#(001~019)Çؼ³

Transcription

1

2 = = = _2= _6= _3= (2_2)_6= _3_2_1=24 4_3=12 4_3_2= _1=2 2 2_2= _2_1= _2= _2_1=6 3_2_1=6 6_6= _4= _4_3= _4= _4_3= =

3 = _4=20 5_4 112= _3=12 4_3 112= _4_3=60 5_4_3 1111=10 3_2_ (1 3)(2 2)(3 1) 3 5 (1 4)(2 3)(3 2)(4 1) = = (1 5)(2 4)(3 3)(4 2)(5 1) = (1 5)(2 6)(5 1)(6 2) = _2=6 2_4=8 6+8=14 003

4 _4= _5=25 8_5= _3= = _2_2_6= _3_3= _2_2= _3_3_3= _3= _6= _4= _4_3_2_1= % 50 % _3_2_1= _3_2_1= _5_4= _9= _4_3= _4_3= _2_1= _3_2_1= _3= % 2 5 5_4_3_2_1=

5 _2= _2_1=6 2 6_2= E 4 4_3_2_1= % 20 % 2 2_1=2 3 3_2_1=6 2 2_1=2 2_6_2= = _6_5= _4= _3_2_1= _6_5= _4= % 20 %

6 _4=9+32= _6= _4= _4= = _9_8= _5_4= _3= _3= _8_7 1111=84 3_2_ _5 112= _6 112= % _3 112= _4_3 1111=10 3_2_1 6_10= _9 111= _5 112= _6_5 1111=35 3_2_1 006

7 _4 112= _7_6 1111=56 3_2_ = step_1 step_2 step_ k k 1 x+y = k k = step_1 step_ _4_3 1111=10 3_2_ step_3 5 1 step_ = _3 112=6 2_ = _4_3_2_1=120 E 4 4_3_2_1= _2= = _4 112=

8 5 2 5_4= _3= _2=6 2 3_2=6 3 3_2=6 1, y, 2, y, 3, y ( { 9 ( { 9 ( { _6_5 1111=35 3_2_ _3_2 1111=4 3_2_1 35-4= = P 3 P 3 3_3= _2_1=6 3_3_3=27 27-(3+6)= _4_3_3= _2_1=6 3 3_2_1=6 6_6= =72 10 % y y _3 112=6 y 2 2 2_1=2 008

9 6_2= _3_2_1= _2= = n n 2 n(n-1) 1111=21n(n-1)=42=7_6 2 n= _3 112= _8 112= _36= (0 0 3)(0 1 2)(0 2 1)(0 3 0) (1 0 2)(1 1 1)(1 2 0) (2 0 1)(2 1 0) (3 0 0) y=ax y=-x+b x 2 2a=-2+b b=2a+2 ab (a b) (1 4)(2 6) _4 112= _2= %

10 _6=36 (1 1)(2 2)(3 3) (4 4)(5 5)(6 6) 6 ;3 6;=;6!; 36 6 ;6!; 3 (1 2)(2 1) 2 ;3 6;=;1 8; 1-;1 8;=;1!8&; ;1 8; ;1!8&; _2_2= ;8!; 1-;8!;=;8&; ;8!; ;8&; ;6@;=;3!; ;6#;=;2!; ;3!; ;2!; ;1 0;=;5@; ;1 0;=;5!; _6=36 4 (1 3)(2 2)(3 1) 3 ;5@;+;5!;=;5#; ;5@; ;5!; ;5#; ;3 6;=;1 2; 5 (1 6)(6 1) 2 ;3 6;=;1 8; ;1 2; ;1 8; ;2 0;=;5!; ;2 0; ;5!;+;2 0;=;2 0; ;5!; ;2 0; ;2 0; ;2!; 3;6!; ;2!;_;6!;=;1 2; ;2!; ;6!; ;1 2; ;4#;=;4!; ;4!; _6= ;5@; ;7#; 010

11 5; ;7#; ;3 5; x+2y<6 (x y) (1 1)(1 2) (2 1)(3 1) 4 ;3 6;=;9!; ;9!; 0110 ;4#;_;5$;=;5#; ;5#; 0111 ;4#;_;3!;=;4!; ;4!; 0112 ;1 0;_;1 0;=;10(0; _4_3_2_1= _2_1=6 ;12^0;=;2 0; ;1 0;_;9@;=;1 5; ;10(0; ;1 5; = = ;8#;_;8%;=;6!4%; ;1 6;=;4!; ;8#;_;7%;=;5!6%; ;6!4%; ;5!6%; _4 121= ;6$;_;6@;=;9@; ;6$;_;5@;=;1 5; _6=36 3x+y=9 (x y) (1 6)(2 3) 2 ;3 6;=;1 8; ;9@; ;1 5; 0115 ;8$;=;2!; ;8@;=;4!; ;2!;+;4!;=;4#; ;2!; ;4!; ;4#; ;1 0; _5_4_3_2_1= (5_4_3_2_1)_2=240 ;7@2$0);=;3!; _5= % 20 % ;3!; ;3 0;=;5!; ;5!; _2_2=8 1 3 ;8#; 0124 ;2!; 0 1 ;6!; _6= p+q=1 p=q2p=1 p=;2!; 011

12 p=1 p= _6=36 3 (1 2)(2 1) ;1 1; _2_2_2=16 1 ;1 6; ;1 6;=;1!6%; _6=36 (1 1)(2 2)(3 3) (4 4)(5 5)(6 6) 6 ;3 6;=;6!; 1-;6!;=;6%; 0129 ={ } 9 ;a@; a 12 2 ;9@; ;a@; 1-;9@;=;9&; _6 121 = _2 121 =3 2 2 ;9&; 20 % 20 % 20 % ;2 1;=;7!; 1 =1-2 =1-;7!;=;7^; ;7^; ;3 6; 8 (2 6)(3 5)(4 4)(5 3) (6 2) 5 ;3 6; ;3 6;+;3 6;=;3 6; 0132 ;1 5; ;1 5; ;1 5;+;1 5;=;1!5);=;3@; _6=36 1 (1 2)(2 3)(3 4)(4 5) (5 6)(2 1)(3 2)(4 3)(5 4)(6 5) 10 ;3!6); 3 (1 4)(2 5)(3 6)(4 1) (5 2)(6 3) 6 ;3 6; ;3!6);+;3 6;=;3!6^;=;9$; ;9$; _6=36 ax-b=0x=1 a-b=0 (a b) (1 1)(2 2) (3 3)(4 4)(5 5)(6 6) 6 ;3 6; ax-b=0x=2 2a-b=0 (a b) (1 2)(2 4) (3 6) 3 ;3 6; ;3 6;+;3 6;=;3ª6;=;4!; ;4!; ;6$;=;3@; ;6#;=;2!; 10 % 012

13 _ =;4!;_{1-;3@;}=;4!;_;3!;=;1 2; 0136 ;3@; ;1 2; % 20 % 20 % 0141 ;4#;_{1-;5$;}=;4#;_;5!;=;2 0; {1-;4#;}_;5$;=;4!;_;5$;=;5!; ;6#;=;2!; 3 ;2 0;+;5!;=;2 0; ;6@;=;3!; 4 ;6#;=;2!; ;2!;_;3!;_;2!;=;1 2; 0137 _ ={1-;3@;}_{1-;2!;} =;3!;_;2!;=;6!; 0138 _ =;3@;_{1-;4!;} ;1 2; 0142 ;1 0;_{1-;1 0;}=;1 0;_;1 0;=;1 0 0; {1-;1 0;}_;1 0;=;1 0;_;1 0;=;1 0 0; ;1 0 0;+;1 0 0;=;1 0 0;=;5@0!; % ;1 0;=;5#; =;3@;_;4#;=;2!; ;1 0º0;_;1 0º0;=;5$;_;5$;=;2!5^; ;5#;_{1-;5#;}=;5#;_;5@;=;2 5; {1-;5#;}_;5#;=;5@;_;5#;=;2 5; ;2 5;+;2 5;=;2!5@; 0140 ;2!5@; 50 % 50 % 0144 ;4!;_;4#;_;4#;=;6ª4; x ;6!; ;4!;_x=;6!; x=;3@; ;4#;_;4!;_;4#;=;6ª4; ;4#;_;4#;_;4!;=;6ª4; 013

14 ;4#;_;5$;=;5#; a+b ab a b ;3@;_{1-;4!;}=;3@;_;4#;=;2!; a b {1-;3@;}_;4!;=;3!;_;4!;=;1 2; ;2!;+;1 2;=;1 2; ;1 2; 0146 {1-;4#;}_{1-;3!;}=;4!;_;3@;=;6!; 1-;6!;=;6%; ;5@; 0151 ;6$;_;5@;=;1 5; ;6@;_;5#;=;5!; ;1 5;+;5!;=;1 5; % ;5@;_;7#;=;3 5; ;1 0;=;1 0;=;5#; ;5#;_;5#;_;5#;=;1 2 5; ;5#;_;7$;=;3!5@; ;3 5;+;3!5@;=;3!5*; ;3!5*; 1-;1 2 5;=;1ª2 5; 0153 ;2!;_;1 0;=;5!; 0148 ;2!;_;6@;=;6!; ;5!;+;6!;=;3!0!; ;3!0!; {1-;3@;}_{1-;4#;}_{1-;5$;}=;3!;_;4!;_;5!;=;6 0; 1-;6 0;=;6%0(; ;1 0;=;5!; 4 ;1 0;=;5!; ;5!;=;5$; ;5$;_;5$;_;5$;=;1 2 5; ;5!;_;5!;=;2 5; 0155 ;1 0;=;5@; 1-;1 2 5;=;1 2 5; ;1 0;=;5#; 0150 ;5@;_;5#;=;2 5; 0156 ;7#;_;7#;=;4ª9; 50 % 50 % 014

15 1-;4ª9;=;4$9); ;4$9); % 0157 ;5#;_;4@;=;1 0; ;5@;_;4!;=;1 0; ;1 0;+;1 0;=;1 0;=;5@; 3_3_3=27 3 ;2 7;=;9!; 0158 _ 3 ;2 7; =;1 0º0;_;9@9);=;9!9^; 0159 ;7#;_;6@;=;7!; 1-;7!;=;7^; 50 % 50 % ;7^; ;2 7; + + =;2 7;+;2 7;+;2 7;=;2ª7;=;3!; ;9!; ;3!; ;8#;_;7%;=;5!6%; ;8%;_;7#;=;5!6%; ;5!6%;+;5!6%;=;5#6);=;2!8%; ;2!8%; 1 3 ;6@;=;3!; 2 ;3@;_;3!;=;9@; 4 ;3@;_;3@;_;3@;_;3!;=;8 1; _3_3=27 ;9@;+;8 1;=;8@1^; 3 3_2_1=6 3+6= ;2ª7;=;3!; 3 20 % _3=9 4 3 ;3!; 3 ;3!; ;3!;_;3!;=;9!; 1 ;9#;=;3!; 015

16 1 ;3!; 3 ;3@;_;3@;_;3!;=;2 7; ;3!;+;2 7;=;2!7#; ;2!7#; step_3 step_4 5 5_4_3_2_1=120 K ;7!2@0); ;7!2@0); ;3!; ;3@; 1 ;3!;_;3!;+;3!;_;3@;_;3!;+;3@;_;3!;_;3!; =;9!;+;2 7;+;2 7;=;2 7; ;2 7; 0167 ;9^;=;3@; ;3@;_;3@;=;9$; p_3 =9p(cm ) p_2 -p_1 =3p(cm ) 3p 12=;3!; 9p ;3!; 0171 ;7!2@0);+;7!2@0);=;7@2$0);=;3!; ;3!; _4_3_2_1= _3_2_1=24 4 4_3_2_1=24 ;1 2 0;+;1 2 0;=;1 2 0;=;5@; ;5@; 0172 ;3!; ;3@; 1 ;5#; ;5@; step_1 _ =;5#;_;3@;=;5@; ;8$;=;2!; ;2!;_;2!;=;4!; ;4!; step_2 _ =;5@;_;3!;=;1 5; step_3 ;5@;+;1 5;=;1 5; ;1 5; 0170 step_1 step_2 6_5_4_3_2_1=720 K K 5 5_4_3_2_1=

17 ;6#;_;3!;=;6!; ;5!;+;6!;=;3!0!; ;3!0!; ( )( )( ) ( )( )( )( )( )( ) 9 ( )( )( )( )( ) 5 ;9%; x=;a; 5 1 4_4=16 ax=bx=;a; a=1b= a=2b=24 2 a=3b=3 1 a=4b= =8 ;9%; y ;1 0;=;5$; ;1 6;=;2!; ;2!; ;5$;=;5!; ;5!;_;5!;=;2 5; 3 ;5!;_;5!;_;5!;=;12!5; 1-;12!5;=;1!2@5$; 6_6= (1 2)(2 1) 2 11 (5 6)(6 5) 2 2+2=4 ;3 6;=;9!; 0176 ;9!; ;5$; ;2 5; ;1!2@5$; _6=36 PQRS 48 2a_2b=48 ab=12 ab=12 (a b) (2 6)(3 4)(4 3)(6 2) 4 Q -a R y b O -b P a S ;3 6;=;9!; ;9!; _6=36 (2 3) (3 2)(4 5)(5 4) 4 ;3 6;=;9!; ;9!; x 017

18 % 20 % 2_2_2=8 P ;8#; 4 3 (2 4 5)(2 4 6)(2 5 6)(4 5 6) 4 (2 4 5)(2 5 6)(4 5 6) 3 ;4#; ;4#; _5_4_3_2_1= _(4_3_2_1)= _2=192 ;7!2(0@;=;1 5; ;1 5; _5= ~ 5+4+4=13 ;2!5#; ;2!5#; _4 112 = ;1 0; (1 a)(2 a)(3 a)(4 a) 5 3 a=8 8 ;8#; 0185 ;3@;_;4#;=;2!; ;2!; 0186 ;1 6;+;2 0;=;8!0&; 0187 ;5#;_;6$;=;5@; ;5@;_;6#;=;5!; ;5@;+;5!;=;5#; ;8!0&; ;5#; ;2!;_;2!;_;2!;=;8!; ;4!;_;4!;=;1 6; ;2!;_;2!;_;2!;_;2!;=;1 6; ;4#;_;5!;=;2 0; 20 % 0184 P -1 P % 20 % ;2!;_;2!;_;2!;_;2!;=;1 6; ;2!;_;2!;_;2!;_;2!;=;1 6; ;8!;+;1 6;+;1 6;+;1 6;=;1 6; ;1 6; 018

19 0189 3_2_1=6 2 ;6@;=;3!; ;3!;=;3@; ;3@; 1 ;6@;=;3!; 3 ;6$;_;5#;_;4@;=;5!; ;6$;_;5#;_;4@;_;3!;_;2@;=;1 5; ab 20 % ;3!;+;5!;+;1 5;=;1ª5;=;5#; ;5#; ab 20 % ab 20 % ab ab ab 0192 Q 1-;7$;=;7#;1-;5#;=;5@; ab ;7#;_;5@;=;3 5; P Q R S P Q R S P Q R S 1-;3 5;=;3@5(; ;2!;_;2!;_;2!;=;8!; ;3@5(; ;8!;+;8!;+;8!;=;8#; ;8#; ;6#;=;2!; 0194 p 1-p 2_2_2=8 3 1 ;8#; 1 1-;8#;=;8%;

20 x= =80 y=180-2_80 =20 x=;2!;_( )=58 y= = x=2_3=6 x=;2!;_8=4 x=80 y=20 x=58 y= x=90 =50 =90 x=180-(50+90)= x=3 2x-5=1 xæ2 xæ =x=5 x=;2!;_10=5 x=2_2.5=5 x= x=2 3x-2=4 x+y=9 x=4y=5 ab ab 0200 x-3=6 x=8 n+1 n = x-2=x+3 x 0204 x=;2!;_( )=64 x=180-2_70 =40 x=;2!;_( )=15 x=180-2_30 = x+2=6 x= a=b c a+c=b+c 020

21 0213 ab ab ab % 35 % a +b =0a=b=0 a=b=0 a +b =0 a=b=0a +b = y3 n 3 n n+1 n a+b=3 a=1b=2 a+b=3 a=0b=3 x =4 x=2 x=-2 x =4 x ab=6 a=2b=3 ab=6 a=1b=6 = EF = F 35 % 35 % E ab>0 a>0b>0 a=-1b=-1 ab>0 a<0b<0 ab>0 a>0b> a+b ab a=1b=3 a+b ab a=0 b=0 ab=0 a=4 a 4 8 a 8 a y b 16 b 8 b=16 b n n ac=bc a=b a=1b=2c=0 ac=bc a+b ab ab a=3b=2 ab a x=4 x-2>0 x+3 x=3 x-2>0 a=-1b=1 a<b ;a!;<;b!; ;a!;>;b!; a<b a=1b=-1 ;a!;>;b!; a>b x=3 2x-3=x 021

22 0222 a=3b=5 a+b a+b ab a=2b=3 a+b a a >b a>b>0 a=-3b=-2 a >b a<b<0 x=;3$; x>1 x<2 x>2 x>1 a =b a=b a=2b=-2 a =b a+b x+5=4x+a x=3 3x+5=4x+ax=5-a x=3 5-a=3 a= k E = E = E ++ = E + E + = = = = = = ( SSS ) = 0232 = = =E E = = E ( S ) =E 0233 E = E = E=+60 = E SS E = SS 0234 = = ( SSS = ) SSS 0229 P =P P =P = PP P =P P = P P= P P P SS = 0235 = = == = = = = == yy yy 022

23 0236 = = = = 180 = ( S ) = =180 -( )= E x =;2!;_( )=50 E E=;2!;_( )= % 0237 = = ( SS ) = = += 180 ==90 = 0238 = ==65 =180-2_65 =50 = ==65 x=- =65-50 = = =;2!;_( )=65 = = =E=62 = ==62 =180-2_62 =56 yy yy x=180 -( )= ==x =x+x=2x 2x 2x x x 105æ E ==2x +=105 x+2x=105 3x=105 x= ==40 = =80 x=;2!;_( )= = =;2!;_( ) =70 E= =110 E=;2!;_110 =55 ==x x+x=55 2x=55 x= æ x x 70æ 55æ E 0241 ==;2!;_( )=74 =;2!;_74 = E x 20 % 023

24 = =;2!;_( ) =50 =;2!;_50 =25 E= =130 E=;2!;_130 =65 80æ x 25æ 50æ 65æ E P=-P P=;2!;_5_12-;2!;_5_x P=;2%;(12-x) ;2%;(12-x)=20 12-x=8 x= x=65 x= E=E=a E=a a+2a+90 =180 3a=90 a=30 E x=a+a=2a= ==x =x+x=2x ==2x E=x+2x=3x EE=E=3x E x+3x+100 =180 4x=80 x= =48 =90 =180 -( )=42 x=42 = y=6+6=12 x+y=42+12= x 2x 3x P x =;2!; =5=90 x 2x 100æ 3x E a x E a a 60 % 0252 =x cm = =y cm =;2!;x(cm)P =;2!;y(cm) P + =;2!;y+x=17(cm) 2x+y=34 + =;2!;x+y=16(cm) x+2y=32 _2-3x=36 x= =12(cm) 0253 = = =16(cm) =7(cm) + =16+7=23(cm) yy yy 12 cm 0254 =180 -( )=50 = =;2!; =4(cm) 0255 = = 40 +=80 =40 = = =80 = = = =6(cm) 0256 = ==;2!;_( )=72 ==;2!;_72 =36 = 20 % 6cm 024

25 =+ = =72 = = = =6(cm) 0257 ==65 ==65 6cm = x=180-2_65 =50 = =4(cm) 0258 EF=GEF HEF=EF EFG=EF GFE GEF=EF=GFE GF =GE step_3 P =P PM PM 4 P =P 2 PM M =M P =P l PMPM M =M yy MP=MP=90 yy P M yy PM PM (SS ) P =P 0259 F=90-65 =25 =F=25 F==25 F x=180-2_25 = step_1 step_2 = =180-2_70 =40 = 0260 =;2!;_( )=55 QP QR QP 20 % 50 % step_3 =- =55-40 =15 15 QPR PQR PQR QPR=PQR QR =PR =8(cm) PQR QPR=PQR QPR=;2!;_( )=62 QP=QPR=62 QPRPQR 8cm E 2 EF 2 x 1 = ==;2!;_( )= step_1 step_2 = = P =P PP = yy P=P=90 yy P yy P P (SS ) E =E E=;2!;_( )=65 EF E =F EF=;2!;_( )=65 x=180 -( )= p

26 5x+2=3(x+2) x=p 5x+2=3(x+2) 5x+2=3x+62x=4 x=2 p=2 5x+2=3(x+2) x=p =2 =;3!;=;3!;_54 =18 =E E=;2!;_( )= x+=e x+18 =63 x=45 G PQ=GQ= P 1 G =G yy = yy =90 +=G yy G (SS ) G Q G QGPQ G Q F P E GQ=PQ yy QG=PQ yy PQ=GQ=90 P=180 -PQ= E 2 E 2 E 2 E = =E =E E (SS ) =E E E=180-2_75 = E 2 x 2 = ==;2!;_( )= x=2 6x+3a=-2ax a=-4a+57a=-7 a=-1 a=-1 a m+n mn m=2n=4 m+n mn mn mn m=1n=2 mn m mn mn mn mn m+n m+n mn m=2n=4 m+n mn m=2n=4 mn m+n m+n mn m+n mn m n mn 0271 E EFG E =E = 50 % 50 % yy yy 026

27 =60 +E=E yy x=180 -(F+E) =180 -(E+E)==67 67 E (SS ) EFG G E FEG=G yy EGF=G EFG=G=60 E F G 60æ yy = ==;2!;_( )=61 E=61-32 =29 E =E =E E (SS ) =E=29 Px= = =180 -( )=30 = =ae=a =a+18 = ==a a+(a+18 )+(a+18 )=180 3a=144 a=48 = = PQ P =Q QP=a PQ=a P=2a = =P=2a P=a P P =P P=P=a 180 a+2a+2a=180 5a=180 a=36 QP= = ==;2!;_( )=67 FE E=E=x EF=EF=E+E=2x FE=FE=EF+EF=3x F=F=F+F=4x = ==4x 180 x+4x+4x=180 9x=180 x= =40 =180 -( )=50 EF E =F FE=;2!;_( )=65 F F=180 -( )= x 2x = ==90 ;2!;_ _ =;2!;_ _E ;2!;_ _20=;2!;_25_12 x F 4x 2x 4x 3x E 3x 60 % 10 % =E F = = F E (SS ) F=E =15(cm) =2_15=30(cm) 30 cm 027

28 0280 PP = P=P=90 P P P (SS ) P =P P P =P P=P=45 P=P=45 PP = =P =6(cm) =2_6=12(cm) 12 cm 0281 = PE=E PEE PE=90 -PE =90 -E =E yy PE=P yy P =P =P =x(cm) = =P +P =x+3(cm) = + 8=x+(x+3)2x=5 x=2.5(cm) 2.5 cm 0282 = M=EM=;2!;_( )=70 MME M=ME=180-2_70 =40 ME=180-2_40 =100 ME p_3 _;3!6)0);=;2%;p(cm ) ;2%;p cm 0283 =H H= = = EF EF=JEF JEF=FE EF=FEE =F H== E=90-60 =30 =E EF RH EFRH 4cm 0285 FERHS 12 cm 0286 PP P= P =90 yy P =P yy P= P yy P P RH PPRH 0287 OP=OP=90-60 =30 x= E =E OF=OF 0289 = =6(cm)x=6 x=;2!;_( )= x =90 x=30 x =90 x=10 x=2_60 =120 x=;2!;_110 = IF=IE I IF x =90 x=35 x =90 x=20 x=90 +;2!;_30 =105 =;2!;H=;2!;_70 = =90 +;2!;x x=80 EJ=EH =E+H = =130 EF=;2!;EJ=;2!;_130 = =;2!;_2_(6+8+10)=24(cm ) 24 cm 028

29 0295 F =E =2(cm) =F =5-2=3(cm) x=3 E = =7(cm)E =F =5(cm) =7+5=12(cm) x= E RH =E =6(cm) =;2!;_6_9=27(cm ) EF =E yy =F yy F E =E =E = EF yy EF SS 0297 =F=90 =E = EF EF =E yy = yy =90 - =90 - = E yy EFS EFES E E E E RH =E =5(cm)E = =7(cm) E = +E =5+7=12(cm) E=;2!;_(7+5)_12=72(cm ) 0303 E RH =E =7(cm)E = =9(cm) E = +E =7+9=16(cm) =E-2_ =;2!;_(9+7)_16-2_{;2!;_7_9} = =65(cm ) 0304 E =E=90 = =90 -E=E E RH E = =8(cm) =E =5(cm) E =E - =8-5=3(cm) 50 % 20 % 72 cm 65 cm 0298 SS RHS RH S =60 RH RHS S 0300 E =E=90 = =90 -E=E E RH =E =3(cm)E = =4(cm) E = +E =3+4=7(cm) 0305 MEM M=EM=90 M =M M=ME M EM RH =E =6(cm)M =EM =3(cm) =M +M =12+3=15(cm) =;2!;_6_15=45(cm ) 0306 F G F G FG FG FG F=G=90 = F=90 -G=G F G RH 45 cm 20 % 20 % 029

30 F =G =4(cm)G =F =6(cm) FG =G -F =6-4=2(cm) FG=;2!;_6_2=6(cm ) 0307 EE E=E=90 E = E E RHS E =E =15-9=6(cm) 0308 E RHS E==90-25 =65 x=180-2_e cm =180-2_65 =50 E E E +E E E E E E RHS = =6(cm) =10-6=4(cm) E =E E +E =E +E = =8(cm) E +E +E =4+8=12(cm) 12 cm 0310 E =E=90 =E E RH E = =10(cm) = =45 E E =E =10(cm) E=;2!;_10_10=50(cm ) 10 % 0311 POPO OP =OP=90 yy OP yy PO= PO yy PO PO RH P =P 0312 POPO OP= OP =90 yy OP yy P =P yy PO PO RHS PO= PO OPOP P RHSPO 0313 E RH E = =4.5(cm)E = =9(cm) E =15-9=6(cm) E=;2!;_4.5_6=13.5(cm ) 0314 E E E 12`cm E E =E=90 =E 4`cm E RH E = =4(cm) =;2!;_12_4=24(cm ) 0315 PMOPNO PMO=PNO=90 OP POM=PON PMO PNO RH PM =PN OM =ON 24 cm 0316 E RH E = =+ ;2!;_5_12=;2!;_13_E +;2!;_ _12 30=: 2 : =: 5 :(cm) : 5 : cm 0317 O =O =O OF F =F OEOE O =O OE=OE=90 OE=OE OE OE RH 030

31 O 0318 O x =90 x=20 y= =50 x+y= =70 x 30æ x40æ O 40æ 30æ O O =O O O=O=25 x=180-2_25 = O = = O =O O =O O = O yy OO O =O=90 yy O yy O O RHS = O OO RHS 0322 O =O O O =O O 24 cm O +O + =O +O +10=24 2O =14 O =7(cm) 7cm 7cm 28æ 28æ O 34æ 34æ 60 % 0325 O O O=x x=90 x=50 = = O x= =55 y=2x=2_55 =110 x+y= = O=2 98 =2_(x+30 ) x+30 =49 x= x =90 22æ 45æ x=23 y=2_( )=134 22æ O y x x+y= =157 30æ 10æ x 30æ O 30æ O 30æ y x 10æ O 98æ x 25æ 30æ 25æ 30æ 0323 O x=90 x=30 35æ x O 35æ x 25æ 25æ 0329 O O=180-2_34 =112 x=;2!;_112 = æ x O 34æ 0324 x y x+y 50 % 20 % 0330 O 50 % 50 % 031

32 4 O= 1111 _360 = =;2!;_160 =80 2 = 1111 _180 = O=2_40 = ;2!;_10=5(cm) p_5 =25p(cm ) 0332 O O =O =O =6(cm) =O +O =6+6=12(cm) 12 cm 0336 O O =O =O O O =O O=O=28 x=o+o= = O O =O O O =O =O O +O=+=2=50 = O : O=5 : 4 O=180 _;9%;=100 O O =O =;2!;_( )= O O =O O=O=;2!; O=;2!;_{;2!;_5_12} O=15(cm ) 0334 M M =M =M PM PMRHS PM=PM QM QMRHS QM=QM PQM=;2!;=;2!;_36=18(cm ) 0339 I =IE =IF I I=IF IE IFIE=IF I % M =90-30 =60 12`cm 60æ M M 60æ 30æ M =M =6(cm) M=M=60 M=180-2_60 =60 M =M =6(cm) M M 6+6+6=18(cm) 6cm 18 cm 0341 I =IF I =IE IE = IF yy IEIF IE =IF=90 yy I yy IE IF RHS IE= IF 0342 x y 50 % x+y 10 % I IEx=8 I'EF I'EF=I'E=y y=180-(130+20)=30 x+y=8+30=

33 0343 I 180 x=180 -( ) =125 25æ 25æ I x 30æ 30æ =90 +;2!;x;2!;x=25 x=50 I=I=a x 0344 =180 -( )=50 I=25 HH=180 -( )=20 IH=I-H=25-20 =5 I=I=b I a+b= =65 x=180 -(2a+2b) =180-2_65 =50 a a I 115æ b b 0345 I x =90 x= x=90 x=24 y=34 x+y= = x=180 -(2_20 +2_40 ) = æ 32æ 32æ 20æ 30æ 30æ 20æ I x x I 34æ 35æ x x x I 40æ 40æ 35æ 0350 I I=90 +;2!; I=90 +;2!;_58 = =90 +;2!;;2!;=38 I=I x=;2!;= % I 50 % += =120 :=1:2 =;3!;_120 =40 I=90 +;2!; 0348 a+b x+y I=I=a I=I=b x a a 2a+2b+80 =180 a+b=50 x=b+80 Ey=a+80 x+y=(b+80 )+(a+80 ) =a+b+160 = = % 50 % 80æ E y I b b I=90 +;2!;_40 = r cm =;2!;_r_(8+7+5)=17 10r=17 r=1.7(cm) 0354 x cm =;2!;_3_x=51 x=34(cm) 34 cm 0355 r : I=;2!;_r_(7+8+9) : ;2!;_r_9 210 : I=8:3 033

34 0356 r cm =;2!;_r_( )=15r =;2!;_12_5=30(cm ) 15r=30 r=2(cm) 2cm 0362 I I=I IE=I E I=I I=IE I=IIE=IE IEI =I E =EI E +E +E = +(I +EI )+E = +( +E )+E = + =12+10=22(cm) 12`cm I 10`cm E 0357 r cm =;2!;_r_( )=24r =;2!;_16_12=96(cm ) 24r=96 r=4(cm) I=;2!;_20_4=40(cm ) 0358 r cm =;2!;_r_(6+8+10)=12r =;2!;_6_8=24(cm ) 12r=24 r=2(cm) 0363 EI I EI EI =E =4(cm) I =E -EI =9-4=5(cm) I =I =5(cm) 20 % 5cm I=90 +;2!;= =135 p_2 _;3!6#0%;=;2#;p(cm ) 0359 E = =5(cm) F = =2(cm) E =F = -F =6-2=4(cm) =E +E =5+4=9(cm) 0360 =F =4(cm) E = = - =10-4=6(cm) 0361 P P ;2#;p cm 70 % P =Q =x(cm) R =P =10-x(cm)R =Q =12-x(cm) =R +R 8=(10-x)+(12-x) 2x=14 x=7(cm) 7cm 0364 =I E =EI + + =( + )+ +(E +E ) =( +I )+ +(E +EI ) = +(I +EI )+ +E = +E + +E = =33(cm) 33 cm 0365 I=I=20 EI=EI=25 I=180 -( )=135 E =I +EI = +E E = +E +E = +( +E )+E = + =14+12=26(cm) 0366 I 130 =90 +;2!; O x=2=2_80 =160 =

35 0367 IO I=90 +;2!;O142 =90 +;2!;O O=104 O O=2104 =2 = x=2=2_60 = = =;2!;_( )=50 I 0368 =90-60 =30 I I=I=;2!; I=;2!;=;2!;_50 =25 E E=90 -I=90-25 =65 65 I=;2!;_30 =15 O O=O=30 P P=180 -( )= =2_20 =40 O O=2=2_40 =80 I I=90 +;2!;=90 +;2!;_40 =110 I I-O= =30 O IO 20 % 0374 =180 -( )=70 I I=I=;2!; O I x 20 % I=;2!;_70 =35 O O=2=2_80 =160 O O=O=;2!;_( )=10 IO=I-O =35-10 =25 25 =180-2_75 =30 O O=2=2_30 =60 O O=O=;2!;_( )=60 I I=I=;2!; 0370 O O=2=2_80 =160 O I=;2!;_75 =37.5 x=o-i= = O=O=;2!;_( )=10 ==;2!;_( )=50 I 0375 step_1 E I=I=;2!; =E=90 I=;2!;_50 =25 =E x=i-o=25-10 =15 E RHS 035

36 step_2 E=E = x=180 step_3 2x=80 = x=40 =;2!;_( )=65 40 step_4 E E=90 -E =90-65 = E F 2 E 2 2 EF E=F=90 E =F E F RHS E=F=90-68 =22 =2E=2_22 = E E x E RH =E =x(cm)e = =7(cm) E = +E =x+7(cm) E 50 cm ;2!;_(x+7)_(x+7)=50 (x+7) =100x+7=10 ( x+7>0) x=3(cm) cm 0377 step_1 O O =O =O O 34æ P 0380 O 4 3 step_2 step_3 step_4 O=O=42 O O=O P =-O =76-42 =34 PO= =118 PO OP=180 -( )=28 34æ 42æ O 42æ 28 =90-30 =60 O O O =O O=O=60 O=180-2_60 =60 O O = =4(cm) =2O =2_4=8(cm) 30æ O 60æ 60æ 4`cm 60æ 8cm I =IE =IF 3 x 2 IEF 3 I I I=I=x I=I=25 I =IE =IF =50 = 25æ 25æ I x x I I EF EF IEF ==50 036

37 r cm =;2!;_r_(6+8+10)=12r =;2!;_6_8=24(cm ) 12r=24 r=2(cm) : 2º:=5(cm) p_5 -p_2 =21p(cm ) 2cm 5cm 21p cm = =9(cm) = - =15-9=6(cm) E=;2!;_ _E E=;2!;_6_;2(;=: 2 :(cm ) 0386 O O O OE OE OF OF O=O=;2!;_4_3=6(cm ) : 2 : cm OE=OE=a(cm )OF=OF=b(cm ) =2_(6+a+b)=52 a+b=20 OEF=a+b=20(cm ) 20 cm 0383 l 90 E =E=90 = =90 -E=E E RH E E = +E =E + =b+a E = =a E=;2!;ab E =a+b E=;2!;_(a+b)_(a+b) E=;2!;(a+b) 0384 E RH =E =5(cm) 30 cm ;2!;_ _ =;2!;_5_ =30 =12(cm) E = =12(cm) E =E - =12-5=7(cm) 0385 E E RHS E =a(cm) E =a(cm) =E+E ;2!;_12_9=;2!;_15_a+;2!;_a_9 12a=54 a=;2(;(cm) 7cm 0387 O O =O =O 30æ O 10æ O=O = =40 O=180-2_40 =100 O O=O=10 O=180-2_10 =160 O= =60 O O=O=;2!;_( )=60 = = O O=2=2_65 =130 O O =O =O OO O=O=x O=O=y O 2x+2y+130 =360 2(x+y)=230 =x+y= =90 O =O =O O OO' 65æ 40æ O x 10æ 130æ O yy yy 100 x y y % 037

38 =90 O =O =O O O=O=35 O=-O =90-35 =55 O'O OO'=2O=2_55 = Q 110 =90 +;2!; =40 ==40 =80 ==80 =180-2_80 =20 P P=90 +;2!; 0390 M M =M M MN=MN=20 M=40 M M=180 -( )= GEF GF =G GF GF=GF=x G=2x G =G G=G=2x E==33 F= =123 F 2x+x+123 =180 3x=57 x= I : I : I=5:6:7 I=360 _;1 8;= =90 +;2!; = I I=I=x I=I=y E 2x+y+88 =180 yy x+2y+86 =180 x=30 y=32 ++= =180 =56 M y y x x 88æ I 86æ 20æ 20æ E N yy 56 P=90 +;2!;_20 = P =R P =Q + + = +(Q +Q )+(R +R ) = +(P +3)+(P +3) 18`cm =2 +6 =2_18+6=42(cm) P I R 3`cm 3`cm Q3`cm ;2!;_3_( + + )=;2!;_3_42=63(cm ) 63 cm 0396 I I=I=40 E=10 = =50 O 30æ O =O =O 50æ OO O 30æ 50æ O=O=30 10æ 10æ O=O=50 O O=O = =10 E=30 +( )= OE E IE OE OE=OE=90 -( )=37 lm E=E= =67 IE IE=90 +;2!;E IE=90 +;2!;_67 =

39 x=3y=2 x=5y= x=70 y=30 =x=50 +=180 y=130 x=70 y=30 x=50 y= ==x x=180 -( )=20 ==70 x=180 -( )= O O = x=2_4=8 y =;2!;=;2!;_90 =45 y=45 = x=2_2=4 y =90 y=90 x=8y=45 x=4y= ;= 0410 x=7 = x=5+3= ==80 +=180 x= =100 ==25 x=== = = =10(cm)x=;2!;_10=5 = =2_4=8(cm)x= O x=35 O=90-30 =60 x=o=60 O=90-28 =62 x=o=62 O O=O=40 x= = x=90 Oy=180 -( )=30 O O (RHS )x=25 O O (RHS )O=25 Oy=180 -( )=65 x=90 y=30 x=25 y=65 039

40 x=3y=2 x=5y= = 2x+2=3x-4 x=6 = =x+5=11(cm) 0400 x=70 y=30 =x=50 +=180 y=130 x=70 y=30 x=50 y= ==x x=180 -( )=20 ==70 x=180 -( )= O O 0423 ==35 O x= = x==50 += (50 +y)=180 y=70 y-x=70-50 = ==y (y+30 )+x=180 x+y= = =10(cm)x=;2!;_10=5 70 % +=180 :=3:2 =;5@;_180 =72 == = x+3=10 x=7 O =;2!; 2y+1=7 y=3 EFG F = ==56 F=;2!;=;2!;_56 =28 F F=180 -( )=62 +=62 +x+56 =180 x=62 F=70 F=H z= =180 = =80 x+y+z=7+3+70=80 E x=180 -( )= O =;2!; =;2!;_10=5(cm) O =;2!; =;2!;_12=6(cm) = =8(cm) O =180 = =40 E=;2!;=;2!;_40 = =19(cm) x=e=20 040

41 0430 E=E=68 =2E=2_68 =136 x== E F x E E=E=68 E=E=68 F F=180 -( )=22 ==68 x=68-22 = ==70 =180 -( )=60 E=;2!;=;2!;_60 =30 20 % E FE F F EFE E =E E=FE E=FE E FE S F = =8(cm) F =F + =8+8=16(cm) 0437 = = FE =FE FE= FE FE =F EF 2_(F +FE )=2_(F +F ) =2_12=24(cm) 50 % 20 % 16 cm x=e= E=E E=E E =E E =5(cm) F=F F=F F =F F =5(cm) E +F = +EF 5+5=7+EF EF =3(cm) 0434 E=E E=E E =E E =7(cm) E =11-7=4(cm) 0435 F=F F=F F F = F =5(cm) F =F - =5-3=2(cm) F=F F=F F =F F=60 F F =F = =6(cm) F =10-6=4(cm) ==60 E E =6(cm)E =4(cm) FE =20(cm) 20 cm 0439 = = ( S ) = = 0440 =+ = + = =+ =+ = 041

42 0441 OO = O= O O= O O O ( S O =O O = O ) = = +=180 = 0442 OPOQ O =O PO=QO OP=OQ OP OQ S P =Q 0443 EF E=F=90 = E=F E F RH E =F 0448 = = ( SS ) = SS 0449 OE EF +F 60 % 0444 = = O =O O =O EO E O E =O E O E =O OE OE EF =FO F =F EF +F =;2!;EO +;2!; =180 += =360 -( )=140 +=180 EF +F=;2!; +;2!; EF +F =;2!;_6+;2!;_9 EF +F =: 2 :(cm) : 2 : cm 0450 O = O yy O = O E =F OE = OF yy FE 0451 E F = E =F E = F F F 042

43 0452 = E=F E=F=90 E F ( RH ) E = F EF=FE ( ) E F 0453 FE EF=EFE=F 0454 = 0460 = = ( SSS ) = = = === SSS 0461 OO=O O =O = O =;2!; =;2!; =;2!;_12=6(cm) x=6 =90 y =90-28 =62 y=62 x+y=6+62= O=O 0462 = 2x=3x-4 x=4 O O SSS O=O=y O O=90 y =90-56 =34 y=34 x+y=4+34= O O =O x=50 =90 y=90-50 =40 x-y=50-40 = =180 =70 SSS = x=;2!; 0457 E==26 FE=90 -( )=38 x=;2!;_70 =35 E==90 EF x+38 =90 x= O =O = +=180 === = = O OO = O O = O O O ( SSS ) O=O O+O= 180 O=O= 90 O SSS

44 x y x+y O=O=30 =60 = ==;2!;_( )=60 x=60 = =12(cm) y=;2!;_12=6 x+y=60+6=66 20 % % = = = = = = =9(cm) 4_9=36(cm) 36 cm 0467 O=O=40 EF x=90-40 =50 = ==40 O y=90-40 =50 x+y= = MN N =N N N=N M N M=N N=;3!;=;3!;_90 =30 N x=180 -( )= = = = = = 0474 E=45 E E+45 =65 E=20 EE = E=E=45 E E E (SS ) E=E= O =O =O =O O O =;2!; =;2!; 3`cm O 6`cm 0471 ==58 OO=180 -( )=90 O =;2!;_6=3(cm) O=90 =2 =2_{;2!;_6_3}=18(cm ) 044

45 0477 E E F F E E+E=E E+90 =115 E=25 EF = E=F=90 E =F E F (SS ) F=E= E =90 E=60 E=90-60 =30 =E = E = E E = E=E E=;2!;_( )=75 =45 x=e- x=75-45 =30 50 % 20 % O =O =O =O O=O=O =O= 90 O O O O ( SS ) = = = ==== = SS = = O O O =O O=O 0485 F EF =8(cm) E F (RH ) E =F =;2!;_(12-8)=2(cm) 0486 EE = yy = E yy E = E E = =E = EEE 0487 O O =O O=O=104 x=;2!;_( )= = ==34 ==34 = =68 ==68 x=180 -( )= E E E E E E = =6(cm) 8`cm E 60æ 8`cm F 12`cm 6`cm 20 % 60æ 60æ 60æ E 045

46 ==60 E==60 E E = =8(cm) =8+(8+6)+8+6 =36(cm) 0490 E E E =E =;2!; 36 cm E 0499 M M SSS = +=180 == EH FE GF HG SS HE =E F =F G =GH + =90 EFGH 90 E H G EFGH F E =E E = ;=E =90 = = E=90 -=90 -=F EF E=F E =F E=F E F S = =180 F+F=90 FF= =90 FGH=GHE=HEF=90 EFGH E 0498 EEF EF = E E =E F E F =F = E =E F =F EF E F PQRS 046

47 0506 EFGH 0512 P+P=P+P P+18=17+13=30(cm ) P=12(cm ) 0507 EFGH EFGH 50 % 50 % 0513 P+P=;2!; =2_(30+18)=96(cm ) EFGH EFGH 5_4=20(cm) 20 cm 0508 O=O=O=O =4O =4_5=20(cm ) 0509 PEF=;4!;EFQEF=;4!;FE EQFP=;4!;EF+;4!;FE 0514 P =7_4=28(cm ) P+P=;2!; P+5=;2!;_28=14(cm ) P=9(cm ) 70 % 9cm EQFP=;4!; 0515 P+P=;2!; EQFP=;4!;_28=7(cm ) =;2!;_10_8=40(cm ) 0510 OE OF EO+OF 60 % OEOF O = O EO=FO OE=OF OE OF S EO+OF=EO+OE =O =;4!; =;4!;_80=20(cm ) 20 cm E = E F =F EP=EP=;2!;P FP=FP=;2!;P EP+FP =;2!;(P+P) =;2!;_40=20(cm ) 0516 E =E =+ =+E =E =;2!;_(5+7)_8=48(cm ) 20 cm 0511 O=O=O=20(cm ) =O+O =20+20=40(cm ) FE FE=4 =4_40=160(cm ) 160 cm 0517 E E= E=E+ =+ = =30(cm ) 047

48 MN=;3!; =E E 50 % 50 % MN=;3!;_;2!;_ MN=;6!; E =E MN=;3!; =-E =40-25=15(cm ) 15 cm MN=;3!;_;2!;_ MN=;6!; MN=MN+MN 0519 ==36(cm ) O=-O MN=;6!;+;6!; MN=;3!; =36-12=24(cm ) MN=;3!;_24=8(cm ) 0520 = E =E =+ =+E =E 0526 N : MN=1 : 2 N:6=1:2 N=3(cm ) M=N+MN 0521 E=E E F E=F F=F =3+6=9(cm ) =2M =2_9=18(cm ) E=E=F=F 0522 F 0527 O : O=1 : 2 18 : O=1 : 2 F==;2!;_8_8=32(cm ) O=36(cm ) E=;2!;_8_6=24(cm ) EF=F-E =32-24=8(cm ) 8cm = =O+O =18+36=54(cm ) 0523 : =2 : 3 =;5#; 0528 =;5#;_30=18(cm ) E : E=2 : 1 P 70 % E=;3!; =;2!;_ _ E=;3!;_18=6(cm ) =;2!;_10_20=100(cm ) P : P=2 : P : P=1 : 2 P=;5#; P=;3!; =;5#;_;2!;_ P=;3!;_;2!;_ =;1 0;_100=30(cm ) P=;6!;_60=10(cm ) 30 cm 048

49 step_1 step_2 step_3 +=180 +(2-30 )=180 3=210 =70 ==70 E x +70 =95 x =25 x=25 28 cm 2_(y+6)=28 y+6=14 y=8 step_4 x+y=25+8=33 33 x 3 y 2 x+y 1 ==62 O O= =90 x=90 = =10(cm) y=10 x+y=90+10= x y x+y +=180 :=3 : 2 =;5#;_180 =108 ==108 EF E=F=60 x =360 -( )=132 x= cm 2_(6+ )=206+ =10 =4(cm) E E = =4(cm) y=4 x+y=132+4= step_1 step_2 step_ ==56 O O=180 -( )=90 = =6(cm) x=6 O=O=34 y=34 x+y=6+34= HE =F G 3 GH =E F 3 2 HEFG E =G yy = H =F H = F yy = yy HE FG SS HE =F G GHEF G =E H =F = GH EF SS GH =E F EFGH = M 2 049

50 MM = M =M M =M M M SSS = +=180 ==90 90 M=;2!; M=;2!;_(7_4)=14(cm ) 14 cm 0535 E 2 E 3 1 E 5`cm E 120æ 60æ 7`cm E 60æ 60æ 60æ E = =5(cm) E == =60 E E==60 E E = =7(cm) =E +E =5+7=12(cm) 12 cm E 3 E 2 =;2!;_15_10=75(cm ) E : E =1:2 E : E=1 : E =E=50 2 yæ 5 = 3 x F 2 50æ 50æ 50æ E ==50 y =180 -( )=80 y=80 =F E =2(cm) =5-2=3(cm) E E = =3(cm) x=3 x+y=3+80= E=EM E=EF EM=EF MF MF =M = =8(cm) M M =4(cm) F =MF -M =8-4=4(cm) 0539 H FH x H +=180 H+H=90 H=90 HF FH=180 -( )=30 ==2_30 =60 H=FG=60 HE x=360 -( )=150 F 60æ G E x H 4cm 150 E=;3@; E=;3@;_75=50(cm ) E E=E=50(cm ) 50 cm 0540 EEP E =E E=PE E=EP E EP S P = = 050

51 FP P FP F =P FP PF=180 -( )=15 FP F =P FP=PF= P Q Q P PQ P =Q Q xq P P =5(6+x)Q =8x 5(6+x)=8x3x=30 x=10 10 EF : EF= :E 150 : EF=15 : 3 EF=30(cm ) =180 F+F=90 FF= =90 FGH=GHE=HEF=90 EFGH EG +FH =24(cm)FH =12(cm) OH =;2!;FH 30 cm 0542 P OH =;2!;_12=6(cm) 6cm 7`cm 4`cm 3`cm {P} 4`cm Q Q=Q Q=Q Q Q = =4(cm) Q =7-4=3(cm) P 4`cm 7`cm 6`cm Q {P} 6`cm Q=Q Q=Q Q Q = =6(cm) P Q 3+6=9(cm) 9cm 0545 EO =FO FE FE OEOF OE=OF=90 O =O EO=FO OE OF S EO =FO FE F = - F =6-2=4(cm) FE 4_4=16(cm) 16 cm 0543 E=E E=E E E = =12(cm) F F = =12(cm) E = F =15-12=3(cm) E F E = F EF 0546 P =P EQ E=Q E ++E =P++Q =PQ =;2!;_8_6=24(cm ) 24 cm 051

52 0547 E E==;2!; F :F =2:1 F=;3@; F=;3@;_;2!;_ F=;3!; FE=E-F FE=;2!;-;3!; FE=;6!; FE ;6!; 0548 P : P= P :P 24 : P=2 : 1 P=12(cm ) =24+12=36(cm ) Q= P+PQ=P+P PQ=P=12(cm ) PQ : PQ= P :P 12 : PQ=2 : 1 PQ=6(cm ) Q=12+6=18(cm ) ==36(cm ) Q=-Q =36-18=18(cm ) 18 cm ;6!; 0549 I I 0550 =90 === =90 ==90 yy +=180 =90 yy ==90 yy === 0551 EE E E 052

53 ªH : = : H = H HªH H :H =H :H H = H H H H H H 0552 H EF :12=2:3 :E =2:3 :9=2:3 3 =18 E==30 =6(cm) :8=3:4 : '' =3:4 9: '' =3:4 3 '' =36 F : 'F' =3:4 12: 'F' =3:4 3 'F' =48 '' =12(cm) 'F' =16(cm) 0555 O :O =6:12=1:2 1:2 :EF =1:2 :10=1:2 2 =10 =5(cm) =F=65 =180 -( )= O :O =4:6=2:3 2:3 :EF =2:3 6:EF =2:3 2EF =18 ==40 EF =9(cm) 2:3 6cm 30 3:4 12 cm 16 cm 1:2 1:2 5cm 80 2:3 2:3 9cm : = : = : =4:5 ª SSS =E=70 ªE ªSSS ªE 0559 =H 6 =3_(3+x) 12=3+x x=9 H =H H x =8_2=16 x=4 ( x>0) :x=4:64x=30 x=: 2 : (10-x):10=8:1280=120-12x 12x=40 x=: 3º: 7 : 5=4 : x7x=20 x=: 7º: 10 : x=8 : (8+4)8x=120 x= : 12=6 : x8x=72 x=9 4:8=x :108x=40 x=5 9 4 : 2 : : 3º: : 7º: 15 6 : 10=(x-15) : 1510x-150=90 x=24 (x-5):5=2:66x-30=10 x=: 3º: :10+5 :8 E 12:3=8:2 E 2:3=4:6 E : 3º: 3 : (12-3)+4 :10 E 053

54 0563 6:4=x :24x=12 x=3 18 : x=(15-6) : 69x=108 x= a a x x : 3=12 : x4x=36 x=9 6:x=12 : (12-4)12x=48 x= : 12=10 : x8x=120 x=15 (20-12) : 12=x :1512x=120 x=10 x : (9-x)=4:22x=36-4x 6x=36 x=6 4:8=x :68x=24 x=3 4:x=6:96x=36 x=6 4 : 2=(x-3):32x-6=12 2x=18 x= H E : =EG :H 4 : (4+8)=EG : (18-6) 12EG =48 EG =4 GF GF = =6 EF =EG +GF =4+6= E : =E I : 3 : (3+2)=E I :10 5E I =30 E I =6 F : =IF : 2 : (2+3)=IF :5 5IF =10 IF =2 EF =EI +IF =6+2= :24=2:3 :F =2:3 :21=2:3 3 =42 ==66 =14(cm) EF F=180 -( )=60 =F= :10=3:2 :EF =3:2 :6=3:2 2 =18 =9(cm) :EH =3:2 18:EH =3:2 3EH =36 E==83 =H=67 EH =12(cm) 0573 :F =3:4 :8=3:4 4 =24 =6(cm) :EF =3:4 :12=3:4 4 =36 =9(cm) =27(cm) 0574 E FG ªEFGH G==85 H==70 EFGH E=360 -( )=105 :EH =6:4=3:2 :FG =3:25:FG =3:2 27 cm 3FG =10 FG =: 3º:(cm) % 50 % : 3º: cm 054

55 :24=1:2 H :LP =1:28:x=1:2 x=16 GH :OP =1:26:y=1:2 y=12 x+y=16+12= F :IL =5:9 F :7=5:9 9F =35 F =: 9 :(cm) :GH =5:9 4:GH =5:9 5GH =36 GH =: 5 :(cm) GHIGHI=180 -( )=30 EF==GHI= :15=2:3 2:3 x cm 4:x=2:3 2x=12 x=6(cm) p_6 _15=540p(cm ) 2:3 540p`cm 0578 (4+6) : 4=5 : 2 x cm x :2=5:2 2x=10 x=5(cm) 5cm 0579 ''' 'Í 'Í 'Í 0580 Í EÍ FÍ H 0581 ''' 'Í 'Í'Í 0582 ª''' O :O ' : '' =O :O ' =6 : (6+4) =3:5 : '' =3:53: '' =3:5 3 '' =15 '' =5(cm) ='''=70 =180 -( )= GÍ EÍ FÍ GEF E : =(3+2) : 3=5 : ªEF= O :OF = :E =6:9=2:3 EF F :EF =2:3 4:EF =2:3 2EF =12 EF =6(cm) O :O =2:3 O : =2: O OªO'' - '-''' ª''' O :O ' =O :O ' =1 : (1+2)=1 : 3 3O =O ' : '' =1:3 '' =3 '' 112=3 '' 0586 EFGH 10 % O :OE =2 : (2+3)=2 : 5 EFGH 2:5 :EF =2:5 :10=2:5 5 =20 =4(cm) :GH =2:5 :15=2:5 5 =30 =6(cm) 055

56 =18(cm) 18 cm 0587 :QP = :RP =3:2=P ªQRP SS GH :JK =HI :KL =GI :JL =2:1 GHIªJKL SSS F=180 -( )=80 E=MF=N EFªOMN 0588 = ª 0589 =180 -( )=50 =E= ªEF a:e=b:f=c:d 0590 =E SS SSS 0594 = = EªE E =x cm E =(18-x) cm E :E =E :E (18-x):x=5:45x=72-4x 9x=72 x=8(cm) 0595 E : =5:15=1:3 E : =4:12=1:3 Eª SS E : =1:3 6: =1:3 =18(cm) 0596 : =4:2=2:1 : =8:4=2:1 ª SS : =2:1 6: =2:1 Eª SS 50 % 50 % 18 cm 2 =6 =3(cm) 0591 =180 -( )=30 :NM = :MO =2:3=M ªNMO SS =P=Q ªPRQ 0597 E =E ªE E =x cm =(x+5) cm :E = : 10:5=(x+5):45x+25=40 5x=15 x=3(cm) 0592 =75 =180 -( )=60 =45 ==E ªFE 0593 = ª : = : :6=6:33 =36 =12(cm) = - =12-3=9(cm) 0598 E EF=F EF=F EFªF E : =F :F E :12=6:99E =72 E =8(cm) 0599 E E==90 Eª = - =10-4=6(cm) 8cm 056

57 E : = : E :6=10:8 8E =60 E =7.5(cm) =90 +E=90 =E =E=90 ªE :E = :E 6 : 12= :16 6`cm 12`cm 16`cm E 12 =96 =8(cm) 0601 =90 -=E E=90 -E =E =E=E ªEªE ªEªE 0602 QM MQ==90 QMª Q =x cm Q =(8-x) cm Q : = M : (8-x) :10=5:850=64-8x 8x=14 x=;4&;(cm) 0603 E F =H =: 3 :_: 3 :=;:$9):); =: 3º:(cm) 0605 ==90 ª ==90 ª ªª ª ª : = : = ª : = : = 0606 = 12 = _9 =16(cm) = =(16+9)_9=225 =15(cm) 0607 = =8_2=16 =4(cm) ;2!;_10_4=20(cm ) Pª 50 % P 50 % P=EP=90 -EP =90 - x`cm P P= E 4`cm P==90 6`cm 6`cm Pª P =x cm =(x+4) cm P : = : 4 : 6=6 : (x+4)4x+16=36 4x=20 x=5(cm) 0608 H 60 % H = =5(cm) = H 5 = _4 =: 4 :(cm) H = -H =: 4 :-4=;4(;(cm) H =H H H =;4(;_4=9 H =3(cm) 3cm 0604 =H 5cm 0609 F+F=90 F+FE=90 F 4`cm 3`cm 5 =3_ =: 3 :(cm) H = -H =: 3 :-3=: 3 :(cm) F=FE ==90 8`cm E 057

58 FªFE E = -E =8-3=5(cm) FE =E =5(cm) :F =F :FE 8:4=F :5 4F =40 F =10(cm) 0610 EFE ==60 yy E+E=120 7`cm 12`cm F E+EF=120 7`cm 5`cm E=EF yy 4`cm E EªFE EF =F =7(cm)F =12-7=5(cm) E :F =E :EF 4 : 5=E :7 5E =28 E =: 5 :(cm) =E =: 5 :(cm) 0611 Q =Q QP P P= =P P=P P Q =Q =5(cm) ªQP :QP = :Q = =8(cm) 6:QP =8:5 8QP =30 QP =: 4 :(cm) P ;2!;_10_: 4 :=: 4 :(cm ) 50 % 20 % + + =8+10+6=24(cm) 0614 x : (15-x)=(12-8) : 860-4x=8x 12x=60 x=5 5:y=(12-8) : 84y=40 y=10 xy=5_10= : 15=(9-x) : x=45 15x=90 x=6 5 : 15=4 : y5y=60 y=12 x+y=6+12= E E = =4(cm)F =4+3=7(cm) F F :F = :E 7:3=6:E 7E =18 E =: 7 :(cm) = =6(cm) E = -E =6-: 7 :=: 7 :(cm) :(6+x)=3:518+3x=30 3x=12 x=4 4:y=3:53y=20 3xy=3_4_: 3º:=80 y=: 3º: 70 % : 7 : cm 0618 G :F =E : G : 5=9 : (5+10) 15G =45 G =3(cm) : 8=12 : x 16x=96 x=6 16 : (16+8)=y :30 24y=480 y=20 x+y=6+20= :6=4: 3 =24 =8(cm) 3:6=5: 3 =30 =10(cm) : 4 : cm 0619 E 6 : (6+3)=FG :8 9FG =48 FG =: 3 :(cm) FH 6:2=: 3 : :GH 6GH =: 3 : GH =: 9 :(cm) 0620 E F 6 : 4=EF :2 4EF =12 EF =3(cm) E 6 : 4=E : (3+2) 4E =30 E =: 2 :(cm) 058

59 0621 : =3 :2 =;5#; =;5@; E E :E =3:2 E F :F =3: : = : 6 : 9=4 : x 6x=36 x=6 : =E :E (4+6) : 6=y : (9-y) 6y=90-10y y=: 8 : 3F =2 F =;3@; x+y=6+: 8 :=:ª8 : :ª8 : : :F =;5#; : ;5@; : ;3@; : :F =;5#; : ;5@; : ;3@;=9:6: FG E 3: =4 : (2+6) 4 =24 =6(cm) FG :FG = :G 6:FG =(2+6) : 6 8FG =36 FG =;2(;(cm) :6+5 :9 6:2+(12-4) : 4 7 : 3=5 : : 7 : 50 % 50 % ;2(; cm 0628 = E = E ªE : E = : EE= E E = : = : 0629 : =3:5 : =3 : 5 24 : =3 : 53=120 =40(cm ) 0630 E 12:9=x :8 9x=96 x=: 3 : 12 : y=: 3 : :8 : 3 :y=96 y=9 9:3+(6-2) : : 9=(15-10) : 10 E :5=12:4 (8-2) : 2=3 : 1 3:6=4:8 4:2+(8-3) : 3 (12-9) : 9=(10-75):7.5 E 3x+y=3_: 3 :+9= % E 50 % 10 : 12=(11- ) : 10 = =132 =6(cm) E 10:E =11:6 11E =60 E =;1^1);(cm) 0625 : =F :F F F =F : 6=(7- ) : 8 = =42 =3(cm) 0632 : = : (12+4) : 12=8 : 16 =96 =6(cm) E SS E = =6(cm) 6cm ;1^1); cm 059

60 0633 : =E :E 10: =5:35 =30 =6(cm) : = : 10 : (5+3)=(6-x): x 48-8x=10x 18x=48 x=;3*; ;3*; E :E = : =10 : (3+12) =2:3 2: :4=x :64x=12 x=3 2 : 4=(y-6) :64y=36 y=9 x+y=3+9= : = : 4 : 3=( +5): =20 =;3%;(cm) :3=x :43x=8 x=;3*; 2:3=y :53y=10 y=: 3º: y-x=: 3º:-;3*;=;3@; 0635 : = : 7: =10 : (10+5) 10 =105 =105(cm) 0636 : =8:12=2:3 : =2:1 : =2 : 1 =;2!;=;2!;_36=18(cm ) 0637 ªE : E = : FE =E E=E E E = : = : E FEE : 2=(x-3) :32x=21 x=: 2 : : 2 : : y=(5+2) : 87y=84 y=12 xy=: 2 :_12= (15-x) : x=8:412x=60 x=5 5 : 12=4 : y5y=48 y=: 5 : x+y=5+: 5 :=: 5 : 0644 x :9=3:66x=27 x=;2(; 6:y=9:129y=72 y=8 x+y=;2(;+8=: 2 : 0638 P Q : =P :P 6:4=3:P 6P =12 P =2(cm) : =Q :Q 6 : 4=(3+2+Q ) :Q 6Q =20+4Q 2Q =20 Q =10(cm) 50 % 50 % 0645 x y xy x :5=6:44x=30 x=: 2 : 6:4=8:(y-8)6y=80 y=: 3º: xy=: 2 :_: 3º:= % 10 cm : = : 10:8=(3+ ) : 10 = =24 =12(cm) 0646 x :3=y :8=6:4 x :3=6:4 4x=18 x=;2(; 060

61 y :8=6:4 4y=48 y=12 3 : 2.5=(8+4) : z 3z=30 z=10 ;:$]{:Z;=4_;2(;_10_;1 2;= H H E : =EG :H 4 : (4+2)=EG :3 6EG =12 GF = =5(cm) EG =2(cm) EF =EG +GF =2+5=7(cm) E : =EI : 4 : (4+2)=EI :8 6EI =32 EI =: 3 :(cm) F : =IF : 2 : (2+4)=IF :5 4`cm E G 2`cm 3`cm 5`cm H 8`cm 4`cm E 2`cm 5`cm 5`cm 8`cm I F F x`cm H 6`cm =x cm E {16-x}`cm F 4`cm G x`cm EG =(16-x) cm H {20-x}`cm x`cm H =(20-x)cm H E : =EG :H 6:(6+4)=(16-x) : (20-x) 120-6x=160-10x4x=40 x=10(cm) 10 cm 0651 H H E : =EG :H 3 : (3+2)=EG :4 5EG =12 GF = =6(cm) EF =EG +GF EG =: 5 :(cm) EF =: 5 :+6=: 5 :(cm) E 6`cm G 4`cm H 6`cm 6`cm F 6IF =10 IF =;3%;(cm) EF =EI +IF =: 3 :+;3%;=7(cm) 0648 E : =EG : 2 : (2+4)=x :12 6x=24 x=4 F : =GF : 4 : (4+2)=6 : y 4y=36 y=9 x+y=4+9= J L IL :I =K :IL 1 : 4=K :6 4K =6 K = =6(cm) =K +K K =;2#;(cm) =;2#;+6=: 2 :(cm) 6`cm K 6`cm E F G H I L 6`cm 6`cm J : (5+3)=5 : (x-3) 5x-15=40 x= `cm 3`cm l 3`cm 5`cm m {x-3}`cm n 50 % 20 % 0653 OªO O :O =6:10=3:5 EO : 10=3 : (3+5) 8EO =30 6:OF =(3+5) : 5 8OF =30 EF =EO +OF EO =: 4 :(cm) OF =: 4 :(cm) EF =: 4 :+: 4 :=: 2 :(cm) 061

62 0654 PO =x cm OQ =(8-x) cm P : =1:3 =3x(cm) (8-x) : 3x=1:3 6x=24 x=4(cm) =3_4=12(cm) :4=3:2 2 =12 =6(cm) + =6+12=18(cm) 0655 EªE E :E =2:3 E : =2:5 F :4=2:55F =8 F =;5*;(cm) 0656 EªE E :E =6:8=3:4 E : =3:7 EF :8=3:77EF =24 EF =: 7 :(cm) 18 cm 0657 ªEF :F =3:2 F :F =1:2 F : =1:3 1:3=2: =6(cm) 0658 FªF F :F =6:12=1:2 x :8=1:22x=8 x=4 1:3=y:123y=12 y=4 x+2y=4+2_4=12 E F EF :20=3:88EF =60 12`cm EF =: 2 :(cm) E=;2!;_16_: 2 :=60(cm ) 0660 step_1 step_2 step_ E F 16`cm 20`cm 60 cm F EF E E=F F E=F EªF EªF : =E :F F =E : =E :E EªEF : =E :E E F EEF EE=EF EªEF :F =E :E F = : =E :E E : EF E EªE E :E =12 : 20=3 : 5 E : =3: step_1 step_2 8:GH =(4+12) : 12 16GH =96 GH =6(cm) GEHªE EH :E =GH : =6:12 =1:2 062

63 step_3 EH :H =1:3 H EF :12=1:33EF =12 EF =4(cm) 4cm 0663 GH EH :E EF 6:GH =(2+8) : : : =20 : 12=5 : 3 : =5 : 3 =;2!;_20_12=120(cm ) =;8#; GH =48 GH =: 5 :(cm) GEHªE EH :E =GH : EH :E =: 5 : :8 EH :E=3:5 EH :H =3:8 H EF :8=3:88EF =24 EF =3(cm) 3cm 0664 x 3 y 3 x-y 1 E x :6=3:55x=18 x=: 5 : FEª y :5=3:66y=15 =;8#;_120=45(cm ) 45 cm 0667 F y x y-x F E F PQ PE =QF =7(cm) `cm l 6`cm x`cm P m 13`cm 8`cm E 12`cm Q y`cm F n 6 : (6+8)=(13-7) : (y-7) 6y-42=846y=126 y=21 6:8=x :128x=72 x=9 y-x=21-9=12 12 y=;2%; x-y=: 5 :-;2%;=;1!0!; ;1!0!; 0665 H 3 H 3 H 2 =H 15 =9_ =25(cm) H = -H =25-9=16(cm) H =H H H =16_9=144 H =12(cm) H=;2!;_16_12=96(cm ) 96 cm 0668 OÍ EÍ FÍ GÍ (0 2)G(1 3) x y G{1,`3} F G 2 y=x+2 x -2 O E x x=-2 (-2 0) (-2 0) 063

64 0669 ªEF : = :E 32 : 24=24 : E 4 : 3=24 : E E =18(cm) E = -E =32-18=14(cm) ªGHE :E = :EH 32 : 14=24 : EH 16:7=24:EH EH =: 2 :(cm) E +EH =14+: 2 :=: 2ª:(cm) 0670 E FªEF F : 2ª: cm ªE =E E FEF F=EF F=EF FªEF ªE : = :E 8: =6:9 6 =72 =12(cm) :E = :E :E =2:3 FªEF F :F = :E F :F =2:3 F =;5#; =;5#;_12=: 5 :(cm) 20 % 20 % : 5 : cm :EF = :F 10:EF =8:48EF =40 EF =5(cm) EF E EF F =;2%;54 E EF F =: 2 :(cm) : 2 : cm 0672 MEM M=EMM =M M=EM M EM S E = =4(cm) E =4+4=8(cm) PEP P=EP P=EP PªEP :E =4:8=1:2 1:2 PE 6_;3@;=4(cm) PE=;2!;_8_4=16(cm ) 0673 E = E+E=120 E+=120 E= Eª E : = : E : 1=4 : (4+1)5E =4 E =;5$;(cm) 0674 GE =GE=GE ªGE :E = :G 20:E =16:1016E = cm ;5$; cm E =: 2 :(cm) : 2 : cm 0671 EF=+= E EF=E+E= ªEF :E = :F 5:E =8:48E =20 E =;2%;(cm) 0675 = =8_2=16 =4(cm) M M =M =M =;2!; =5(cm) M =H M 4 =H _5 H =: 5 :(cm) : 5 : cm 064

65 0676 ='E=90 '+'E=90 '+'=90 '='E 'ª'E : ' =' : 'E : x=10:5 =2x(cm) E = -E =2x-5(cm) ' = -' =10-x(cm) ' :E =' : 'E (10-x) :(2x-5)=2 : 1 4x-10=10-x5x=20 x=4 4 EF=;7#;E=;7#;_;5#; EF=;3ª5; EF 1112 =;3ª5; ;3ª5; 0680 : I :I : = : =4:5 =;9$; =;9$;_6=;3*;(cm) 0677 E 6 : 4=E :E FE x : (6-x)=E :E x : (6-x)=6:4 4x=36-6x10x=36 I I :I = : I :I =4 : ;3*; I :I =3:2 3:2 x=: 5 : 0678 = ª : = : 12 : 24= :20 =10(cm) : = : 12 : 24= :12 =6(cm) =24-6=18(cm) E :E = : =10 : 20=1 : 2 E =;3!; =;3!;_18=6(cm) : 5 : 6cm : 12=4 : x6x=48 x=8 6 : 12=y :1012y=60 y=5 12 : z=10:1210z=144 z=14.4 x+y+z= = E :E =2:1E : =2:3 E : =EN : 2 : 3=EN :213EN =42 EN =14(cm) E :E =2:1 :E =3:1 :E = :EM 3:1=15:EM 3EM =15 EM =5(cm) MN =EN -EM =14-5=9(cm) 0683 EF GE :G =8:20=2:5 GE :E =2:3GF :F =2:3 9cm 0679 E :E =3:2 E =;5#; =;5#;_10=6(cm) E EF :F =E : =6:8=3:4 EF : F=3 : 4 EF=;7#;E yy F =;2#; GF EF EH :H =8:20=2:5 EH :E =2:3FH :F =2:3 F =;2#; FH =21 cm =F +F E :E =3:2 =;2#;FH +;2#; GF E : E=3 : 2 E=;5#; yy =;2#;(FH +GF )=21 GH =FH +GF =14 (cm) 14 cm 065

66 MN =;2!; x=;2!;_8=4 =2MN x=2_7= PQ =;2!; =;2!;_6=3(cm) QR =;2!; =;2!;_10=5(cm) PR =;2!; =;2!;_8=4(cm) PQ +QR +PR =3+5+4=12(cm) 3cm 5cm 4cm 12 cm G =GG' +G' =10+5=15(cm) G :G =2:1G :15=2:1 G =30(cm) 0692 ;2!;_18=9(cm ) ;3!;_18=6(cm ) 10 cm 15 cm 30 cm 9cm 6cm :6=2:3 2:3 2 :3 =4:9 2:3 2:3 4: M x=;2!;_18=9 =2MN x=2_8= :8=3:4 3 :4 =9:16 3 :4 =27:64 3:4 9:16 27: MP =;2!; =;2!;_20=10 PN =;2!; =;2!;_30= cm_50000= cm=4000 m=4 km 4km MN =MP +PN =10+15= km_;300!00;= cm_;300!00;=20 cm 20 cm 0688 MP =;2!; =;2!;_4=2 MQ =;2!; =;2!;_10=5 PQ =MQ -MP =5-2= =;2!;=;2!;_50=25(cm ) :x=2:12x=8 x=4 3:y=1:2y=6 6:x=2:12x=6 x=3 y=;2!;_12=6 x :15=2:33x=30 x=10 y=9 25 cm x=2_7=14 y :4=3:1y=12 x=4y=6 x=3y=6 x=10y=9 x=14y= GG' : G' =2:1GG' :5=2:1 GG' =10(cm) 0697 =2PQ x=2_5=10 MN =;2!; y=;2!;_10=5 MN MN= z=85 x+y+z= = N =N =;2!; x=;2!;_8=4 MN =;2!; y=;2!;_10=5 x+y=4+5= MN MN==70 MN x=180-(70+65)=45 =2MN y=2_15=30 x+y=45+30=75 066

67 0700 PM =;2!; =;2!;_10=5(cm) 0706 PN =;2!; =;2!;_10=5(cm) 50 % PM +PN =5+5=10(cm) EF 50 % 0701 F = E E =E =2E =2_8=16(cm) FE F =E =8(cm) F = -F =16-8=8(cm) 50 % 50 % 8cm F E FE EF SSS EF=;4!;=;4!;_32=8(cm ) 0707 EG =x cm FF =2EG =2x(cm) EE =2F =4x(cm) G =E -EG =4x-x=3x(cm) 8cm 3x=18 x=6(cm) 0708 FGE =;2!;F =;2!;_8=4(cm) 0702 MN E 16`cm EE =2F =2_8=16(cm) G =E -GE =16-4=12(cm) E M N 0709 E =x cm EM =;2!; =;2!;_6=3(cm) 6`cm EF =;2!;E =;2!;x(cm) GG =2E =2x(cm) EN =;2!; =;2!;_16=8(cm) GF =G -F =2x-;2!;x=;2#;x(cm) MN =EN -EM =8-3=5(cm) 5cm ;2#;x=36 x=24(cm) 0703 E =;2!; =;2!;_7=;2&;(cm) EF =;2!; =;2!;_9=;2(;(cm) 0710 E F E F E F =;2!; =;2!;_14=7(cm) F =;2!;E =;2!;_16=8(cm) 16`cm G EF F E +EF +F =;2&;+;2(;+7=15(cm) GE =;2!;F =;2!;_8=4(cm) 0704 =2_EF 0711 =2_2_GHI =2_2_6 =24(cm) 0705 F =F E =E EF = E =E E =;2!; =F =EF F =E F F EF SSS =EF E =F E F EG G E F E F =;2!; E =;2!;_20=10(cm) F EG =;2!;F =;2!;_10=5(cm) 20 % E G F 20`cm E EF SSS G =E -EG =20-5=15(cm) F=E 15 cm 067

68 0712 L HN N HN M =MH ML HN L =LN L H =H L HN LN =N L =LN =N yy 24`cm L 24`cm M N H yy G G EG EF S G =F =6(cm) F = G F F =2G =2_6=12(cm) = F +F =12+6=18(cm) G E F 6`cm 18 cm L =;3@; =;3@;_24=16(cm) 16 cm 0717 PQ =;2!; QR =;2!; 0713 EG G EG =;2!; =;2!;_24=12(cm) EFGF FEG=F E F =F EFG=F EFG F S =EG =12(cm) E 24`cm G F RS =;2!; S P =;2!; PQRS PQ +QR +RS +SP =(PQ +RS )+(QR +SP ) = + =18+16 =34(cm) 0718 P =P Q =Q 0714 EG G EFG F S GF = F =12(cm) G =24(cm) E =E EG G =G =24(cm) =2_24=48(cm) 0715 GE G =x cm GFE F S GE = =x(cm) =2GE =2x(cm) 30`cm = + =x+2x=3x(cm) 3x=30 x=10(cm) E G 12`cm F G F E PQ PQ = ;2!; S =S R =R yy SR S R =;2!; yy PQ S R PQ = S R PQRS 0719 ;2!; SR = =12(cm) PQ =SR =;2!; =;2!;_12=6(cm) G F 20 % PS =QR =;2!; =;2!;_12=6(cm) PQRS =24(cm) 068

69 0721 PQRS PQRS PQRS 20 % PQRS PS =;2!; =;2!;_8=4(cm) PQ =;2!; =;2!;_6=3(cm) PQRS=4_3=12(cm ) 12 cm 0726 EF P EP =;2!; =;2!;_4=2(cm) PF =;2!; =;2!;_6=3(cm) EF =EP +PF =2+3=5(cm) IEF GH =;2!;EF =;2!;_5=25(cm) I 4`cm H G y`cm P E F x`cm 6`cm x=5y=25 x+y=5+25= MP =;2!; =;2!;_8=4(cm) MQ =;2!; =;2!;_12=6(cm) 0727 E=;2!; E=;2!;_{;2!;} E=;4!;_48=12(cm ) PQ =MQ -MP =6-4=2(cm) 0723 EG =;2!; =;2!;_10=5(cm) GF =;2!; =;2!;_4=2(cm) EG -GF =5-2=3(cm) 0728 =2 =2_(3EF) =2_3_6=36(cm ) 0729 H =2=2_18=36(cm ) ;2!;_ _H =;2!;_8_H =36 50 % 50 % 0724 H =9(cm) 9cm MP MQ 20 % 0730 G G =;3@; =;3@;_36=24(cm) G =;3!; =;3!;_36=12(cm) MP =;2!; =;2!;_10=5(cm) MQ =MP +PQ =5+3=8(cm) =2MQ =2_8=16(cm) 16 cm G'G GG' =;3@;G =;3@;_12=8(cm) G' =G +GG' =24+8=32(cm) 0731 G G =;2!; G =;2!;_10=5(cm) 0725 MP =;2!; =;2!;_6=3(cm) MQ =2MP =2_3=6(cm) =2MQ =2_6=12(cm) =G +G =10+5=15(cm) =;2!; =;2!;_10=5(cm) x=15y=5 x+y=15+5=20 069

70 0732 G G =;3@; =;3@;_24=16(cm) M M =;2!; =;2!;_24=12(cm) GM =G -M =16-12=4(cm) 0737 G G =;3!; =;3!;_12=4(cm) GE =;2!;G =;2!;_10=5(cm) E =E = E =;2!; =;2!;_16=8(cm) 0733 G G =2G =2_5=10(cm) =G +G =10+5=15(cm) = = =15(cm) =2_15=30(cm) 0734 G GG' = = =;2!; =;2!;_18=9(cm) G 20 % GE G +GE +E =4+5+8=17(cm) 0738 G :G =2:1 x=g =2G =2_6=12 = =12(cm) GF G : =GF : 12 : 18=y :12 y=8 x+y=12+8= G G =;2!; G =;2!;_4=2(cm) =2+4=6(cm) E =E F =F EF =;2!; =;2!;_6=3(cm) G =;3!; =;3!;_9=3(cm) G'G 0740 GG' =;3@;G =;3@;_3=2(cm) 2cm EF GG' 50 % 50 % 0735 O r cm pr =4p r=2 G =2_2=4(cm) G :G =2:1 G =4_2=8(cm) O' 4cm p_4 =16p(cm ) 16p cm GG' E =E F =F EF =E +F =;2!;( + ) EF=;2!; =;2!;_24=12(cm) EF G :E =G' :F =2:3 GG' :EF =2:3GG' :12=2:3 3GG' =24 GG' =8(cm) 8cm 0736 G G =2GM =2_3=6(cm) M =6+3=9(cm) M M N 0741 G GE =;3!;E =;3!;_12=4(cm) N =;2!;M =;2!;_9=45(cm) x=6y=45 x+y=6+45=105 GFªGE GF :GE =G :G =1:2 GF =;2!;GE =;2!;_4=2(cm) 2cm 070

71 0742 G G=GE=GE=5(cm ) EG=G+GE =2_5=10(cm ) 0748 G F =F F=;2!;=;2!;_36=18(cm ) GE F G :GF =E :E =2: G G=;6!;=;6!;_48=8(cm ) GE =E FE=;3@;F=;3@;_18=12(cm ) G :GF =2:1 GEF=;3!;FE=;3!;_12=4(cm ) 4cm GE=;2!;G=;2!;_8=4(cm ) 0744 G =;2!;_8_6=24(cm ) G 70 % 0749 OPQ O =3PO O =3OQ =O +O =3(PO +OQ )=3PQ =3_4=12(cm) P M Q O 4`cm N G=;6!; G=;6!;_24=4(cm ) 0750 O =;2!; =;2!;_18=9(cm) 4cm F F =;3@;O =;3@;_9=6(cm) 0745 G G=G=;3!; G=;3!;_24=8(cm ) EFG G GE+GF=;2!;G+;2!;G GE+GF=;2!;_8+;2!;_8=8(cm ) 0751 OPQ PO =;3!;O OQ =;3!;O PQ =PO +OQ PQ=;3!;(O +O )=;3!; M 48`cm O P N Q 0746 G'G G'G=G'=G'G=4(cm ) PQ=;3!;_48=16(cm) G=3_4=12(cm ) G G=G=G=12(cm ) =3_12=36(cm ) 0752 MN 60 % 0747 = F E F =FE E=2F =2_15=30(cm ) E =E =2E =2_30=60(cm ) = =2 =2_60=120(cm ) OPQ O =3PO O =3OQ =O +O =3(PO +OQ )=3PQ =3_12=36(cm) MN =;2!; =;2!;_36=18(cm) Q O 12`cm N P M 18 cm 071

72 0753 OP P :PO =2:1 O =O P :P =2:4=1:2 =3P =3_4=12(cm ) =2 =2_12=24(cm ) PMªP P :P =M : =1:2 =3P =3_4=12(cm ) =2 =2_12=24(cm ) 0754 ==;2!; =;2!;_72=36(cm ) P PE=PO=;6!; =;6!;_36=6(cm ) Q QO=QF=;6!; M P O =54(cm ) =- =54-24=30(cm ) 0757 ª : =15:9=5:3 : =5 :3 =25: Eª E : =9:18=1:2 E : =1 :2 E : 52=1 : 4 E=13(cm ) 0759 E : E Eª : =3:5 E : =3 :5 18 : =9 : 25 =50(cm ) E=-E =50-18=32(cm ) 32 cm =;6!;_36=6(cm ) 6_4=24(cm ) 0755 =8_6=48(cm ) =;2!; =;2!;_48=24(cm ) P PM=PO=;6!; PM=;6!;_24=4(cm ) OMP=2PM =2_4=8(cm ) 0756 ª : =6:9=2:3 : =2 :3 24 : =4 : 9 8cm 0760 OªO : =6:8=3:4 O : O=3 :4 O : 32=9 : 16 O=18(cm ) 0761 EFGH 3:1 3:1 : EFGH=3 :1 =9:1 EFGH 1 : (9-1)=1 : S1 {;6!;}2 _S=;3 6;S 2 =2_;3 6;S=;1 8;S =S-;1 8;S=;1!8&;S

73 0763 FGªHE 2:1 FG : HE=2 :1 =4:1 FGEH : HE=3 : 1 FGEH=6(cm ) 6:HE=3 : 1 HE=2(cm ) FG=4HE=4_2=8(cm ) G :G =1:2 FG : FG=1:2 FG=;2!;FG=;2!;_8=4(cm ) FGª 1:3 FG : =1 :3 =1:9 =9FG=9_4=36(cm ) 36 cm : 25=4 :5 4:5 4 :5 =64 : 125 V cm 128 : V=64 : 125 V=250(cm ) :5 2 :5 =8 : 125 V cm 24 : V=8 : 125 V=375(cm ) :6=1:2 1 :2 =1:4 S cm 60 : S=1:4 S=240(cm ) 0767 EFG 1:;3@;=3:2 3 :2 =9:4 EFG S cm 90 : S=9:4 S=40(cm ) 0768 Q Q Q 20 % Q 2:3 2 :3 =8:27 Q V cm V :81=8:27 V=24(cm ) Q 81-24=57(cm ) 57 cm :2 =1:8 x 5:x=1:8 x= = :1 2 :1 =4:1 18 (4_1) : (1_8)=1 : 2 1: ªE : = :E : ( +4)=10 : = =8(cm) 8 cm_50000= cm=4 km 0772 Eª E : =E : 10 : 60=15 : =90(m) ;10 00; 90 m_;10 00;=9000 cm_;10 00;=9 cm m=2000 cm 5cm ;20 00;=;40!0; =29 cm_400=1160 cm=116 m =132(m) cm_500000= cm=30 km 60 km ;4^0);= : : =1 : km = m = cm _;40000!0000;= 112=500(cm ) 4 073

74 : : 1000 =1 : _3=15(cm ) 15 cm _ = cm =1500 m cm 10 cm = = km cm cm_50000= cm=15 km 4 cm_50000= cm=2 km 15_2=3(km ) 3km 0778 step_1 step_2 step_ P P F = E =EF E F E F =FE E GF E =2GF =2_2=4(cm) F F =2E =2_4=8(cm) G =F -GF =8-2=6(cm) 20 % 6cm E =E F =F EF EF P :PE =3:1P EF P :EF =P :E =3:4 P :8=3:4 P =6(cm) =2EF =2_8=16(cm) P = -P =16-6=10(cm) 10 cm 0780 step_1 step_2 step_3 step_ =E =EF =F F=;4@; F=;4@;_60=30(cm ) GFEM F GF GEF=GFM=;6!;F GEF=;6!;_30=5(cm ) GEFM=GEF+GFM =5+5=10(cm ) G 10 cm G EF GF=GE=;6!; FEG=GF+GE=;3!; =3FEG=3_6=18(cm ) =E =E =;2#;=;2#;_18=27(cm ) 0782 EF F :FP :P P E =E EF EF =;2!; =;2!;_2=1(cm) EFPªP FP :P =EF : =1:5 F =F F :FP :P =(1+5) :1:5=6:1:5 P =;1 2; P=;1 2;_6=;2&;(cm) cm ;2&; cm 074