nci'ts 4ttl~~'i5h '1 UJ

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cb

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25

50

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56

39

42

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30

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59

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43

52

26

53

34

53

64

57

46

42

35

28

58

38

46

33

47

40

48

61

44

31

39

44

22

55

54

32

42

47

37

56

36

41

54

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fnnht11ntLtinti

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90

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ms-Hmfi ..

&Lun~!

1

45-50

2

IN

9

2

50-55

3

3

55-60

6

4

60-65

4

8 7 6

5

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9

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tsin~U~nHHi:t'HS c::;GVU

t~HttlntYtSUtS"HGl 6\IQii

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l

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n

x 1 +x 2 +x 3 + ... +x n n 'i

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'i§Uj'i§ x =

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79

158

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82

246

4

67

268

5

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25

150

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9

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57


A

: t'i:HlJl g~1_,tH~Wl ~ f.fh~ t,?i ~ Al M I

~U

f•.Hl4osW ffl'i~~on.nrsr~~rutl:l ruu~tsit~""il t U

.A "" ""' 0 Q~UHAlM ABC ~~ AC bill~s~ 9

l

1

L.B ~~ AB bill~S~ L.C

ru AC>AB

t5irlmrh

'1

B

~~

1

L.B>L.C

tsitrn'lt:l~ AC tf:liUMts D ~tl5 lJ I 'W

ru AD= AB

'1

A

1

ttlQi 2

AB = AD ts-Jg MBD

A~ru A il~ LB 2 ~t~

=

dl1_,?itm M

fd~Qi~

L.D2

dl~t1_,nltS MCD ttlQiS

L.D 2

=

L.B 1 + L.C Gfl~ L.D 2 > L.C

thtu L.B 2

=

L.D 2 &s-Jg L.B 2 >L.C

&9J~ L.B

=

(1)

L.B 1 + L.B 2 tSH L.B > L.B 2 (2)

} Gll~

L.B>L.C

&r:J9l mm s1g ~unw21~ tim~ '1 ~ Li n u l.j

: Q~t,?itm

ru

1

d51d~ rh@su1 2 ffl ~ttl rubill~a~'id~ iJ~ fiHS d~@su~Hfl ttH ttfi tu~tl:l blibill'l§~~ lJ q I l.j I q I I

I

0

0

0

~~Gdl~ ct19Gctl~ 1 ®

'iuHu~n1 m tu~ri~@sus ffl'id~tl:l rum5~s~~il~rius gfhn sus ffl t'tu ttfiru'id~ Li ~ 1 1ql) 1 jq Li 1

Cll

eJ

0

0

1

0

ttl blibill'l§S~9Gt:il~ctl~~Gctl~ '1 I

n~ MBC'b'lS LA= 6x+4° , L.B q 1

dJu~~ ~s MBC ffl~ 1

58

thtH1~

= 7x+12°

~~ LC

= 6x-7°

'1


..

rufJw: nb MBC t!'im s

""

l

LA+L.B+L.C = 180째 (drutin~nbls MBC) If l<'l 1

L.C = 6x-7째 = 6(9째)-r = 47째

~t.H!H lJbffl~rntnti

~:t:llru

LB>LA>LC &Sl8&!'ili1Sl AC>BC>AB

W1~ti~ AC>BC>AB

<J

I

B

1Vifufl: nbm21bMtS8tt:i2~ tn .. If G'l tJ

l..i

1

AB = AC =AD

of

Sb

L.ABC<LBAC

""

2U1'i.fi1M: ABC thl!it1'1HWl~ru '1 t!'iti~ru

L~b sc 2Jms eM &'L:Jru CM AB

Sb

= CA '1

A

~HLti]mtsJti

BC+AC <J

..

nb MAMtf!i(flS L.BAM

= L.BAC+L.CAM

B

1

sl2J L.BAM> L.CAM ""

0

MCMYlS CM = CA tSl8 MCM dlHHnH1JlM~li151n~ru C '1 tf!i91ffi(flS L.CAM = L.CMA ....., t'Ul~&ag

L.BAM> L.CMA 'Y_ L.BAM> L.BMA

Qb MAMYlS L.BAM>L.BMA sl2J BM>AB I

t~::llru

BM = BC+CM = BC+AC (&Lmg AC = CM)

~ti&S3 If

AC+BC>AB <J

159


Wifmff:ft: 'itl'tmhn sยงHrillti s firuntit94 tu~ ttl-e1m8 n'ifitm nn-eru tu~'i::llth~m II l.Jc>~; U 1.1 I eJ n lj 1.1 lJ &

u

l:H15-efig tuStn'eli5ntStl 1 "' 1.1 n 1.1

'l

t~tl ~sfiruntitntl'i::ll S 2m, 4.5m, 5.8m

IN

1:fl SlJ ss

r:g n.

Sib

10.2m '1

ftHlH1j~ ffim@ tut1 tu& ru5{5 fi run ti ttl-ejm~ nLfit mnn

tl ~-en~ f!JS~

2m, 4.5m

Sb

'l

~~nm@ tut1 tutisJ~ti~tltLm-e

5.8m

stl 10.2m tl. 2m' 5.8m sb 10.2m lli. 4.5m ' 5.8m sb 10.2m 2. 2m' 4.5m

t tl-ejfi ru1 tim 'i5 sJ s~ li5') tS'i5 sJ

9l blJ s ffi tiqy ML'i::llU~ til slJi t mrul~ li5 ttllj1 ~ u

1

hl1 n

sJ 9'1-l::lH tliot m n.

f~ b ~s~b 9'1-l::lti~:~b ~ti1 tu-em nlJit mnn

sb 5.8m

2m ' 4.5m

4.5 + 5.8 > 2

"'nntit9? ("'nn ) "'-

~ 5.8m

fi run tit ru59lbti ts gffimLli

2 + 4.5 > 5.8 "' b1

2. 2m ' 4.5m

sb

10.2m

2 +4.5 > 10.2 rinm9? (-@srin) 'l "'10.2m

tl.

2m' 5.8m

sb 10.2m

2+5.8> 10.2

2m

"'t151Y.t9? 10.2m

\

fi run tit ru59lt!ti ~: s g@s ffititLti ttl-ejm~51Lfitmn.n~rumst9 '1 160


ill. 4.5m, 5.8m ~b l0.2m

4.5+5.8>10.2 rinB_t9? (rln)

10.2m

4.5+ 10.2>5.8 ilnm9? (rln) "'-

5.8+ 10.2>4.5 nny_t9? (nn) '1

Luifuu: Firu~fim ~:~~~n5!Eh i

n. 12, 11 , 17

g,

G~~j~GfSj~

4.

1. u~ ri f fii.1Sil u~ ri <!)

0M

1

f!i. 4.7 ' 9' 4.1 'i

' 2' 3

G

fl A

l:HiJ{hd~ ~H S"J t 1.1

fS A

AHl.!J. 'i Hh~ AH n

&'if!i

!J.

4.2. iLu]uitaJuu~ri

n

ri

L~tfilM AHB rtlL~tfilMtnh1Jl~ H tf!'lms LH> LA

sl~ AB > BH

LH>LB

sl~ AB>AH

!:lmsg nh'i~bfilM u

"' l

l.i

f1H9Jnmlish~fnh

H

B

A

Hthr~sMt~hm 1

u

i

'1

61


" : tHlllts B "' !'lb C 1

A 6i BC '1

H

) '1

tt?]mtijti AB Sh AC A

A

c

c nh ~AHB 'BlS LABC dl~tifflts LABH "'

l

l

l.j

t?i'QlS LABC = 90°+LHAB

i::lts~:sg nh MBC 1J

dl~tmru I

LABC> LACE sl§1 AC>AB

"'I

u

B Sh C tsl!Uh:&lh H (mg 2)tt:!ithlilu C' 'tHiHsl&rntiS'l~ ~ 1J 1 !.! .:: HC' = HC '1 t?i'QlS AC = AC>AB

162

tt!ru

C


o

~tl~~~fiqgnfl~ ~~riqJn1:llS~rulnthn~~riqJnU

o

~n~~~fiqgnfl~ ~~fiqgnudl~~riqgnt'c:~rn1:lls~Mnfi '1

dfunl'ff!tr t?12J ABC dl~tfilrul~rutl::lru AB<AC

'1

'1

tsiQ~~tfilrultsg

fU

I

n~n5 AH S~i:'i:ll::lJlS AO '1 t1_Y]mtsJ'u AH, OA S~ AC '1 ~~fi AH dl

tJtgw: ""

n

rifn~

A

,U)ru AO dl~~riqgn t?l'Q'1SAO>AH

ttnru

(1)

AB<AC (N'i:l~n'i:l) ...; ...;

ttfl ru13 rLJlti H ij n t

g B S~

0

t?19lQ)U1S HO<HC s12J AO<AC

ffl'i:l ( 1 )S~ (2}(?1tf1S:

B L----i..:,J,----l...,....----..,:,Y.

(2)

AH<AO<AC '1 !!ABC '1

'i5-lrlmm AB+BC+AC>AD+BE+CF 1.11

"""

A

163


l.

MBC =. !::JJEF BC = (2x + 30)cm EF = (5x-90)cm

?'HlJl Sl B C '1 p

tLfilYtsgtf:i2J

2.

=

PR

Sb

LPST

=

LPTS

MQSStl MRT '1

M

3.

hf:i2J

MA = MO '1

MT = MB

mdl !:MTO=.!:MBA '1

"

T A

4.

i:fi2J

AB = BC

tclJu

Sb

MED

AD = CD '1

Stl

B

D

!:£ED '1

A AB

5.

II CD Stl

TR = TS '1

um mm U1

"

MBT=. !::JJCT '1

A

6.

fi2J

LEAD = LCAD

stl AD j_ BC

mm MBD=.MCD sb AB = Ac

"

'1


DiD

7.

A

t?i~ P rtH~MG'tHi515ntsitrnnsgu2lrimls LA I 1J "' .,;; I

.

"" mMLnl:fllrulM'l:Hfln ABC '1 0<:$

Uult15U{]Gl PB

=

PC '1

c

B

8.

A

ABC ctlLntfflrulhl'tHilnn~ru A ~~ ""

M sb

0

N ctlcrMGnrun rutSLJ=ih AB sb AC tUb ffi 1

G'1

1

ttfiru P mcrrt.nGLUMblts BN 1

"'

sh cM

'1

"

B

ummm MBC dlL~tfilrulhl'IHiln '1 l/1 -..:>

c 9.

t?i

§UAB

~

0

CD Sb AC = BD tl1Jm2lb fiJ1 '1 IJ IJ G'1

=

tLu]umJuL~tfil rul ABC

sh BDC

D

'1

A BA

MWm~Ablru B -..:> IJ

10. ABC ctlL~tffl M'l:§ru '1 fi'l:§ IJ S'l

c ffl rilll b bill'\:§ Ln~

D shE

1

m"" BD

=

sh

ffi'i umm l/1 -..:>

"'

CE &SUL.ABC = LACE '1 B

ll.

t?i~ HOJ..OB, DB.lOB OP = BE, HO = DB '1

fi. I::J!OE := t;.DBP

12.

nbm2lbw1r;sg r;r:;§1 "'I

u

AC = BD

it.l

G'1

Sh

LC = LD

Uirlmm BC =AD l/1 -..:>

Sb

90° '1

BCIIAB '1

c


0

3. mm

tfflMSl:l u

21~ 'Lffll:l M~ t M~~ ffll:l

mtH1ih91r~u ij

E

K

A

c

Scm 3cm

D

mgL~tffl n.ns~

14.

B

F

4cm

M

21~ 'Lffll:l M~ &Ml~~ ffll:l

mti~f~~t912...,

1

B

s

F

R

15. PQR dl~tfflM~

PR

PQ '1

=

ru QR> QP ~~

mm LP>LQ '1

"'

A 16. ABC dliJHfflMMl:lQ'Hin~ru A '1 ""

0

U.1ti~tl5~~ BC ~018 CD= AC '1 1

tiblmm LACD>LCAD '1 U'l

"'

17. ABCdlL~tfflM~

A

~AMdlt1:11:lJ1S

ru LAMB< LAMC '1 tiblmm LB>LC '1 U'l"'-"

""

0

8. ABC dl1JHfflMM1:101~n~ru A '1

tiSlfif!lMtUm~O IJ

&

"'

fflfitiSlfif!ltummn &

ij

"'

A 1Mti~~id~ BC L:i

c 'ini:l D L:i

'OinmffiAD+AB>CD 'i tn " '

66

L:i 1

t~um21~nn '1 ij

ij

"


B

'' '

LB fflflLdtl AC H'~~ D '1 H mthn.mrufntl l

"

'S D

.., ' till15S"H'i .:;

''

\

BC '1

'\

H

''

'' \

15trlmctl AD< CD '1 lll .....,

' ,/'

\ / ' , AW-----~''~--------~

A

~-

Oeb

Q)'-::1

0

1

UMID15tictldru15nn't:HtHntmts LlABC u n ~

~

~mtl

N

L15 t' Hm~'i:fl H1 ~15 ni tl '1

B 1:..---.,!-:J------___;::,.c

21. ABC dl~tfflM~tlJtf;jru AB

=

3 Stl AC

=

4 '1 ttli1ti.ri::UllrJUhfflM 15~£!)

l <BC<7 '1

0

GM13 M '1 l n. tt15]mt{J15 MBM stl WCM

~- LMIDtl~Gl AC;AB <AM<AC;AB '1

c ~-

Ql

0

tn13M13 D, C, E I

~

~

~n1ntldH1ltlt9? LJ Ill "' "'-

(15ITTlR : t'!M 21 LDCE) c.s0

A

24. ntl~~tffl M ABC fi@g152lfArlll tS LB Stl L.C c; L.:; ~ 1

t'l.HH111n~ I '1 ffl'i:§" I l.J ,Oc;rj;

¢V

1

~IDLfl.mstm~fl BC ~UliDfflfl15~fl AB Hi~ D stl AC Hi~ E

'1

Oeii

LMID15.0Gl DE= BD + CE '1 25.

ntlt~tfflM ABC nS:Sli2lfltllltS LA 'ilit\Hl BC 'in~r3n.nts D '1 152lfil3rutt:Jrut'lli5 , "".:; l l.i .I LJ l <Ill u

ttsmn ....,

C

ttniD1Jii515Stl152lfi AD fflfi152lfi BA 'inti E '1 15trlmm AE "'

"'

LJ

lll-..:1

=

AC '1


----~~------------~~--------------d' B C

LABM

Sb

LMBC '1 21 ~ d , d' ,;

27.

6?Jtltl LBCE

LBAC = 90° , LABC =

bt

90° '1

60°

=

Sb

A B '1 D

Sb

ri LBDA = LDAB Sb

LCAE =LACE '1

n.

?l!lf!Sl LBCA , LACE , LCAE , LDBA

Sh

c

LEAD '1

E

28. ABC rtl'i~lltfil!lfl'i:Hi5 '1 fiSgti2l~r12tS LB l.j

!.!

""

IUWQ)rl A

,;

I

168

DE= AB+AC '1

LC

uuu~bti~~ BC 'if~ D Sb E dJtl[!

n. MEC Stl !'i.ABD rtlt~tfil !lfl IU'i:Hf!Gi ~.

Sb

'l

'1

1.,t1fltm5~m


0

0

'

"

nrulf!UH.RtHSu~tfilrul

o u~ £!) ruQ nn: sb@ ~159 tstytr~59JLfil~ 1J

o um mrun9 nn: sb'i'9 f'6u 9 tSufl1 r; m nn t m nn lin lfl"'-'

cr~tmnndlrl'Ujtfilnn

'i u~&mnn

rul:flsi_Eib4 I

S~ t15']'i:fl Si_Eib 4 sb~ 4 &Ul ti5'i:fl Su~& fil rul &dJb WJfiBl S I

run rul :u tS"e~ t Olb Sg L:lu2lb 9

"'

1J

iJDti~

ABCD 0

'1

m"" ABCD 'i:flS

dluf!tmnnmru I 01

II

'i

tytrubiltm~ dlu~tmnnt'1:lrul:flsi_Eibm5~ 1J

I

uuu~ "" m'] '1

"" ABCD m

tn59JLfil~ 1J

I:RUl S [AB] e

II [CD] sb

II [BC]

a~tmnnfnt! mtyr;ru9JLfil~

'1

rul:fls~tnt!

u

~ru '1

ttl ABCD dltU&ru9JLfil13 sb

LA

IJ

n~----------~c

B

&Sm ABCD

dltif!&filrul I

~~S~ '1

ttl ABCD dltmru

AB = BC &S'HABCD

=

c

A

Sb

dlun&filrul!;hl 'i 1

""'

D

169


nH~

B

ctlDJ ~ruSJLfflt3 &'i::Hlil:fl s~~ riHtl'ci~~ s ~ s~ u

l:flS~fn~~ru

1

ABCD

'i

u

90° S~ AB

LA

ctlDJ&ru9JLfflt3 ttfiru

=

A

BC tSH ABCD ctlfilt~ 'i

D

- - - - - - /t._tJUiflfj'{fn1!

~

/

/

7

Lm ru 9J 1J11 '1:3 m11 ~ t mru1 rt~ rul:fl s Ltl ~ ru5'1:3 u

~Cl~'J 'i

1

ttl ABCD ctlLmru9JLfflt3

t~ms n~--------------~

u

II [CD] s~

II

'i

l}fgfir~g 1 : »~rl1J~S~ti5'J ttinDJ&rulULfflt3ctll!itmMria~s~ u

ABCD

mm !J.ADC =. !J.ABC

ctlDJ&b159JLfflt3tt!ru

-...:>

u

L~, m ru1 A De

sh !lAse l:f1 s

AC LA 4

=

0

'

LC 2 (t3~Hun~) 'i IGV ell 1

t!msg u

!J.ADC=.LlABC

'1

u

(nHUl

'1:3-d-

'1


&~LilS llADB:!lDBC &~Lil

2 : AD

=

(nHL.fi '6-d-

= DC

BC , AB

LA = LC , LD = LB

1mn : 151iHlli'6sh~rn5'6'&s trn9JLfil'6~s ~ 1

ABCD

'1

ll

dlL'iHill9JLfil'6ttlrn "

LA

sh

LB dl~n~ '1

"'

0

u

ummm U'l

LA+ LB =

1soo

'1

A

"

ML"l:f7 W'iJ

n;p !'# :

t~'Hls [AD]

II [BCJ msht:tH.l5~~ "'

l}tgug@ 3 : ~~~1Jh tsLmru9JLnl'6LunJ~~Ln~linf1unn!Jl rnt{Jh~ o tUTl u

u

mon~g '1 .!!

""1

ABCD

dlDHill9JLfil'6ftlru'!:fls»~~1Jh [AC] sh u

Uhlmm U'l

"

0 GliTMUnrunrut~Qb'&s 1

ML"l:f7 W'iJ

LUnJ~~Ln~ 0 "'

u

C]

G1

Sh

'1

n;p !'# :

Lfitmrul AoB sh

lloDc 'tfls

LOAB = LOCD

A

B

('thnfdnb) 1GV "' 1

AB =DC

(Ldhrn5'6Lutru9JUD'6) u

1

LOBA = LODC

(~ffihlnb) 1GV

~msg

u

AAOB:AODC

tf-1012

OA = OC <I

sb

OB = OD '1

~fitS g0 u

G1

1

(nHJl '6-d-'6)

o mnMunrun ruts o moMunrunruts 0

"

i

G1

1

G1

0

dliTMUnMrl rnt{Jh tS 1

"'

C]

"

[AC]

Sh

"I

'1

O~tfilllil ABCD 'inS AB = CD ShAD= BC '1 U~QJGl ABCD

dltytrt59JLfil'6 '1 u


fiiJhAC u

L~tmn.n ADC AB

=

sb ABC 'i::flS ~n'i:3) ....

CD

Ac Loha'i:3 1

!:Jm:::lg AADC:t!.ABC (~laM d-d-d) '1 u

lcnn: LA 1

=

LC3 m9mh~mn5nhtf.lms i<v ..

II

(1) '1

l

LA 4 = LC 2 m9mb~mMnbtf.ltnS jG\1 c;

II [BC] (2)

l

r11m~ s ~ il ~ 'J n:n gu~t m M ts 8ctli,YtilllilJLffli:3 '1 u

m'ibfflrul ABCD 'i::flS LA l

= LC

Sb LB

=

f!Jrfl

LD '1

ABCD ctli,Ytill9JLffli:3 '1 u

' '

tf.l'i::flS LA+LB+LC+LD

'1 (

=

ornun u

r;m M) LA

=

LC Sb LB

=

tf.ltnS 2LA+2LB LA+LB

= 1800

LD ( tu'i:3~n'i:3) .... ....

=

360°

Sb

sh LA+LD

""

LB

=

LD

= 1800

(rlilltin'i:3nbm2lh) u jc; !.1 0

I

II

II ~msg u~tffln.n ABCD

W'ILtitill9JLffli:3 '1 u

GSHAlM ABCD 'i::flS l

72

II

sb AB =

DC '1 ti1;fl£!JG1 ABCD ctlLtitill9JLffli:3 '1 u


9m

M['i:n l!J'iJ f[{l If

:

M~H~fl1Jh AC u

1_,fitnHl.!l f].ADC Bh !].ABC 't:llB AB =DC LACD = LBAC

AADC=:f].ABC (d-~-d)

tSlg

~tfln : LDAC

LBCA !\5msi9mh~m

=

"'

II

IN

sb [ABJ n[Dc]

II

tH'itnH1.fl ABCD 't:llS l

"~

tltH!H tHHffHlJl ABCD II l

7 : dhHHnH1.fl~ttl't:ll2Hhfl19bi'tinH1 ffiH'i~G n u n Li Li Li lJ9MfJ99 1

1J

Unrunru n

<lot

h

tSlg

U~tnH1.fHSgdl1JHru9JLnl~ '1 1J

~1JhU~tA'lMn

0 dlGn.f1UnruJHUG2

rudJb

II

ABCD dl1_,titru9JLA'l~ '1 1J

M['i:n l!J'iJ f[{l If

: A

1_,fitA'lM AOB Sh LWDC 't:llS OA = OC 0

•

"

L.AOB = LCOD (~9run~

D 0

dlUMUnrunru&S 1 n

OD = OB

~tfln : L.CAB

ttfl ttl

"

'1

L.ACB = LCAD

II

'1

II

'1 tru9J1_,1ll~ '1 1J ~

0

fiJ'i.fTUif.'it: tl!l't:llSUntnlM ABEF Sh EFDC dl'i'i.H IJ

!

ABCD dlLmru9J1_,1ll1:1 '1 u

l2

C

II

~msg U~&A'lM ABCD I

l>?J

LACD

=

UntnlM ABCD 't:llS 1

0

B

Li


..

F

.----------------. E

b{j ABEF dl'U5WHilJl,iil'i:HS'U AB

=

FE ,

ij

II

(I)

t{j EFDC dlt,utru9Jl,iil1HSlg FE= DC , II

II

(2)

fl)'t§ ( ) 2b tf!'lQlS

(2)

II [DC]

AB =DC ,

~msg u~tfil M ABCD

<t

dl'U5tru9Jlfll't§

'1

II

"' tmru D

0 " dlun.nu~8ts

l

ru9Jl,iil't§

.

o.,

ru'i:fls9u1b\jru

'1

.

II ~

A

""1

A; - - - - - - - - - - ,B

t tn ru Wl~u~tm nn tnt! nmt,m rul{lt,Al't§ t Sl gl,f!'lti II 0

~

~

I

I

nn:9lbHtum tu'U5Ul59Jl,iil't§ndl ruQnn :m tuu~tm nn IJ

tSlg

LA = LC , LB = LD

11 D''-'----------:c

llli't§tStytn511Jlfll't§) IJ

t'lflru

LA =

=>LC

A,-,--------,8

=

_j

LA+L.B = 1 +L.B =

tlmsg IJ

=> L.B

=

LB = L.C = LD

900 t Sl g L.B = LD = 90o '1

DL----------'c


f)ffl

ML'i:fll111J f[fl ?#

:

t{j ABCD dltHWilM i

..

nh !:s.ADC

&lrJg AD

= BC

ru:rl§ hn:s 61 t mnn fnb ) A~----------.,~

ab !!.BDC 'tflS

I

AD= BC LC = LD = 90o

!!.ADC=.!!.BDC (n~

0-'1§-d) '1

~tnn: AC = BD '1

titH£H AC u

= BD '1

tf!i'HlS ABCD

ML'i:fll111J f[fl

dlLU&ru~Lffl'l§ttiru AC

= BD '1

tl~[gdl ABCD dlu'ttfflM

II

n:

&u ABCD dll}5tru9JLffl'l§tlrlg II

AD = BC (~hru5'1§tstmru~Lffl'l§) u

l

AC = BD ( DC

dl~hJ'I§ I

&~012 !!.ADC=.!!.BDC

~Oiii :

n~

tl-d-d) '1

AD = BC '1

LADC = LDCB

nJiru

LADC , LDCB m'l§dltitltS'I§ I

tlrJg LADC+ LDCB

"'

=

2LDCB = l80o si2JLDCB = 90° '1 l:H'HS!l ABCD u

t:htHHffln.fl l

'1

175


fil~ffiY M 2jma MR

'l5

Rffi MP+MQ

~

= BH '1

A

Qb1.f\tfilrul BMPffiS LPBM+LBMP = u

Qb1.f\tfilrul MQC ffiS LQMC+ LQCM

=

u ~

0

ttfltu LQCM

Q

lfOlntntfi1lJHuYQ1n ABC

= LMBP

f:jtJtS8 LOMC = LPMB 1J

-

ru

= LRMB

LQMC

~SU

= LRMB

LPMB

'1

1.f\t fil nil BMP SbtWitfil MBRM ffi S : MR = MP ( fUY~fiY)

'"*

LPMB

'"*

MB (~b~Y)

LRMB

=

l

llBMP:!J.BRM

(mnfi r:l-Y-0)

lmn : LPMB = LRMB

=

= MP

90° , MR

=

~Qlfi RQ = BH tn RQ = MR+

sg

'1

L.RQH

=

'1

MP+MQ = BH '1

: tf:i"tf!StJ£11 filrultfih ABCD SbHb~ n

tihl un

'1

g

-*

I

2.

LCAD = LBDA '1

~

nnt m nn t fij

m1m !.J

~'i9h SYtuC) ttJfifj£1 tfil nn' Mdl'i~tfil nn

'"* w 3. idhrumsb~ntiYtS11ntfilnnti6usm wl l l '"* l "" 4. Hh~'i9btS1Jntfiln.flt n w 1 !.J1J

1J

76

1.1

'1

dlnnt fil n.n fnb ttfi rul!l m u

, He

.1

= MP

u

'1

n

LQRB

=

900 dltJntfilrultfih '1 I


tf!l'i:!lS ABCD ct"J1!.Hru~un~ttlru AB =AD '1 tl~(gGl AB = BC =CD= DA '1 iJ

ML'f:fl UJfj rrJ7 fi

:

t{j ABCD thijl&ru~un~

B

l.l

tSH AB

CD Sb AD = BC (!Jlbru5~tS

=

I

c

A

D

tlmag u

AB = BC = CD = DA '1

ML1f'l UJfj rrJ7 fi

: B

dj ABCD thtHHffHlfl& I !:.ABO Sb !:.ADO 'i:fl a AB =AD OD = OB

D

AO (!Jlb~~) 1

si~

t:.ABO:=t:.ADO (Fi~

~Qln : LAOD

tmru

=

d-d-tl)

LAOB '1

LAOD , LAOB th~dlUtltS~ I

2LAOB

=

1800 , LAOB

"'

=

900 '1

tf!1'i:!l2 ABCD dlijltru9JLfil~ttl II

177


.

B

!iABO Sb !iADO 'tllS : OD

OB

=

LAOD

LAOB

=

D AO (~b~'i§) I

2J

!iABO: MDO nHW(d-'i§- d) '1

l(fln :

AB = AD '1

ABCD th1YU15~Lfll'i§ttlru'tlls AB =AD ffi'i§Stl5'i§SttHI!'i(flS u

ABCD thtHHfi1fl1HM '1 I ~

.. B

!iABO Sb AADO 'tll S OD

=

OB

LAOD

=

LAOB

AO (~b~'i§)

D

I

il2J AABO:!iADO l(fln : LBAO

=

n~

(d-'i§-d) '1

LDAO '1

ri 1J b '1 II

A

78

mm AOBJ th13WHfi1rult

-...:J

I

'1

1

m11 fl.fJ ti'\3 ru f tl ru


d5 AOBJ mnHru9JLn1l:H~Ol2

=

OB , IB

=

OB

ll

ABCD

I

tiltHHffiMtntl 1

t~OlS

AO =DO= OB = OC

t~OlS

AO =AI

~msg AOBJ mnHru~Lmattlru'tf!S ll

;ot~mti Ao =AI lJ I

mmHmMtM--& "~ 1

'i'i.J~fi~: ~MiSfUUl trl <II

LDAB

l..i

tHHffiMthl ABCD

LBDC

"!

~

I

Stl

c 2

rugn.n:mu mt~ tilti~tmn.nr~t'!:lru'tlls~&ntl'\1ru "~ rr:nrucr~&mn.n&~mnnru~Lma&su ll

mw~mLmru9JLma

"!

u

tilLmru~tJLma u

m&H:hu~tmMtnht!:lruffisiJlhmtir~~

..

rr:nruu~tmM

"!

1

tSl8n1UntilTIHru9JLma "!

~msgffic~ffis

ll

tMshmHmMtnh --& I

"~

3. '~Ohru.mmttutHnshrMm lJ c:;l.j c; ~q1

4.

" »ru~g

tatijl9itS1Jlh I

I

5. Hh~'i9htlSffi n lJ 1 "~

ffi'ini.1dn.ncrn lj

6.

I

<'I

u

mi:!Jl9atsiJlhru.mmiinJ~g

.

I

1

7. »h~HilhtilnSllUSl~m'ts~n.tla&Uirumiin;~g '1 n

lJ

u

w

,:;

1

tiw

1

1

l}igfffJYJ : Qh~tffi M»~~tti ru.lJIUU 1

1

ttflrutMshmRnrunru;ot~gti '1 »h~rsgctfTlm ""'

~

tmru;prutSLdh rhLn~uutiShiJlhgu

l,'; I

n

ll

nn

I

"~

79


0

,13

13 E nrunrn [ACJ '1 G1

II

'

uinmm lt1

"

DE= l

A

u~ru

~ms DE= EF

.

D

.. ..

0

M ~ [1U1~13

13n

t blililJ1J1l'ij

rn E

"'

.........

' ''

' ,'

B~--------------·=·c

lJ

I!

tEm AD= CF ,

sl~ DB= CF

ttntllAD =DB

II

136HffHl.ll BDFC "ddS DB= CF , 1

tmg DF

''

F '

= BC ,

I I ruDE= -DF =

II

2

1

II

"' ' DE= -BC 2

' '

II

"'

tf:'ifflf;l

13&'Hfi'HWl BDFC "ddS [AB] II [CF] ' [DF] II [BC] 1

~ffln: BD = CF"' DA

= DB (G"

13 D n

136'Hfflru1 DAFC "ddS DA 1

t?l01S H~~lJ~

=

rn CF ,

S~

lJ 0 " t:Jmsg E dl13ru113nrunrnts [A lJ G1 j

180

) !:Sl8 DA = CF "'

] II bliE"'


t~'Hl2 b.ABC fnhUi~ B BO =

~AC

c]

'1

um Ill

'1

ML'i:!7 UJ'iJ fJJ1 rf :

U~t1Hl:H:iJ12

2Jms

BO == OD '1

t~Ql2tHHfiHl11 ABCD ft~ru'HlSHh6h9hiUnHlffl Li

n

1

L'1~Gn.f1unn.JJ1 ru

IJ

Li

.o"'

o £hLUHl59JLfil'l§ '1 IJ

TIHru!ilJLfil'l§ ABCD ft~ru'l:fls

dluntfiln.n I

LABC =

IJ

1mn : BD o ....'5f

=

o

1JtgVfUI4 :

i12J

AC

~AC

BO =

c::;

QhL5itfil

'1

bn~:l~bu;~sbn &Sl::~~:filn.ntm::

t'l§1:ljlS&

1

l

IJ

m~tfil n.n &nb&1:! ru'l:fl s~bu;~sht'l§i:lJl sm IJ

I

l S BO = -AC '1 2

ML'i:!7 UJ'iJ fJJ1 rf : U~ti5t'l§i:lj12 [BO] 2Jms BO

tHHfilnfl 1

ABCD

=

OD '1 t~QlS

'1

ttnru

f1:lru'HlSHbn

&2'H BO + OD

=

1 BO = 2.AC

C+!Ac = BD 2

BD U

"'-

= BD '1 1_?tru9JLfil'l§ ABCD ft~ru'i:flS

AC

fllJh

IJ

AC

= BD dlu~&filrulfnb

'I

IJ

~m~a b.ABC fnhLn~ B '1

2.5.

runnn:mnmnn 9

I

u'1tfilnnmru dluntfilnn 1 c; a ~hLruu~&sgnmmmn Li 1

m '1 "

I

ru~bfh

I

'~db '1

ru'l:flS'idh LJ

n~sLruu~

l

untfilnnmrufr:Hli'Hl l

"'

mruru'I§Qln(m9 "'

tsiruh:nbts~hm

1 Htfi

IJ

'i:l'ru t~tUTlm~Ql'1tSuntfilnnmruru'i:l'Qln I

IJ

1

"'

1J

1

'1

un filnnmru l

&t~ru'l:fls~fnb'i:l'rutUTlmun&filn.nmru&nb I

A.-----,B

l

"'

"'

2) '1

c


tl'i

LD st~ Lc

ru

tunm

~m~ '1 l

. II

II

A

IJ

ru DA

=

B

,.---'\~Z~7

ti?:'iQlS EBCD dlttnilllijLf'O'i:j 'i ti?:'i'i:flS DE= CB

E

CB (1_Elb l

tffH1.1l UltllM'i:jQl~)

~ DA = DE 'i

!lADE dltli&nH1.1l n5'i:jtfl~ '1

1mn

:LA = LE

ttfiru

LE = LB (~L~~

) ~~

IJ

~ ABCD ttlru

..

A

DA = CB ('idtifi~tffHUlmtllM'i:jQl~) lJ I 01 I

'i:j LD = LC ('i:jQl~fi~tffHUl Q

l

I

n AC =DB

182

tH!lmttl AC lll

L~tffHlll ADc st~ !lDBc 'tfls

"

'i

l

'1

tllM'i:jQl~)

= DB 'i

"'

B


t~'i:flS ABCD tHHnHl.ll I

ruftHli'i:flSO'l~

II [AB] &tfi ru

n

i'Hl{fl &li hq_~ tl ij ~ Htni G1 01 fi'i:HiJU t S

tHi &ffl M

1

ummm [DCJ 11 Ul --.:1

mru '1 <I

a~

11

EF = !(AB +DC) '1 2 ML'ln wu fJJI

n:

ffi'lยง C ~MliSln CE ffl ~

II

Ui~ G L~hfflnn AGE a~ EDC 'i:flS rdn~) "'I

LGAE = LCDE

1

" ED (E dltiMtHHl.ffi&li 1 51

AE =

."

rnn~

LAEG = LDEC

lifin :

AG

= DC a~

GE

= EC

'1

'1

Q~l!itfflM CGB 'i:flS I

E mttnru:;nrunrula I 1"1

II l l I EF = -GB = -(GA +AB) =

2

2

16Mf!fJ94: n~n~tfflM L;n cs 1 I

II

+

ruannnnrunrnts'itltl 1 n lJ i

lJ~ ~msiHliu~rir~~ruftlrnLM'iHms~m~ '"~ II

&~'i:flS

ABCD tHHfflM I

'lJ~ [AD] ' [BC] S~H~rilJ~ II

&li'i:flS E , Fa~ G , H dlGMfinrunru I Gl '1 ti!rlmm E , Fa~ G , H ~~tsiUtlli IJl --.:1

83


. ~~Uitmn.n ADC ma I

" ruts

" G marup:sn

ts-12 [EG] d1Qln1H:$J~laU~tffirul ADC '1 [DC] II

U1(fl~

'1

a [DC] II ~Jl~teJs;

" s;~a'l~taafitffin.nmu:ns-H tJ I <t

a

m~

"" "" Lrirl"l&ru

11 [EF]

(3) '1

"' maatlH:tl E ,

.. Fa~ G , H ,e. un

IJ 0

GM1 G E ,

g

C::.

&rutlSlntn~ru '1 <I

N~ts~~tlยงlrl

a~

a~ H

nfJti19N~tSH~fllยงl~ AC a~ BD

I

'1

G

: Uitfnrul OAB N~Q'ln t'iH~JlS

rl LA

= LB)

G

A

dltU!:W

n~ l!.ADC , l!.BDC oe

'i:flS

I

AC

= BD H~rilยงI~Grl t ffi M n 1

!llNUQlri '1

II

CD AD =

sc

Ul~iaantmn.nmru I <t

0

&'1'1

I

~mas

llADC: ABDC '1

ttlQlS LDAC = LDBC LDAB = LABC t?l(fllEl LDAB-LDAC

=

m~ AHAB mU~tffirul

mu (1) a~ (2) t?l(fl a

LABC-LDBC m~ LCAB

n tSlUUf:.lJlS dltU mt~l:lJl

"ts

u:rhruumrifn~ru, <I

184

'1

U

O,H

tt'iQlS

IJ

" " AB '1 G dlGMGnrunru&a I ~

: ttl'i:flSGrltffiMmruNUQ'lri ABCD i <t 0

G e/

Q

Fa~ G , H

II

=

LDBA

"' " [AB] (2) '1 9US

B


0

nnmn

2.

n.

t,tn'lhrtyHt,~hfilM ABC '1 ttn~ij ?

2.

ttnthru.mtfitfilM i.j .... i.j

!!!.

tfi

16

&tnnH

11ABO:I1ADO ii(g ? ~

I 6

II

tS [AC]

&UlW

ffl~ I '1

timmt:n

? D

?

nnmu1mru I 6l

Qbt,utruf{lt,fil~ ABCD , J l

3.

ttnnH

ADO '1

[EF] t:h~tH%~rufl:lrufilri n

Ul"'-'

!.1

IE = IF '1

U:hW&l_.tlG~&filM EFGH

n. t!!l2J

EH

= IF Sb~ LEHI = LFIG '1

ti~(!JGlG~tfilM EFJH t:h,YUU9~t,fil'tf '1

2. t!!!2J [EH]

II [FI]

, EH = IF

Sb

FG = IF

ru~LfilY '1

t'dn~l:lbis~uwt9'ln .... i !.1 \J '1 nnns·umfJ~2'1§WCJ 6 i !.1

4. l.Y'ruf{}Lfil~ '1 II

5.

d5~~ru&snHru9JLm~ms

N"'....' (2x+ 20)

II

" " x '1 (x-50) '1 !!!MSlnt~ta 6.

N~l,Y' ruf{lt,fil~& f:ll ru £)[1 II

n.

LA = 60° , AB = 6cm , AD = 4cm

2. AD = 4cm , AB = 2.5cm , BD 7.

t!!ltflSUHruf{ll_.fil'tf

=

3.5cm '1

ABCD

II

[CD]

tUb~lJl~ A' sb

c

'1

u ri

11 ~tiH9Jnmriffl'l§ 0

mri

[BC]

Stl

l_.n~ B' sb D' '1 U~(!)Gltl~tfilM A'B'CD' m,ytru~ilJLfil'l§ '1 II

185


"'

9.

0

B

..,

t fi'H1Jl ABC 'tf1 S E Si:l D th tHlJH1 fi ClJTH1H S I lil

8.

tl='l'tflStH'jtfi'HlJltnh ABCE shTIHrn9J1§1i:1 BCDE

'1

ll

u

10.

ifl fD m 15i' nH1Jl A cD mL5' m nn N'i:Hi1 fl '1 Ill ABCD t~rn

tl='l'tflSUfltfilrul I

II

" r munnunnm I

lil

Sl AB

1='1 rul

2.

l='lrulSlflt~tS

" "

=

XY

fi.

x

12.6

Si:l

DC

=

3 '1

DC= 4x-7 , XY

=

2x + 1l

B

AB = 2x+1 '1

1 . tt'i'tflSUfltfilrulmlllN'i:1'Q1fl ABCD t~rn I

"'

sh LA = 67° .,

12.

?'inn

g'i '1

tt'i'tflS ABCD

L.CDE

ill AD= CE

L.CED

=

'1

ABCD UfltfilrultM '1 l ...

.1 [BC] '1 tll:rl mdl BE = DF '1 Ill .......

0

0

L.OCD tn'i:1tl t nm ffi '1 I

186

'-'"'

II

A

;:

C

~

D


o

rHl1lnt~Lni{JlTI5'ru9JLm'iยง

o

nnnnt~u;I{Jlu~'mfl.fl

0

'"

IJ 0

ru

'"

t j:'j m~u;:J nJlJ 131:1 n ttfl

m~ fi nn 21 &~ Ln 1{11

hl13ntm nn &nil ttl ru&Mtl ruj:'j nn ~nil am 115 l

I

'-'o

IJ

1361 tm ru1 &nil ti:l rut24 ;;n~

has gtnsm n~m 115 4 tJ nm 2~

1

I)

ttl'in9nts13ntmrultn~~:sgms~m ,; lJ i.l' l "

8tlnmttl ,;

'I D

"" Lm1:1mnH15

&S"J&fn~j:'jnflS"J

Lni{Jl lswcru9JLm1:19lR9h tlh~an IJ

... run sh ma~ n td'in9n tS13nt mnn &l.J i.l' ~

~

':)

':)

~

fn~ 'I

1

TI5till9JLnl1:1 ABCD uHHl"" IJ l eJ

If'.}

'?

0 Q

cy

13~tm fl.fl tni:l tth ruun 2 &61~ fi ru t~(Jirfn fl.fl (tnHtfl

druj:ifl.fltsHnnhd~mn2hn't1 1 l,j ยฃ'1 I)

'I

I

n~ I'Jtm ru 9JLfil't1th H ~ fi

ru ~ M m ()] tl fi ~ ru

IJ

t9ifnhsh~i:lru.J~ 1

ctfiru~hru.J~tsnmmmmn 'I l

c


.. dln~~Tiltrul{jLfilY ABCD

[AE] ,

tel rulJl

u

tf16'i [DC]

u

dl n~ ~Lm ru

ABCD

.

A

B

.1

llAFD S~ llBEC "!

dj

ru

ABCD

thTI5&

" LADF = LBCE (Y'i6iHil) l

uu

0$

LAFD = LBEC = b =DC= AB

t~Ln~G~tfilrultn~ ABEF

=

t~~~G~tfilrultn~

t~Gn~G~tfilru1£PID

t~~~Tiltrul{jLfilY

ABEF =

ABCD

u

t~:mt~~~TI5tru9JLfilY

bh

= t~~ijlfi~tfilrul

ABCD =

u

ABED+

t~~~~&filrul

ru ABED+ t~~ijl~tfilrul

t~Ln~G~tfilrul

AFD BEC

ABEF = bh

~mag "'t~~~TI5tru9JLfilY ABCD = bh '1 u

: tl:h ruH~E'ilJ~ s~1Ji:ITI5tru9JLfilY m~ nm s~tfil n.n tia~s [1 tmg l~1fijl llJ

" • MnMntl:hru s

=

l

l

llJ

bxh '1

2

: cutmrueJunY

D

fJlt~cru

llJ

ntl\'fsi:l ...

NSi:l ...

Scm

l~Lfi~TiltrueJunY u

l~~~L~tfilrul

188

3cm r;mg

s = 3 x 8 = 24cm 2

S

=

~(3x

;]·:···················...

'1

= 12cm

2

A '1

/

8------~

B

c


muntffttj91: ttl'i:flS ABDF th'UHbl59J

A

JOcm

B

II

Lfi1Ytl:1ru'i:flS AB

fi.

=

lOcm , BD = 7cm

" x '1 t:Hl.fl SHH'H

""

" "" ~. ~nt~U'i!ffl'[!Hfil

n.n AFG

ocrJw: IN

&tlQlS FDxAE

= DBxAC

(t~Lfi!ff!LtHru~LfilY ABDF)

lOxx = 7x9 X

= 7X9 =

63

" ""' ~. ~nt~Lfif{JllJHfilM AFG

dht1tltun

t~1Jif{Jlt!hmn.n AGF u~sl:l 3.15cm '1 2

FE= FD-ED

t~LnijliJhmn.n

t~Ln!ff!L~&mn.n

AFG = = =

1

~titS:! t~1Jif{JlUHfi1M AFG 0

muntittj92 : tlMSlt~Ln~

=

5xl4+5xl4+5xl4

= 3(5xl4)= 3x70= 21

l3

AFE-

2FExAE-3.l5 2l X 2 X 6.3 - 3.15

= 3.!5cm "

= 10-8 = 2cm

2

&

= 3.1

'1

t~Ln~L~tmn.n

AGE


: ABCD

dlTIHru9J1.fll"dtf.Hl5 u

= 9cm, AD= 6cm S~ BK = 8cm '1

'i:ll8 AB ~Hlll

£fl :

ts~tffHl.flt~~dltutrulilJLffl"d

~msg ~~Uiltflts~~:mrult~RruHh~ru

'1

u

a

~

':l>

C1

n

s=

t s g t?inffits?l ru1 m t~tn~trts~ &m ru1 t ~ t~ rut'iY»~ R1J~m hltlm s tr:a '1

'i5

u

1

ms =

'i5 ir1 m U'l

"

xd ' B

~~Lf'iltflu~tfflrult

fflrul

ABCD =

t~Uiltfltfltfflrul

ABD+

sA seD

=

l

t~tnltJl

BDC '1

1

1Ao x BD + 1co x BD

D

= !BD(AO + OC) 2

1 !:!UtS g S u

=

xAC =

1 xd'

xd' B

G%1J~1Yt~~ l3cm s~

?irul£fl~~

14cm '1

u "" tSuRtfflrul&f\.HS"Jg

'>

1

'1

""

D 'i:ll ::::n~~G%'Hi'~~irl n

0

Li

&

u

l3cm s~ 14cm

firul6'Hi:!lli5 S 90

u

=

l

xd"

1 2

=-X

13

X

14 = 9lcm

2

cl

bh '1


~-,

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fH:l

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l

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sb

0

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nn.Jlntf:illi5

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2

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2

= 37.68m '1

50.24cm

2

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2

'1

5

?

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15

(tlnmtd) .::

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