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1 (, 4), (4, ), (, 5), (5, ), (, 6), (6, ) , 50, 0 (,, 0), (, 0, 5), (,, 0), (,, 5), (0, 5, 0), (0, 4, 5) 6, 6, 9 5 5, =5() 5 4 5_=5() 5 5,, =7() =4() 4, 4, 6, 8, 0 5,, 6, =7() (, 5), (, 6), (5, ), (6, ) 4 5(, 6), (6, ) 4+=6() 6 5 4_=(), +=() 6 x=y<6 (, ), (, ), (, ), (, 4), (, 5) 5 x=y<4 (, ), (, ), (, ) x=y< (, ) 5++=9() 7 00, 50, , (,,, ), (,,, ), (,,, ) (,,, ), (,,, ), (,,, ) 6,, =6() 6 () () 5_4 =0() () 5, I.

2 4 (), () 5_4=0() (), () (, ), (, ), (, ), (, E), (, ), (, ), (, E), (, ), (, E), (, E) 0 () 0 () 0, 0 (), E yy(, ) yy(, ) yy(, ) Eyy(, E) yy(, ) yy(, ) yy(, ) Eyy(, E) yy(e, ) yy(e, ) yy(e, ) yy(e, ) () 5_4=0() (), (, ) (, ) () ;!;_5_4=0() (),, 4 6 () 5 y() 4y(4) 6y(6) y() 4y(4) 6y(6) y(5) 4y(54) 6y(56) 4 6 4y(4) 6y(6) y(4) 6y(46) y(6) 4y(64) yy(, ) yy(, ) yy(, ) Eyy(, E) yy(, ) yy(, ) yy(, ) Eyy(, E) () _+_=5() () 5 5 () () () 5 5 () 4 () 6 () 5 () 5 { 0 } { 0 } 4 4 0,,, 4 4,5 4 4_4=6() 6 0yy(0) 0yy(0) yy() yy() 4yy(4) 0yy(0) yy() yy() 4yy(4) 4_4=6() 4,,,, =6(),, 6_=() 5 () K O R, E, () =6() () E E K, O, R, () 4 =4() () 4 E () 4+4=48() () 6 () 48 4 yy() yy() 4yy(4) 0yy(40) yy(4) yy(4) yy(4)

3 ;!;_4_=6( ) () () 0_9=90() () 7 7_6 =( ) () 90 () ( ) ( ) ( ) ( ) ( )_=() () 5 () 5_4_=60() () () () 4 5 () () =8() () 60 () 8 4 { 0 } { 0 } () =8() 5,,,,, 4 4_=( ), =6( ) _4 =0() 0_=40() 40 7,,,, E,,, E 4 4 =4() 4,,, E 4 ;6!;_4 =4() _=6() 4_6=4() 5_5=5(), ;!5!; ;!5!; ;!;_4_=6() (, ), (, ), (, ) ;6#;=;!; ;!;, I.

4 6=4(), (H, H, ), (H, H, 4), (H, H, 6) ; 4;=;8!; ;8!; 4, 6_6=6(), ;b;< a<b a<b _4=0() () () () 4+4+4=() () ;!0@;=;5#; () () () 4+4+=0() () ;!0);=;!; 5 ;!6%;=; ; ; ; () ;5#; () ;!; 4 u, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c} 8, b {b}, {a, b}, {b, c}, {a, b, c} 4 ;8$;=;!; ;!;, 6_6=6() () 5 () (, ), (, ), (, ), (, ), (, ), (, ), (, 4), (, ), (, ), (4, ) 0 () ;!6);=; 8; () 4 () (, 5), (, 6), (5, ), (6, ) 4 () ; 6;=;9!; () ; 8; () ;9!; 4 4_ =6() (, ), (, ), (, ) ;6#;=;!; 5 4++=9( ), ;9#;=;!; 6 6_6=6() x+y<6 (x, y) (, ), (, ), (, ), (, ) 4 ; 6;=;9!; ;9!; _4=6(), =8() 4

5 ; 6;=;!; ;!; = = = = () () () 0 () () 0 ;!; ;6!; 0 ;!; () 0,, 5, 7 4 () ; 0;=;5@; () () () =-( ) () =-;5@;=;5#; () ;5@; () ;5#; 4 () 6_6=6(),, 6 () ; 6; () 5 () -( 6 )=-; 6;=;#6%; () =8() (), ;8!; () () -( )=-;8!;=;8&; () ;#6%; () ;8&; p+q=, 0{p{, p=-q, q=-p 4 =7(),, ( )_=9() ;ª7;=;!; 5 ;!;_;!;_;!;_;!;=; 6; -; 6;=;!6%; 6,, 6 ;!;_6_5=5(),,, (, ), (, ), (, ) ; 5;=;5!; ( ) =-() =-;5!;=;5$; 7 () () (, ), (, ), (, ), (4, 4), (5, 5), (6, 6) 6, 6 () ; 6;=;6!; () I. 5

6 =-() =-;6!;=;6%; () 0, 6, 9,, 5, 8 6, 7 7, 4 7 () ; 0;+; 0;=; 0;=;5@; () ( 7) () =-( 7) () =-;5@;=;5#; () ;6%; () ;5#; ; 0;+; 0;-; 0;=;ª0; ;ª0; 4 8 ;8#; 7 ;7@; ( ) =-( ) =-{;8#;_;7@;}=;@8%; ;@8%; 6_6=6(), 4 (, ), (, ), (, ) ; 6; 6(, 6), (, ), (, ), 0 ; 0; 7 ; 0; (6, ) 4 ; 6;, ; 6;+; 6;=; 6; ; 6; ;@; ;6#;=;!; ;@;_;!;=;!; ;!; _6=8(), _=6() ; 8;=;!; ; 0;+; 0;=; 0;=;!;, (, ), (, ) ;4@;=;!;, 4 ;6$;=;@; ;!;_;@;=;!; ;!;, -;4#; _ -;5$; =; 0; -; 0;=;!0(; ;!0(; 0,7 7, 4 ; 0;,, 5, 7,,, 7, 9 8 ; 0; ;!; -;!;=;@; ;5#; ;!;_;@;_;5#;=;5!; ;5!; 6

7 5 6_6=6(), (, ), (, 4), (, ), (, 5), (4, ), (4, 6), (5, ), (6, 4) 8 ; 6; (, 4), (, 5), (, 6), (4, ), (5, ), (6, ) 6 ; 6; x+y _4=() x+y=4 (0, 4), (, ) x+y=5 (0, 5), (, 4), (, ) ; ;+; ;=; ; ; ; ; 6;+; 6;=;!6$;=; 8; ; 8; 6 ;8%;, ;7$;, ;8%;_;7$;=; 4; ( ) =-() =-; 4;=;ª4; ;ª4; 7 () ;6@; () ;5#; () () _ = (),, () () _ + _ = = () () 5 step =6(), ;6@;=;!; _5=0( ) 6-6 +_5=6( ) ;!0^;=; 5; 4, =7() () 9 7 = 4 () - = () ;!; () ;@; 5 ;7$;_;6#;=;7@; ;7#;_;6$;=;7@; ;7@;+;7@;=;7$; ;7$; 6 6 _6_5=5( ) I. 7

8 E F E F =5( ) 7,, =6() (,, ), (,, ) ;6@;=;!; 8 4 _4=8() 8 9, ;6@;_;8^;=;4!; ;6$;_;8@;=;6!; E ;4!;+;6!;=; ; -; ;=; ; ; ; 0, 4, 6, 8 4 ;8$;=;!; ;!;_;!;=;4!; 4 =4() F E F E F (, ),,, =6(), 6_=() ;!4@;=;!; 0 0,, 4 0, 5_4_=60(), 4_4_=48() 4, 4_4_=48() =56() (,, 8 ), (,, 7 ), (,, 6 ), (, 4, 5 ), (,, 6 ), (,, 5 ), (, 4, 4 ), (,, 4 ) ,,,,,,,,,, 4,,, 4 =4() 4 step x ;@; x =;@;, x=(6+x) 6+x x=( ) P(')=P()+P()-P(;) 0 9= P(;) P(;)=0 8 ;!;_8_7=8(), 5, 8

9 5_=5() ;!8%; 4 6_6=6() 5 (, 4), (, ), (, ), (4, ) 4 6 (, 6), (, ), (, ), (6, ) 4, (, ), (, ) 4+4-=6() 6 =;6!; ;6!; 6 5 a +b }50 a, b (6, 6), (6, 5), (5, 6), (6, 4), (4, 6), (5, 5) 6 6 =;6!; ;6!; 6 6, _ = _ = = = () 5 ;!;_5_4=0( ) () 5 ;6!;_5_4_=0( ) () 0 () 0 (),,, E,,, E,, E, E 0 (),,,,,,, -E E E -E -E E 0 8 ( ) =-(,, ) =-[{- }_{- }_{- }] =- = 0 0 ( ) =( ) 9 =4() =4() =6() =5() 5 0 Q R Q R 6 6, Z, _ =6() (Z, Z, _, _), (Z, _, Z, _), (_, Z, Z, _), (_, Z, _, Z), (Z, _, _, Z), (_, _, Z, Z) 6 ; 6;=;8#; ;8#; =6() 4 ;!;_4_=6() I. 9

10 ; 6;=;8#;, =( ), 5 5 _5_4=0( ) _0=0( ) ( ) =( )_( ) 5_4 =0() (,, 4, 5, ), (,, 5,, 4) ;!;_5_4=0(), 0_=0() 0 = =6() H, T (H, H, T, T), (H, T, H, T), (H, T, T, H), (T, H, H, T), (T, H, T, H), (T, T, H, H) 6 (H, H, H, T), (H, H, T, H), (H, T, H, H), (T, H, H, H) = _4_=6(), 4 _4 =4() = 6 8 ;5@;, ;5#; ;5@;_;5@;=; 5; ;5#;_;!;=;5!; ; 5;+;5!;=;ª5; 6_6=6() ;ª5;, 5a+b 4 5a+b 8,, 6, y a=b= a=b= b=6 a=b= b=5 a=4b=4 a=5b= 0

11 a=6b= b=6 9 ;ª6;=;4!; 4 =6() ;4!; 5a+b 4 4 P, (,,, ), (,,, ), (,,, ), (,,, ) 4 P ; 6;=;4!; ( P ) =-;4!;=;4#; ;4#; P cm 6p cm, 4cm 6p cm, cm 4p cm () =( )-() =6p-4p=p(cm ) p = 6p TTTH, TTHT, THTT, 4 HTTT = 6 4 THHH, HTHH, HHTH, HHHT ; 6;=;4!; + = 4 4,,,, ' '' ' 4, '' () ( ) () 4 8 {,, 4},{,, 4, 8}( ) 8 4() ( ) () ( ) ac=bc a=b () ( c=0 _0=_0, +) a=b ac=bc ( ) II.

12 () () () 4 (), (), 5, 6,,, 5 O O= O OO 80 O+ O= yy O+ O =80 yy, O+ O= O+ O O= O 80 O 80 O O O, ().( ) a<0, b<0 x= > {x x>7},{x x>},,, {,,, 4, 6, }.{,,, 6}, 4 () <90 () (<90, ) () () = =80 x=80-(80+80)=0 () =80-4 =66 = x=66 () = =0 () = =5, = =60 = =5 x=5 = (), = = =80-60 =0 + x+ x= x=80 x=0 () 0 () 66 () 5 0 E= =70 E=80-70 =0 E= =55 4 = = x = + = x = = x 55

13 , E= + 05 = x+ x x=05 x=5 5 ( ) ( ) = = =0 = =80 - =67 = =67 = = =75 = =, = = = =(80 - )_;!;=74 =74 _;!;=7 x=80 -( + ), x=80 -(7 +74 ) = =50 = =(80-50 )_;!;=65, = = =50 x= - =65-50 =5 5 = =70 () = =70 () 5 =80 -( + ) =80 -( ) = = = =70 =80-70 _=40 = =40 x=80-40 _=00 00 MME(RHS ) = =;!;_(80-50 )=65 65 OE =O =OF OF =8cm 8cm 4 E(RH ) =E, =E E = +E =+4=6(cm),, E(RH ) =E =8cm, =E =6cm E = +E =6+8=4(cm) E ;!;_(8+6)_4=98(cm ) () O=90 -;!; () O=90 -;!;_80 () O=50 () OE =O =OF O =5cm 4 () = = =45, EE =, E= =90, E EE(RHS ) E= E=45 _;!;= 5 6cm 98cm () 50 () 5cm E=80 -( E+ E) E=80 -( ) E=67 5 () EE E =E yy =45, E=90 II.

14 4 E=45 E =E, =E =E =6cm E=;!;_6_6=8(cm ) () O O =O =O O= O=40 O= O=0 O= O= x, + + =80 yy () 67 5 () 8cm (0 +40 )+(0 + x)+( x+40 )=80 x=60 x=0 () x= =_55 =0 () O =O =O () O= O=0 () O= O=40 () =0 +40 =70 () x= =_70 =40 M MÚ =MÚ =MÚ =;!;_4=(cm) M MÚ =MÚ =MÚ = M=7 =90 - =90-7 =5 x+ +0 =90 x=48 () O= x () 0 = x x=65 () O =O O=4 () 0 () 0 () 40 5 () O=80 -(4 +4 )= () = xx=56 () O=90 -( O+ O) =90 -(5 +45 ) =0 (), O =O () O= O=0 () x= O =80 -( O+ O) =80 -(0 +0 ) =40 () 65 () 56 () 40 () O= =( O+ O) () O =O () O= O=5 () x= O=_(45 +5 )=40 4 () O =O =O () = () EOEO O =O, EO= EO=90, OE () EO EO(RHS ) () OE= OE () O O(RHS ) () O= O () () O () = =5cm, E =E =6cm, () F =F =7cm () () + + =( +E +F ) =(5+6+7) =6(cm) () () 6cm 5 M =M =M, M = M=6 M= + M =6 +6 =7 7 4

15 6 O O =O =O =0cm O= O = O=96(cm ) _ _;!;=96 =6cm 6cm () I= I= I= I=5 + + =80 ( + )+(5 +5 )+ x=80 x=66 () I=90 +;!; x 5 () 4 =90 +;!; x () ;!; x=4 x=68 () 66 () 68 I, =80 (6 +6 )+(8 +8 )+ =80 =5 F =0cm F =;!;( + - ) 0=;!;(+8- ) 0=50- =0cm rcm = I+ I+ I ;!; 9 =;!;_5_r+;!; r+;!;_9_r 54=7 5r+6r+4 5r, 8r=54 r=(cm) 5 0cm cm 4 E = +E 4 =4+ =7 7,, I 6 4 () x=;!;(5+6-7)= () =F =cm =7cm, F =5cm, =E, F =E x= =E +E =7+5= () ;!;(9+7-x)= () 6-x=4 x= 5 E I =IÚ, EIÚ=E ( E) = +E +E = + +E +E = + =9+7=6(cm) 6 rcm = I+ I+ I =;!;_0_r+;!;_6_r+;!;_8_r () () 6cm =5r+r+4r =r yy =90 =;!;_6_8=4(cm ) = r=4 r= rcm, =;!;r( + + ) 0 I r r r 6 8 yy cm II. 5

16 ;!;_6_8=;!;r(0+6+8) 4=r r= step 60, x, y, x+=x+, ( ) ( a=, b=) ab a+b () ( _=6 +=5 ) () ( ) ()( ) 4 () 5,,, 9 () x=;!;(8+-6)=6 5 () =O =x x=;!;(+5-)= () 6 5 () 0 = () = (), = 80, = =65 =80-65 _=50 E =, E =, E ( SS ) E =, =E= P= P P P =P PEP P =P, P= EP, P= PE PEP(S ) P= PE, P =PE yy yy 50 step O=90 -;!; 6 ( { ª 7 I=90 +;!; =90 +;!;_80 =0 MME(RHS ) = =(80-50 ) =65 65 I'=90 +;!;_0 = = x E= x 0 = x x=40 = = =70 =80 -_70 =40 =80 - =80-70 =0 6

17 =80 -(40 +0 )=0 = = =70 = = =70 =80 -( )=40 = - =70-40 =0 4 =acm, =bcm, =ccm = O+ O+ O 4=;!;a_+;!;b_+;!;c_ a+b+c=4 yy 4cm EF 9 H = H=90 = H, H(RH ) H = =cm =;!;_ _H =;!; =8(cm ) cm H cm 8cm 5 = =;!;_(80-48 )=66 =;!; =, E= + = =4 =;!; E=57 = + = = =80 -( + ) =80 -( + ) =4 6 =90-70 =0 P=;!;_0 =0 ( I ) O O =O P= =0 P=80 -(0 +0 )= = =(80-0 ) =80, O= O=0, I I= I=40 O O= O=0 OI= I- O OI=40-0 =0 8 I I =IE =IF 0, IEF, I 0 E(RH ) =E =7cm E = =cm E =E - =-7=5(cm) E = E=90 = + E=90, + =90 = E,, E(RH ) I=90 +;!; =90 +;!;_80 I=0 5cm yy yy yy E+ =0 yy + =80 yy + + E+ + =0 + =80-80 =00 + E=0-00 =0 + E = E+80 =;!; +80 +;!; +80 =;!;( + )+60 =;!;_ =0 0 II. 7

18 E I rcm E =;!;_4_0=0(cm ) E = I+ I+ I 0=;!;_ _r+;!;_ _r+;!;_ _r 0=;!;_( + + )_r 0=;!;_(6+4+0)_r r=4 I=;!;_6_4=5(cm ) 5cm OO' OO'=0 OO'=0 +0 =60, OO' OO'=60 OO' = I+ I+ I I E(RH ) =E =4cm, E = =6cm E = +E =6+4=0(cm) ( E ) =;!;( +E )_E =;!;_0_0 =50(cm ) = E =;!;_4_6=(cm ) = E-_ =50-_ =6(cm ) 6cm ;!; 7 ;!; cm 0 4cm 6_5_4_=60(), _=9() (, ) (, ), (, ), (, ) ;9#;=;!; , 7 8

19 ; 4;_; ;=; ; 4 5_4 =0() (4 )_=48() ; 0;=;5@; 5, -;5@;=;5#; ;!;_;@;_;5#;=;5!; 6, =8() (H, H, H), (T, T, T) ;8@;=;4!; 6_6=6() 6 ; 6;=;6!; ;4!;_;6!;=; 4; 7 6_6=6() ;[};<;!;,, y<x (, ) (4, ) (5, ), (5, ) (6, ), (6, ) 6 ; 6;=;6!; 8 ;6#;_;6#;=;4!; -;4!;=;4#; 9 0 ( x=-4) { a=;!;, b=} ( a=-, b=) ( a=, b=-) I= b, I= c = b, = c x+ b+ c=80 ( b+ c)=80 - x b+ c=90 -;!; x I y+ b+ c=80 y=80 -( b+ c) y=80 -{90 -;!; x} y=90 +;!; x = = I I= I= EI= I E I= I(), EI= I() IEI E IÚ=E = -E =-8=4(cm) IÚ= = - =-8=4(cm) E = I +EIÚ=4+4=8(cm) I= II IÚ=IÚ, I= I, EI= I IEI(S ) = () = () = = =50 =80 -( ) =

20 4 5 = O =O =O O O 44 O (SSS ) x O= O= O= O= O=;!;_44 = OO Æ =Æ O O =O Ú(O) OO(SSS ) 6 a+b a, b {;!;_;!;}+{-;!;}_{-;!;}=;6!;+;!; {;!;_;!;}+{-;!;}_{-;!;}=;6#;=;!; 7 8 8_7=56( ),, 5, 7 4_7=8( ) ;5@6*;=;!; 8 O, O O= a, O= b a+ b=50 O= a() O= b() x= a+ b =( a+ b) =_50 =00 9 = I+ I+ I 96=;!;_ _4 a O a b a b I b 96=+;!;_ _4+;!;_ _4 96=( + + ) + + =48(cm) 0 I, IE = IE=60 ( ) = IE=60 ( ) IE, I I=;!; =0 I I= IE- I () I=60-0 I=0 I =IÆ =E E =IE =I E =;!; =;!;_=4(cm), 0 5, 5 5_5=5() ; 5;+;!5!;=;!5@; 0 5 0

21 =80 + =80-6 =44 = = = =;!;_44 =7, =;!; =;!;_7 =6 = + =6 +6 =7 4, 4_=() + = ; 5; 7 ;!8#; cm, 6_6=6() 6 (, ), (, ), (, ), (, 4), (, 5) (, ), (, ), (, ), (, 4) (, ), (, ), (, ) (4, ), (4, ) (5, ) = 6 =;5!; 0, 8 4 = _ = ,, 4 ;6#;=;!;, _=4() (H, T), (T, H) = 4 _ = 4 5 ( )_( ), ()= 0 0

22 0,, 4 _=9() 6 p q -p 9,,,,, x-<x+6 x-x<6+ 0<7 -;4#;=;4!;, -;@;=;!; _ = 4 - = 7 0 6, =9( ) ;+u, P(')=P()+P()-P(;) 0 p q q p ( ) () ( ) ab=0 a=0 () ( b=0, a+0) a+b a, b () ( +=4, ) () (,, ) n ( ) ;!;n(n-) I, I =90 +;!; I 4, 6 0_9 =45() 6_5 =5() 5 = 45 I I=90 +;!; I=90 +;!;_80 I=0

23 5 O, O =O =O O SSS SS S O O =O =O O, O, O O= O=40 O= O=0 O= O= x, + + =80 ( x+40 )+( x+0 )+(0 +40 )=80 x=40 x=0 x=;!;(b+c-a) c y=;!;(a+c-b) z=;!;(a+b-c) cm =xcm =;!;(+5-x) 4=7-x x= x b I z y a x cm cm cm cm 5 cm = () = ( SS ) 6 x 5, y 5 5_5=5() x+y>8 y>-x+8 x=,,, 4, 5 x=5, y=4, 5, (5, 4), (5, 5) 5 7 x+y>8 y>-x+8 x=,,, 4, 5 x, y y -() 4 O, E O F _ = = O =O =O O =OE =OF 4 4

24 4 4 =4() 9, 4 _ = = = = = E,, 4 = (), = = 80 (80-60 )+ x+ x=80 x=60 x=0 0 E E(RH ) E = =cm 0 cm E = _ _E = _0_=5(cm ) cm RHS RH, 6 _ = O I 0 cm O R 8 cm I R= _0 R=5(cm) 6 cm, rcm = I+ I+ I _6_8= _0_r+ _8_r+ _6_r 4=5r+4r+r r= 5p+4p=9p(cm ) 4

25 O= O= x + =80 (9 + x)+( y+5 )=80 x+ y=89 + =80, =5 4 =5 x, =4 x 5 x+4 x=80 x=0 = =4_0 = POQO O =O yy OP= OQ() OP= OQ(),, POQO(S ) OP =OQ OPOQ(S ) O =O 4 E =E =8cm E =E - =8-6=(cm) yy yy cm () E= E (), () E= E= E=56 () = = () =80 - =68 () () y=80-(0+5)=5 () = x=0 () E () E= E yy (), () E= E() yy (), E= E () E () E = =5cm () x= -E = -E =8-5=(cm) () x=68 () x=0, y=5 () x= () x= -H =9-=6(cm) () y= -F =7-=5(cm) () EPG () a= =80 (), b= GPF( ) ( EF ) () b=80 - a=80-80 =00 () x=6, y=5 4 E= E() E= E= E () a=80, b=00 E =E E = =cm = =E +E =+=5(cm) 5cm 5 E E =E, E= FE() F E= FE() EFE(S ) =F, = =F = F = +F = + F =7_=4(cm) 4cm O =O, O +O III. 5

26 P+ P=;!; OP+ OQ=;4!;_00 P+ P=;!;_8_5 OP+ OQ=5(cm ) 5cm P+ P=0(cm ) P+4=0 P=6cm 6cm, O =O yy, O =O yy E =F yy - O -E =O -F OE =OF yy EF F= = O =_0=60(cm ) F= =4 O =4_0=0(cm ) = = O=_0=60(cm ) O= O=0(cm ) FE= =_4 O =_4_0=40(cm ) 4 E, =E E 5 MPNQ=;4!; O= O=;!; O=;!;(80 - ) O=;!;(80-70 )=55 55 O =O = = = = =, = = = = = () = = 0=;4!; =40cm 6 OPOQ PO= QO(), O =O, 40cm 4 5 EFGH HEF=90 90 OP= OQ() OP OQ(S ) + =80 OP= OQ OP+ OQ= OQ+ OQ OP+ OQ= O OP+ OQ=;4!; E+ E=;!;( + ) E+ E=90 E E=80-90 =90 6

27 HEF= E=90 6 E E E = =;!; =E =;!; E = -E =;!; yy yy, =;!; () yy,, E =E = E = E=60 E 60 5 () HFH =, F = () =F yy (), HF= H() yy () H= FH() yy (),, () HFH(S ) () H =H () = () =H yy () () GEG(S ) () G =G =G yy (), =H =G =HG () GH () GH, FPE=90 () FPE=90 FPE () () 90 () R Q R;Q=P () () () (4) () =6+5=(cm) x= () = () = =6 () =80 -(6 +6 )=08 () =80-08 =7 x=7, () () +70 =80 () () =80-70 =0 x=0 () 5 cm () 6 cm E E 60 6 cm E 5 cm x cm E =6cm () 0 () () 7 4 =4_ O =4_;!;_4_ =4(cm ) 4cm = + = + E =8+6 =4(cm ) 4cm FF F F= F=6cm 6cm P PP P= P E= E= E= E E III. 7

28 E= - E = E- E =7-8 =9(cm ) = = 6=, =cm, =4cm =;!;_4_4=8(cm ) 9cm 4 O =O ==, =, E E= =8cm 4 E E = E = 5 E = 5 8cm, EE= 5 E= 5 E=60 E=0cm 5 hcm 0_h_;!;=60 h=6 =;!;_(0+0)_6=90(cm ) 0cm O= -( + O) =90-(60+0) =0(cm ) 0cm 6 E= E EF E= F F= F 5,, 6 Q R 7 O =O, O =O =90, 8 =, 9 P P+ P = P+ P + P=4+6 P=8cm, P 8cm step =, = 7=x+y, 9=x-y x=, y=- x+y=, 0 E= EF= E() E = =cm E = -E =8- =6(cm) FE= =;!; EF=;!;_6 EF=8(cm ) 8

29 ( 4) 8cm step () 90 () () (4) (5) 90 () () () (4) (5) E= E() = E() E = =7cm E = -E =-7=4(cm) = = x= x =, =, 80 x+ x=80 x=6 = = x=_6 =08 = = x=_6 =7 = =08, = =7 4 H=40 ( ) + =80 () =80-80 =00 60 HE+ E+ E+ H=60 E=60 -( ) E=0 0 5 PMPMQ= M MQ 6PMQ= PMQ=8 PMQ=9cm, P Q P= QP PM= P+ PM = QP+ PM = PMQ =9(cm ) 6 E E= = + = + E = E =;!; 6 =6(cm ) 7 E= E() E= E 9cm 6cm E EF= F= x = x, + =80 x+56 =80 x=6 8 + =80 =80 _;4#;=5 E=;!; E=;!;_5 E=45 =80 _;4!;=45 E= E+ E = = O =O =cm OO O=0 = =60 = =60 = = =4cm 0 OEOF OE= OF=45 O =O 4cm III. 9

30 OE=90 - EO= OF OE OF(S ) ( )= OE+ OF = OE+ OE = O ( )=;4!; ( )=;4!;_8_8 ( )=6 6 Q= Q( Q ) PQ Q= P( ), Q= P yy yy, P P = PP= =60cm =0cm P=0_;!;=0(cm ) Q=0cm P =E E =, E =P, E= P=90 EP E =P yy E= P yy, PQ=45 P+ Q=45 yy, EQ= E+ Q=45 = QP yy EQPQ Q,, EQPQ(SS ) Q= QP =80 -( )=80 O =O, O =O 45 0cm 55 P E Q 80, PQRS OP =O -P =O -R =OR OQ =O -Q =O -S =OS PQRS O =O, O =O OP =OR OQ =OS + =80 =80-76 =04 P=;!; =5 P=80 -(90 +5 )=8 = =76 x= P= - P =76-8 =8 8 P P x E = E E= + E = + = =50cm 0

31 , = E=5cm O=cm OE= E- O =5-=4(cm ) 4cm = E E= OE ( ) ( ) ( ) ( ) ;!; ;9$; () 'Ú' 8= () '= =80 -(5 +7 )=90 () 'Ú' = 9 'Ú' = 'Ú' =8 'Ú' =6cm (4) 'Ú' = 0= =0 =5cm (5) ;#; () () 90 () 6cm (4) 5cm (5) ;#; 'Ú' 'Ú' = 'Ú' =4 5 x=4 5, 4x=0 x=;%; 'Ú' =4 5 y=4 5, 4y=5 y=: 4 : E 'ÚE' =4 5 6 z=4 5, 4z=0 ( ) z=: : ( ) x+y+z=;%;+: 4 :+: :=: 4 : 'Ú' =O 'ÚO =4 6= =x 9 x=6 ;; 4 ;; O O O O =5 y y=: : x=6, y=: : =64 GH =4 7= FG = =FG EH = 0 EH = EH =5cm () IV.

32 () 4 () 4=x 8, 4x=4 x=6 () () 4 () 4 () 6cm () (), ( ') () ' = 4 (4+ ' )= (4+ ' )= ' =cm () = ( '''') ( '''')=8cm () ( ') () cm () 8cm = 6 =(+x) 6 +x= x=9 () = ª ( ) 6 x +x = 5 =x 5 x=5 x=: : () 9 () : : () E = E=65, ª E( ) () EE E= E() E E = 4= E E = 6=, Eª E(SS ) () = () ª E ª ( ) () Eª E SS () =6 4= =9 6= ª (SS ) () E = E ª E( ) () E E =9 6= E =6 4= =9 6= ª E(SSS ) () = E=65 () ª (SS ) () ª E( ) () ª E(SSS )

33 = E() ª E( ) () =0 4=5 () = =60 (4) a b 5 a b=5, a=5b a=;%;b () () 5 () 60 (4) a=;%;b () Eª F 8 cm cm F 4 cm E E 4=8, E = E =: :cm () E, F () : :cm () ª E( ) E = E 0 x=8 4, 8x=40 x=5 () ª E( ) E = E 4 x=6 0, 6x=40 x=: 4 : () ª ( ) = 5 4=x 5, 4x=5 x=: 4 : (4) E 6 x 8 E 5 4 =x_5 x=: 5 : 5_y=_4 y=: 5 : x+y=: 5 :+: 5 :=: 5 : = + =6+64=00 : 5 : =0cm 6=0_x x= 6 64=0_y y=6 4 6 ;]{;= =;ª6; ;ª6; E =6 8= = 6= ª E(SS ) 6 8=x 5, 8x=80 x=0 () 5 () : 4 : () : 4 : (4) 0 4 () EEF E, E= EF( ) Eª EF( ), FEF F= FE() F= EF() Fª EF( ) =H =x_6 x=9 y =x_(x+6)=9(9+6)=5 y=5 x=9, y=5 () = + x =44+5=69 x= () H = H=90 ª H( ) H= H x=40 () () 40 IV.

34 4 () HH H= H=90 + H=90 + H=90 + =90 H= Hª H( ), H H= =90 Hª ( ) () H =H _H 4 =x_ x=8 y =x_(x+)=8_(8+) y =900 y=0 () H, () x=8, y=0 5 () ª KHª Kª H ( ) 4 () 5 6 K ª KH K = H 5 0=6 H 5H =0 H =8 () 4 () 8 0 H () 0 y= 6 () y=60 () y=5 () x=, y=0 () x=4, y=5 6 4=x (-x) 4x=6(-x) 4x=7-6x 0x=7 x=: 5 : : 5 : 8 (5-x)=4 x 4(5-x)=8x 60-4x=8x x=60 x=5 5 4 Q R Q =RF Q 9=RF RF =cm EF =ER +RF =9+=0(cm) E 6 cm cm 9 cm 9 cm R F Q cm 0cm () 4 x=6 4 () 6x=6 () x= () y 0=6 4 () 4y=480 () y=0 () 8 x= 6 () x=48 () x=4 () x (x+)=6 8 6(x+)=8x, x=8 x=9 7 5 y=6 8, 6y=60 y=0 () 5 4=5 5 x, 5x= x= =6 y, 5y=4 y=4 8 E = 0 E =5, 5E =0 E =6cm () 4 6=6 x, 4x=6 x=9 () x=9, y=0 () x=4.4, y=4.8 6cm 4

35 () 4 x= 5, x=0 x=: º: () 9 6=0 x, 9x=60 x=: º: () 9 6=y 4, 6y=6 y=6 () x=9 () x=: º: () x=: º:, y=6 4 5=6 P, P =0 P = _4+9_ EF = =: 6 :=7(cm) 7cm +4 6=PF PF = EF =EP +PF EF =6+ EF =7(cm) 6 () PP, P= P() P= P() Pª P( ) =P P = 6= P =PH =PH PH =6 PH =cm () P = =9 H H =9 H =cm _6 () PH = =: 9 :=(cm) +6 _9 () H = =: 9 :=(cm) +6 E 4 P cm 9 cm H () cm () cm P F =xcm, =(0-x)cm = 9 6=(0-x) x 9x=6(0-x) 5x=60 x=4 4cm =xcm, =(7+x)cm = 8 =(7+x) x 8x=(7+x) 5x= x=: 5 : : 5 :cm = 8=6 4, 4 =48 = = 5 =( +6) 6 ( +6)=0, +6=0 =4 4 = = =7 4 4 =8 6 =4 4 =_ =(cm ) cm 4+ 5 = 8 4=4 =cm =6cm =E E 8 4=(6+E ) E 4+4E =8E E =6cm IV. 5

36 () x=;!;( - ) () x=;!;(0-6)= () 9 () MÚP =;!; =MÚP =_=6(cm) NQ =;!; =;!;_6=(cm) cm 4 PQ =;!; =;!;_0=5(cm) PS =;!; =;!;_8=4(cm) E F MFEM (S ) F =E F M cm E (5+4)_=8(cm) 8cm () P, S, PS, PS =;!; yy F =;!;_ =;!;_=6(cm), Q, R, E =6cm 6cm () x=;!;(6+)=;!;_8=9 () x=;!;(4-6)=;!;_8=4 () 9 () 4 QR, QR =;!; yy, PS QR, PS =QR, PQRS 5 E, F, x=_7=4,, E E =E EF =;!; F, G, FG =;!; y=;!;_=6 x=4, y=6 = EF =FG EFG M, N, =MÚN =_6=(cm), P, Q, PQ =;!; =;!;_=6(cm) RQ =PQ -PR RQ=6-=4(cm) () MÚN =;!;( + ) 7=;!;(5+x), 4=5+x x=9 4cm 6 () E G, E =G EG, H F, H =F FH PQRS PH =a S S =a R RS =S =a PQRS QP =RS =a 6

37 P Q =QP =a Q QP PH =a a a Q QP PH = PQ =;5@; H =;5@;_=: 5 :(cm) PS =;5@;G =;5@;_=: 5 :(cm) PQRS {: 5 :+: 5 :}=0(cm) () H F FH, FH=;!; H=;!; FH H=;!; ;!; H=;4!;, H PH =5 PH=;5!; H PH=;5!; ;4!; PH=; 0; E, F, G, H, PQRS PH= QE H P E S Q G R F = RF= SG= Q QP PH = S SR RF = P PS SG = R RQ QE = PH =;5!;H, RF =;5!;F, SG =;5!;G, EQ =;5!;E fi H= E= F= G fi H=;4!; fl P= Q= R= S fl P= PQRS=;5!; 4 PH=; 0;_60 PH=(cm ) () P=;5$; H PH=;5$; ;4!; PH=;5!;, P= Q= R= S PQRS= -4 P PQRS= -4 ;5!; PQRS=;5!; PQRS=;5!;_60 PQRS=(cm ) () 0cm () cm () cm =;5!; 4 P M P=;!; M M= M = M=4 P 8=4 P P=7cm M M = M = M =6cm G =;@; M =;@;_6=4(cm) M =M =M G G= G= G G=;!; G=;!;_6=(cm ) 7cm 4cm M cm IV. 7

38 4 =PQ =_6=8(cm) MÚN =;!; MÚN=;!;_8=9(cm) 9cm 6 () OQ =;6!; =;6!;_=(cm) () P PO=;6!; =6 PO PMO=;!; =;!;_6 PO PMO=_=6(cm ) () cm () 6cm G = M =E =_9=8(cm) G =;@; M =;@;_8=(cm) G 'M =;!;G G' =;!;_0=5(cm) G M =G G' +G 'M =0+5=5(cm) M =G M =_5=45(cm) GG'=;@; G GG'=;@;_{;!; } GG'=;@;_;!;_{;!; } cm 45cm 5 Eª E=6 6=4 6 E 4 6= 6 =, =8 =9cm 9cm GG'=;9!; GG'=;9!;_6 GG'=4(cm ) ª ( ) =4 6= = =4 9 =4 (9-4)= G G=90, G' M G G M = M = M =;!; =;!;_8=9(cm), G G' =;@; G M =;@;_9=6(cm), G G =G M =_9=8(cm) G' =G +G G' =8+6=4(cm) 5 E =E =F =F EF =;!; =;!;_=6(cm) GG'EF GG'ª EF(SS ) G E = G G' EF = G G' 6=, G G' = G G' =4cm 4cm 4cm 7p 64p=7 64= = '' = '' 8000 = _ 5 = =0000cm=00m 00m ª ''' '' =80m cm=8000 = OO OO=O O =0 0= O=;@; =;@;_60=40(cm ) 8

39 , Oª O OO= = 4 O=;4!; O=;4!;_40=0(cm ) O=40cm, O=0cm () xcm () =8 7 () 8 7=x 8 () x=4 () () x=5 () m n x () m n =54 8=7 64 = 4 () m n= 4 () 4 =9 6 () 9 6=7 x () x=48(cm ) () 4cm () 5 () 48cm m=00cm00cm, 5cm 00 5=0 0 = () 8000 () S () S=400_600=40000(cm ) () 40000cm =4m () : º:m () 4m () S=4_6_00 =40000(cm ) () 40000cm =4m 4, =7 8 xcm 7 8=08 x x= cm 5, (+), (++) = 8 7 = (8-) (7-8) = (V-''') (V-) 8 = '''= =4 9 ''' 6cm 6=4 9=6cm 7 9 6cm step, m. m 8 m () xm () x=8 8 () x= =: º:(m) () ()=( ) () () 4cm () 4 =400(cm) 00 () 6cm () 6 =600(cm) 00 MN Oª NOM( ) NM =O MO =6 4= M =M MO O = (+5)= 7 OMNª O( ) MO O =MN 7=4 =4 4 '' = IV. 9

40 O O' = O ' = (-)= '' O= O'' OO''= ', ', ', ' O,, 5 () 0 x= 8, x=80 x=: º: () M ÚN = NM (), ENM () E= NM, () Eª NM( ) () (+x)= 6, (x+)= () x= () Eª ( ) () E =E () 0 50=8 =45 (), FE () F =E () x= -F = -E =45-8=7 () : º: () () 7 6 = =8 0=4 5 = =4 5 7 RPQR = Q=90 R= PRQ() Rª PQR( ), PQ =R QR ( +0) 6=0 =0 +0=60 =40m 8 P=;6!; =;6!; =;!; P=, P = 40m P = P =4cm 9 Oª O, =9 8= O = O =EO =EO 9 EO =6cm, O = O =OF =OF 9 OF =6cm EF =EO +OF =6+6=(cm) 0 = = E = GE = GE 4= GE GE=cm Oª O = OO= O=7cm O 7=4 9 O=cm, OO=O O = = O=;#; O O=;#;_=8(cm ) = O+ O =+8=0(cm ) '''ª """ O' O" =0 8=5 4 '' "" =5 4 '' 4=5 4 '' =5cm 4cm cm 0cm step E E E= E 5cm 40

41 E=;!; E=;!; ;!; E=;4!; =;4!; G E=;4!; 4= = G E=;4!; G =G G =4_=4 G =, M M =M = M =;%; (), G =H M =H ;%; H =4_;5@;=;5*;(cm) FG =G -F FG =;@;H -;!;H FG=;6!;H H =6FG =6_=(cm) F =;!;H =;!;_=6(cm) 7 = = 5 E = 5 E= 5 =9 5=: : E=: :-=: :, E EE E=: :_;8%;=: º: : º: 8 E E = = 4 G =acm, FG =xcm E EG E =GF (6-a) 6=x 9 6x=54-9a, G =GF a 8=x 8x=a 6x=54-_8x, 0x=54 x= 8 yy yy 5 = _6=0( ) =;#; F F =E E = F =;@; F =;@; =;@;( + ) F=;@;{;#; + } F=;@;_;%; =;%; F = 5 9 G G= G= G=;!; EG=;!; G EG=;!; ;!; EG=;6!; FG=;6!; 6, E, E Fª H, F =FH =;!;H G =;@;H ( EGF )= EG+ FG ( EGF )={;6!;+;6!;} ( EGF )=;!; ( EGF )=;!;_0=0(cm ) 0cm IV. 4

42 0 PM PM= =4 ( ) PN PN= =80, PN=00, PMN PMN= PNM PMN=;!;(80 - MPN) PMN=;!;(80-4 ) PMN=;!;_8 =9 4 5 P R RQ ª RQ 9 4, RQ=9 4 Q 6RQ=9 4 RQ=6cm, RQ QP PQ=;!;_ RQ PQ=;!;_6=8(cm ) P EF Pª PEFª P EF =;!;(4+6)=5(cm) 9 8cm PPEFP=4 5 6 =6 5 6 PEFEF = P ( PEF- P) ( P- PEF) =6 (5-6) (6-5)=6 9, EFEF=9 9 =8EF EF=cm E R P 4 cm 6 cm P F cm = =8 = =0_;5#;=6(cm) =0_;5@;=4(cm), E, E= Eª ( ), =E 6 0=E 0E =7 E =7 cm 7.cm, Eª =E E G G=;!; G=;!;_;!; G=;!;_;!;_60=0(cm ) GEG GEG=GE G = 5 GE=;5@; G=;5@;_0=4(cm ) 4cm G=;!; =;!; G GEG GE 4

43 = E () ª E (SS ) EF E EF, _E 00_0 = = =50(cm) EF 8 5m.5m 8= =8 7 x 8 7=6000 x x= M, M M= M= M M= M= M 80 + =80 M+ M= M+ M M+ M=;!;( + ) M+ M=;!;_80 M+ M=90 M=80 -( M+ M) M=80-90 M=90 M cm 8 0cm 9 9cm 0 90, =, =,, =, = =7 H H=;!;_7 =6 H=54 E= E=54 E=80-54 =6 4 5 O =;!; =;!;_4= E OE =;!; O =;!;_=4 6 : = :E =: 8 E E= F FE= F () FEª F ( ), F :F =E : (6-x) : x=6:0 6x=60-0x 6x=60 x=0 9 E E = E = + = + E =8+0 =8(cm ) 0 P, P+ P = P+ P P+ P=;!; 0+ P=;!;_50=5 P=5-0=5(cm ) P 4

44 E =; ;=;!; =; 5;=;!; Eª (SS ) 4 = E =6 = =8cm ª ( ) = 4 = 4 =6 =8cm Eª ( ) =E 4 8=5 (4+ ) 6+4 =40 =6cm 4 : 4=x 8 x=4 : 4=(y-6) 6 y=9 x+y=4+9= 7 E+ E=;!;( + ) E+ E=;!;_80 =90 =, ª ( ) = (4+x) 6=6 4 4(4+x)=6, 4x=0 x=5 (4+x)cm 8 = M, M= N = 5=0(cm ) 9 E = E= = 4 E 6= 4 E=9cm 6 cm 6 cm 4 cm 5 = _ =9_4=6 =6cm M = M = M =;!; =: :(cm) M =H M 6=H _: : H =6_; ;=;&@;(cm) 0 HFH H= HF H= FH =F H FH (S ) H =H = =H =HG =G, GH 90 EPF=90 P G H E F 6 EFGH HEF=90, E E=90 E+ E=90 + =80, E=;!;, E=;!; H E G F 6 0= 5 5 =7 5 7 (5-7)=7 98 cm 44

45 ;!;p_ _6=8p(cm ) xcm 7 98=8p x 7x=764p x=:;!(:^;p P, P+ P = P+ P P NM M N, M =N, =90, = M MN NM P= PN= PNM= PM PNQM= PNM PMQM=_;4!; NM P+ P=;!; P+ P= P+ P 9+ P=5+0P=6cm, PMQM=_;4!;_6_6=8(cm ) NM, MN PNQMPNM PNQM P.Q.R.T, P.Q.S.T R();S( )=T() cm 7 7cm 8 cm 9 8cm 0 cm O 45

46 = =0 () = =65 () OO O=0 +65 =95 O x+ y=80-95 =85 5 = (x+4) 8=8 4 4(x+4)=64 x= 8 m n m n m n m n 7 64 m n =7 64= 4 m=, n=4 4 =9 6, =, = + =80 + =80 6 9,, 7 '''', O O 'Ú= = ''' Oª O'' O= O'' ' ' ' ' = '' = =_=6 8cm 4cm (x+4)cm 8cm, = ª ( ) 0 l m n a b=a' b' a' a b b' 4 =x (-x), x=4(-x) 7x=48 x=: 7 : l m n 46

47 =, = =, 5 = 6 4=, 6 = =cm PMPMQ= M MQ 6PMQ= PMQ=9cm P Q P= QP PM= P+ PM = QP+ PM = PMQ=9(cm ) ª ª Eª E E 6 ª ( ) G G G M = G M =;!; M M G 80 G 'M =;!; GG ' =;!;_4=(cm) 80, G M =GG ' +G 'M =4+=6(cm) = =80 _; 0;=6 M =G M =_6=8(cm) 7 a+ a=80 a=8 =7 a=7_8 =6 4 a 7a a 7a =, =90 = 7 c =ax b =ay h =xy a =b +c ah=bc c x a h y b = O =O, O =O, =9(9+ ) 9 =6 =7cm 47

48 8, M, N,, MN =;!;( - ) M N =8 7, xcm 8 7=6 x x= =8(cm ) 9 PQ =;!;( - )=;!;(4-0)=(cm) E E =E E E= E, yy E= E() yy, E= E E =E =8cm 0 ab x= a+b y= ac a+b 6x =xcm = x+6 (x+6)=6x, 4x= x= a y x c b MÚN =;!; P =PQ =Q Q P N O M =MN =_8=6(cm) M M, O =O O P P PO = yy Q Q QO = yy, P =PQ =Q P =;!; =;!;_6=(cm) m n m n P Q P P 48