¹®Á¦ÀºÇàÇØ´ä(8³ª)01~39ok

Q uestion Bank 3, 6 2 1, 2, 4 3 2+3=5 2 3 5 1, 3, 5 3 2, 4, 6 3 3 3 5, 3 5+3=8 4500 6000,,,, 5 5 KTX 7, 2, 2 7+2+2=11,,,,,,,,,,,,,,,, 4 4 4, 8, 12, 16, 20 5 9 9, 18 2, 5+2=7 1 10 2, 3, 5, 7 4 7 (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) 6 (100, 100), (100, 50, 50), (50, 50, 50, 50) 3 1 (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 5), (5, 4), (4, 3), (3, 2), (2, 1) 10 4 (1, 5), (2, 6), (6, 2), (5, 1) 4, 10+4=14(),, 3 3_3=9() 5 4 5+4=9 3, 7 1

3_7=21, 1, 2, 3, 4, 5, 6 6,,,,,,,,, 4, 6_4=24 4, 3 4_3=12 X 1, 3, 5, 7 x, Y 2, 4, 6, 8, 10 y x, y 4_5=20 A4 BA 3 CA, B 2, 4_3_2=24 24,, 2,, 1, 2, 3, 4, 5, 6 6 2_6=12,, 4+7+3=14 1 3, 1 6 3_6=18,,,,,,,,,, 3 4+3=7 Question Bank 1, 3, 5, 7, 9 5, 8 1, 2, 4, 8 4, 1 5+4-1=8 11 12 13 14 15 16 17 18 19 10 11 12 12 5, 4 5_4=20 x, y x+y=5 (1, 4), (2, 3), (3, 2), (4, 1) 4 2

(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6) 15 7 2 7+2=9 A 4, B A 3, CA, B 2, DA, B, C 1 4_3_2_1=24, 2, 3, 5 3, 3 3, 6 2. 3 3+2-1=4 6, 2 6_2=12 12 A C 1, A B C 2_3=6 1+6=7,,,,,,,,,,,,,,,, 4 5, 6 5_6=30 350 Q uestion Bank 100 3 3 2 2 1 1 0 0 50 1 0 3 2 5 4 7 6 10 0 5 0 5 0 5 0 5 11 12 13 14 15 16 17 18 19 10 11 24 12 6 2_2_2=8 2_2_2_2=16 3_3=9 (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) 5 6, 5, 6_5=30 4_3=12 2 12-2=10 3

5 (1, 4), (2, 3), (3, 2), (4, 1) 4 10 (4, 6), (5, 5), (6, 4) 3, 4+3=7 A, B, C, D 4_3_2_1=24 5 3 5_4_3=60 12 1, 2, 3, 4, 6, 12, 30 1, 2, 3, 5, 6, 10, 15, 30 A 2 2, 4, 6, 12 4, B 2 2, 6, 10, 30 4., 4_4=16 A P B A : 2_3_2=12 A B P A : 2_3_2=12, 12+12=24 24 A 5, B, C, D 4, 3, 3 5_4_3_3=180 4_3_2_1=24,,,, 4_3_2_1=24 a 3_2_1=6 b bacd, badc, bcad, bcda, bdac, bdca bdac 6+5=11 3_2_1=6 6 B, E 4_3_2_1=24, B, E 24_2=48 2 3 3_2_1=6, 6_2=12 4

2 4_3_2_1=24, 2 24_2=48 6, 5,, 4 6_5_4=120 3_2_1=6, 6_2=12 12,, 3_2_1=6,,, 3_2_1=6 6_6=36, 3_2_1=6, 2, 2 6_2_2=24 0 1, 2, 3 3, 3, 3_3=9 31 110, 12, 13, 14 4 220, 21, 23, 24 4 330 1, 4+4+1=9 527 5 532, 537, 572, 573 4 7 7 3_2=6, 4+6=10 1, 2, 3, 4, 5 5, 4., 5_4=20 1 4, 3, 5 4 4_3=12 20 12 0 2 4. 0 5_4=20 2 4_4=16() 4 4_4=16, 20+16+16=52 5

., 4_3=12 12 10, 6 ;1 0;=;5#; ;5#;,,,,,,,,,,, 6 20, 5 5, 10, 15, 20 4 ;2 0;=;5!; ;2!;_4_(4-1)=6 5_4=20,,, 2 A B, C, D, E 4, 1 4_3=12, ;2!;_8_7=28, ;2 0;=;1 0; 4_3_2_1=24 (3_2_1)_2=12, ;2!4@;=;2!; 5 2 ;2!;_5_4=10 3 1 3, 10_3=30 A 2 =16, A c 2 =8 ;1 6;=;2!; 4_4=16 23 5 2 2, 23, 24 2 ;2!;_5_4=10 3 4, 4+4=8, ;1!6);=;8%; 6

x=1, y 1, 2, 3, 4, 5, 6 x=2, y 1, 2, 3 6_6=36 (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) 6 ;3 6;=;6!; 3_3=9 ;3ª6;=;4!; ;6!; ;4!; 2_2_2=8 1, 2,,,,,,,, 3, ;8#;, ;3ª6;=;4!; 11 12 13 14 15 16 17 18 19 10 11 12 Question Bank 2 4, 4 4 4_2=8 3_3=9,,,,, 3, ;9#;=;3!;, 9_8=72 6_6=36 8(2, 6), (3, 5), (4, 4), (5, 3), (6, 2) 5, ;3 6; 3 3_2_1=6, 6_2=12 2_2_2_2=16,,,,,,,,,,,,,,,, 4 C C A, B, D 3_2_1=6, C 6., 6_2=12, ;1 6;=;4!; 6_6=36 3x+y<10 5 2., ;2!;_5_4=10 7

, ;2 0;=;5@; 0 1, 2, 3, 4 4, 4,, 3., 4_4_3=48( ) ;6!;_5_4_3=10 ;2!;_4_3=6 10, 6 1, 2, 3, 6 4, ;1 0;=;5#; ;1 0=;5@; Q uestion Bank 2_2_2=8,,,,, 2 11 12 13 14 15 16 17 18 19 10 11 12 ;1 2;, ;8@;=;4!; 6_6=36 0 (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) 6, ;3 6;=;6!; 5_4_3_2_1=120 A A 4 4_3_2_1=24, ;1 2 0;=;5!; 4_3_2_1=24 0 2, 3, 5, 7 4, 4, 4_4=16 4 4_3_2_1=24 5_4=20 3 12, 15, 21, 24, 42, 45, 51, 54 8 7 2 ;2!;_7_6=21 8

,, 2 ;2!;_3_2=3 5_4_3_2_1=120 3_2_1=6 6_2=12 40 4 41, 42, 43, 45 4 5 51, 52, 53, 54 4, 4+4=8, 2 2, 2 2_2_2=8, ;1 2 0;=;1 0; 6_6=36() ;ab;<1 b=1, a 2, 3, 4, 5, 6 b=2, a 3, 4, 5, 6 b=3, a 4, 5, 6 b=4, a 5, 6 b=5, a 6, ;3!6%;=;1 2; ;1 2; 5 0 5. 0 5_4=20 5 4_4=16, 20+16=36 2_2_2_2=16,,,,,,,,,,,,,,,,,,,,,,,, 6, ;1 6;=;8#; 9 3 3, ;9#;=;3!; 2 2 ;2!;_5_4=10, ;9@; 1 3_2=6 0, 0, ;1 0;=;5#; ;3!; ;9@; 0 9

5 2 5_4=20 30 12, 13, 14, 15, 21, 23, 24, 25 8 ;5@; 11 1 6_6=36,, 6 =1- =1-;3 6;=;3#6);=;6%; ;5@; 1 0{p{1 10, 10 10 10 1, 1 0 4_3=12, 3 =1- =1-;1 2;=;1ª2;=;4#; ;6%; 0 1 ;2!; ;3!; 4, 1 1 5_4=20, 45 51, 52, 53, 54 4 45 =1-45 =1-;2 0;=;2!0^;=;5$; =1- =1-;1 2;=;1!2!; ;1!2!; 2_2=4,, 1 =1- = =1- =1-;8%;=;8#; =1-;4!;=;4#; 2_2_2=8, 3 1 10

1=1-3 1=1-;8!;=;8&; Question Bank ;2!;_10_9=45, 2 11 12 13 14 15 16 17 18 19 10 11 12 ;1ª4; ;2!;_6_5=15 1 =1-2 =1-;4!5%;=;4#5);=;3@; 5, 5 ;5%;=1 ;2!;_5_4=10, ;2!;_3_2=3 =1- =1-;1 0;=;1 0; ;1 0; 6, 6 1, 2, 3, 4, 5 5 6 ;6%; =1- =1-;10*0;=;1ª0 0;=;2@5#; 6_6=36, 5 5_5=25 5 =1-5 =1-;3@6%;=;3!6!; =1- =1-;1 0;=;1 0;=;5@; ;2!;_7_6=21, ;2!;_3_2=3 3_3=9,,,,, 3 =1- =1-;9#;=;9^;=;3@; =1- =1-;2 1;=;2!1*;=;7^; 6, 20 x 11

1, 2, 4, 5 4 20 { } x 20 =1-{ } x =1-;6$;=;6@;=;3!; 6_6=36,, 3_3=9 =1- =1-;3ª6;=;3@6&;=;4#; 1 25 4 6, 9 2 4 9 8 4 9 =1-4 9 =1-;2 5;=;2!5&; 8_7=56,, 5_4=20 1 =1-, =1-;5@6);=;5#6^;=;1ª4; ;1ª4; 6_6=36,, 7 (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) 6 7 =1-7 Q uestion Bank 11 1 12 13 14 15 16 17 18 19 10 11 12 =1-;3 6;=;3#6);=;6%; 4_3_2_1=24, 3_2_1=6 =1-, 1 1, 6 0 =1-;2 4;=;2!4*;=;4#; 2_2_2_2=16, 4 1 1 =1-4 =1-;1 6;=;1!6%; p+q=1, p=1-q, q=1-p, 0{p{1, 0{q{1 =1- =1-;2 0;=;2!0(; 12

15, 2, 3, 5, 7, 11, 13 6 =1-2_2_2=8,,, 1 =1- =1-;1 5;=;1ª5;=;5#; =1-;8!;=;8&; ;6!;_6_5_4=20, ACE, BDF 2 =1- ;2!;_6_5=15, ;2!;_3_2=3 =1-;2 0;=;2!0*;=;1ª0; 1 =1-5_4_3_2_1=120, A D (4_3_2_1)_2=48 A D =1- A D =1-;1 2 0;=;1 2 0;=;5#; 6_6=36,, 10 (4, 6), (5, 5), (6, 4), (5, 6), (6, 5), (6, 6) 6 10 =1-10 =1-;3 6;=;3#6);=;6%; =1-;1 5;=;1!5@;=;5$; ;2!;_6_5=15, ;2!;_4_3=6, 1 =1- =1-;1 5;=;1 5; A 2 =16, A 1 2 =8 1 =1-1 3 3, 6, 9, 12, 15, 18 6 ;2 0;=;1 0; 8 8, 16 2 ;2 0;=;1 0; 3 8 =1-;1 6;=;1 6;=;2!; ;1 0;+;1 0;=;1 0;=;5@; ;1 0; ;1 0; ;5@; 13

43+19+26+12=100 B O = B + O B O =;1 0ª0;+;1 0 0;=;1 0 0;=;2ª0; A B ;6$;=;3@;, ;5@; ;3@;_;5@;=;1 5; 1 ;8@;, 3 ;8!; A B ;6@;=;3!;, ;5#; ;3!;_;5#;=;5!; ;8@;+;8!;=;8#; ;3!;_;5@;=;1 5; ;1 5; ;5!; ;1 5; 6_6=36, 5(1, 4), (2, 3), (3, 2), (4, 1) 4 ;3 6; 6(1, 5), (2, 4), (3, 3), (4, 2), (5, 1) 5 ;3 6;, ;3 6;+;3 6;=;3ª6;=;4!; =1- =1-;4#;=;4!; =1- =1-;3@;=;3!; =;4!;_;3!;=;1 2; ;4!; ;3!; ;1 2; 5_4_3_2_1=120 T 4_3_2_1=24, Y 24 ;1 0º0=;5$; =;5$;_;5$;=;2!5^;, ;1 2 0;+;1 2 0;=;1 2 0;=;5@;, =_ 4_4=16, ={1-;1 0;}_;1 0;=;1 0;_;1 0;=;1 0 0;=;2 5; 10 10 1 ;1 6;, 23 23, 24, 30, 31, 32, 34, 40, 41, 42, 43 10 ;1!6);, ;1 6;+;1!6);=;1!6!; =1- =1-{1-;2!;}_{1-;5#;}=1-;2!;_;5@;=;5$; 14

=1-;9&;_;8^;=1-;1 2;=;1 2; 2 =;8#;_;8#;=;6ª4; ;8#;, 7 2, ;7@; ;8#;_;7@;=;2 8; = =;1 6; 10 4 ;6ª4; ;2 8; C C = 9p-4p = =;9%; ;9%; 9p =;1 0;_;1 0;=;2 5; ;2 5; 103 3, 6, 9 3 =;1 2;_;1 1;=;3 3; ;4!;, ;4!;_;4!;=;1 6; K, I, N, G ;1 6;_4=;4!; ;1 0; ;1 0; B = B _ B =;4!;_;5!;=;2 0; ;2 0; 2, 1 3 3,,,,,,,, 3 ;1 0;, ;9&; ;2!;_;2!;_;2!;=;8!; ;8!;+;8!;+;8!;=;8#; ;1 0;_;9&;=;3 0; ;6!;_4_3_2=4 =1- (2, 3, 4), (2, 4, 5), (3, 4, 5) 3 ;4#; 15

11 12 13 14 15 16 17 18 19 10 11 12 ;5#; Question Bank 4, 1, 2, 3 3 10-2 =;8#; ={1-;6!;}_{1-;1 0;}=;6%;_;1ª0;=;4#; 2+5+3=10, ;1 0;, ;1 0; =;1 5;_;1 4;=;1 5; ;1 0;+;1 0;=;1 0;=;2!; 2 ;3!0%;=;2!; =1- =1-;2!;_;2!;=1-;4!;=;4#; 5 ;3 0;=;5!; 2 5, 10 ;3 0;=;1 0;, ;2!;+;5!;-;1 0;=;5#; = + =;1 0;_;1 0;+;1 0;_;1 0;=;2 5;+;2 5;=;2!5@; 4_3=12, 3, 3, ;1 2;+;1 2;=;1 2;=;2!; =1- =1-;2!;_;1 0;=1-;2 0;=;2!0&;, 1, ;2!;, ;9%;_;8$;=;1 8;,, 1, ;6#;=;2!; ;2!;_;2!;=;4!; ;9$;_;8%;=;1 8;, ;1 8;+;1 8;=;1!8);=;9%; 16

4 ADEB, BEFC, DGHE, EHIF, ADFC, DGIF, AGHB, BHIC, AGIC, BDHF 10 ADEB, A D G B E H C F I BEFC, DGHE, EHIF, AGIC, BDHF 6, ;1 0;=;5#; ;5#; Q uestion Bank =;1 0;_;9^;=;1 5; A, B =1- =1-;5@;_;4#;=1-;1 0;=;1 0; 11 12 13 14 15 16 17 18 19 10 11 12 =1- =1-;3!;_;8%;=1-;2 4;=;2!4(; =;8#;+;1 6;=;1 6; ;5!;, ;5$; 0(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) 6, 5 (1, 6), (6, 1) 2 =1- =1-;5$;_;5$;_;5$;=1-;1 2 5;=;1 2 5;, ;3 6;+;3 6;=;3 6;=;9@; A, B 5_4=20, ;7$;_;8%;=;1 4;, A, B 13 12 1 ;2 0;, 43 43, 45, 51, 52, 53, 54 6 ;2 0;=;1 0; ;7#;_;8#;=;5ª6;, ;1 4;+;5ª6;=;5@6(;, ;2 0;+;1 0;=;2 0;; =1- =;6%;_;3@;=;9%; =1-;2!;_;4!;_;5@;=1-;2 0;=;2!0(; 17

2 = 2+ 2 =;7$;_;6#;+;7#;_;6@;=;7@;+;7!;=;7#; 1, 1 5_4=20, 2 ;2!;_5_4=10 a+b=20+10=30 P C 2, 7, 12 P C = 2+ 7 =+ 12 =;3 6;+;3 6;+;3 6;=;3 6;=;9@; Q uestion Bank 11 12 13 14 15 18 16 17 18 35 19 10 11 12 13 14 ;3 6; 15 16 ;2ª5; 3_3_3=27, 3+6=9, 27-9=18 18 B, 3_2_2_2=24 4 (1, 3), (3, 1) 2, 10 (1, 9), (2, 8), (3, 7), (4, 6), (6, 4), (7, 3), (8, 2), (9, 1) 8, 2+8=10 A 2, 4, 6 3, B 1, 3, 5 3 3_3=9 0 1, 2, 3, 4 4, 4, 4_4=16 =;6!;_6_5_4=20 x=20 =;2!;_6_5=15 y=15 x+y=35 35 3_2_1=6,,,,,, 2, ;6@;=;3!; 2, 2 2_2=4 1 2 =;5 0;+;5 0;=;5 0;=;2 5; 18

;5#;_;3!;+;5@;_;5@;=;5!;+;2 5;=;2ª5; ;2ª5; 1-{;1 2;+;4!;}=;6!;, ;4!;_;6!;=;2 4; Q uestion Bank =1- =1-;4#;_;4#;=1-;1ª6;=;1 6; 11 8 12 16 13 4536 14 8 15 22 16 20 17 ;2!5@; 18 38 =1- =1-;3!;_;7#;=1-;7!;=;7^; 19 ;3@2!; 10 ;9%; a, =1- x=1 ax-b=0 a-b=0, a=b (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) 6 ;1Å0;_;1Å0;=1-;1 0 0;=;1 0 0; a =64 a=8 a>0, 8 8 1 ;3 6;=;6!; x=5 ax-b=0 5a-b=0, 5a=b1, 5 1 5 ;3 6;, ;3 6;+;3 6;=;3 6; ;3 6; 1, 2, 3 2 y 12, 3 y 13 1 4 y 14 4 5 y 15 3_4=12, 4, 41, 42, 43, 45 45 12+4=16 16 a+b = a, b + a, b =;4#;_;9$;+;4!;_;9%;=;3!;+;3 6;=;3!6&;,, 1~9 9, 9, 8,,, 7, 9_9_8_7=4536 4536 10 (1, 1, 8), (1, 2, 7), (1, 3, 6), (1, 4, 5), (2, 2, 6), (2, 3, 5), (2, 4, 4), (3, 3, 4) 19

8 8 8 ab, 3 3 a+b=33 a+b=65 a+b=98 a+b=124 fi a+b=152, 3 3+5+8+4+2=22 22 A, B, C, D, E, A B, C, D, E (D, E, C), (E, C, D) 2 2 ;2!;_5_4=10 10_2=20 20,, 3 5 5_5_5=125, 5_4_3=60 CA 2 AB 4, B 2_5=10, AB, BC, CA 1, 16+9+10+3=38 38, A 1 ;2!; A 3 1, 2, 3 ;2!;_;2!;_;2!;=;8!; A 5 1, 2, 3, 4, 5 ;2!;_;2!;_;2!;_;2!;_;2!;=;3 2;, ;2!;+;8!;+;3 2;=;3@2!; 3@2!; A ;3!;, C ;3!;, A, C ;3!;_;3!;=;9!; ;3!;+;3!;-;9!;=;9%; ;9%;, ;1 2º5;=;2!5@; ;2!5@; AB 4 BC A 3, C 4_4=16 BC 3 CA B C 2, A 3_3=9 A C =1- A C =1-;3@;_;3@;=;9%; 20

Q uestion Bank {1, 2, 3, 6, 9, 18},{1, 2, 3, 4, 6, 9, 12, 18, 36} x =16 x=4 {4, -4} {4} a=0 b=0 a +b =0,,,,, c=0 a+b, 8 6 6 8,, x}3 x}8 x=4, x}3 x}8 xy x, y a, b a+b a+b>0 a>0, b>0 a=3, b=-1 18 36 3x+1=4 x=2 -a>-b a<b 4 16 ab a, b a=2, b=3, 21

,, AB =AD, BE =DC, AC, AE, A, SAS Question Bank, 11 12 13 14 15 6 16 17 18 19 10 11,,,,, AOC+ AOD=180 AOC=180 - AOD yy AOD+ BOD=180 BOD=180 - AOD yy, AOC= BOD.,, ac>bc a>b c<0 ac>bc, a<b 8 4, PAMPBM AM =B M, PMA= PMB=90 PM PAM PBM SAS PA =PB, PAM= PBM QAM QBM SAS QAM= QBM PAQ= PAM- QAM = PBM- QBM = PBQ 180, ACE, ECD, ACE, ECD 60 ab=0 a=0 b=0 a=0 b=0 ab=0 a=1, b=3, a+b=4 22

a+b a, b 2 5 5 10 3x+5{ax-1 x}2 3x+5{ax-1, (3-a)x{-6 x}2 x} -6, -6 =2 3-a 3-a -6 =2, 2(3-a)=-6, -2a=-12 3-a a=6 6, AC =BC, CD =CE, ACD= BCE=120 ACDBCE SAS,AD =BE, DAC= EBC, ADC= BEC CAD+ CEB= CAD+ CDA =180 - ACD =60 Q uestion Bank 11 12 13 14 15 16 17 18 D, ASA 19 10 11 12 ASA,,,, 1,,, {1, 2, 3, 6},{1, 2, 3, 4, 6, 12} ABODCO B= C, BO =CO, AOB= DOC ABO DCO ASA AB =DC x =0 x=0 SAS { 3>2 ;3!;<;2!;} ;a!;>;b!; a>b ABCECD ACDBCE 3+(-1)>0 3>0, -1<0 x>0, y>0 x+y>0 x+y=5 x=3, y=2, 23

, ECD+ BFC= FBC+ BFC=90 FGC=90 x+3=5(x+1), x+3=5x+5-4x=2 x=-;2!;, a -;2!; ABCADE AB =AD, A, ABC= ADE ABCADE(ASA ) ASA D, ASA 180 -(65 +50 )=65,, ABCDCB BC, ABC= DCB, ACB= DBC ABCDCB(ASA ) ABC A= B= C, AB =BC =CA, AD =BE =CF BD =CE =AF ADFBED AD =BE, AF =BD, A= B ADFBED SAS FD =DE yy BED CFE SAS DE =EF yy, FD =DE =EF B=180 -(56 +62 )=62, ABC AB =AC AC =AB =4cm, x=4 ABC=180-130 =50, ABC BA =BC C=;2!;(180-50 )=65 x=65 4 65 A=40 B= C=;2!;(180-40 )=70 BCD C= D=70 DBC=180 -(70 +70 )=40 ABD=70-40 =30 BCFCDE CF =DE, C= D=90, BC =CD BCF CDE(SAS FBC= ECD, BFC= CED B M =C M, A M BC, CAM, A M, ABM, SAS, AMC, AMC B= CABC 24

x=47, y=3 x+y=47+3=50 AB =AC ACB= B=32 CAD= ABC+ ACB=64 CA =CD CDA= CAD=64 DBC DCE= ABC+ CDA =32 +64 =96 AB =AC ACB=;2!;(180-70 )=55 DC =DE DCE=;2!;(180-58 )=61 ACD=180 -( ACB+ DCE) =180 -(55 +61 )=64, RHS, RHA, AB =BC C=;2!;(180-48 )=66 ADC AD =AC ADC= C=66 DAC=180 -(66 +66 )=48 DAC= ACB(), AB =AC ABC= ACB=67 ABC= EAD( )EAD=67 ASA RHS RHA SAS ABCC=38., ECD=;2!; C=19 AB =AC B= C=;2!;(180-72 )=54 DEC=90 - ECD DEC=90-19 =71 71 DBC=;2!; ABC=27 DBC BDC=180 -( DBC+ C) =180 -(27 +54 ) =99 ACB= ACD=69 ( ), B A BAC= ACD=69 () 69 69 69 C D BCA ABC=180 -( BAC+ BCA) =180 -(69 +69 )=42 BOP, AP, BP, BOP, OP, RHA, AP, BP ABDBCE AB =BC yy ADB= BEC=90 yy DAB+ ABD=90, ABD+ CBE=90 DAB= EBC yy,, ABD BCE RHA AD =BE, DB =EC AD +CE =BE +DB =DE =10 cm 25

, AD =CE =5 cm, AE =BD =12 cm DE =AE -AD =12-5=7(cm) EBCDCB(RHS ) EBCDCB=;2!;(180-56 )=62 ECB=90 - EBC=90-62 =28 28 Question Bank BMDCME(RHS ), C= B=55 ABC AB =AC A=180 -( B+ C) A=180 -(55 +55 ) A=70 11 12 13 45 14 15 16 17 18 19 10 11 12 59 A= BABC AC =BC AC =8 cm ABC B=180 -(90 +50 )=40 BEDBEC BDE= BCE=90, ED =EC, BE BEDBEC(RHS ) EBC=;2!; B=;2!;_40 =20 C ABC CA =CB C=90 B=45. 45 ADEACE AD =AC, AE, ADE= ACE=90 ADEACE(RHS ) DE =CE, BD =4 cm BED =BD +DE +BE BED =BD +BC BED =4+8=12(cm) ABDCAE l A AB =CA, 12cm D ADB= CEA=90, C ABD= CAE 5cm E B ABDCAE(RHA ) ACB=180-114 =66 BA =BC x= ACB=66 ABC AB =AC, DB =EC AD =AE ABEACD AB =AC, AE =AD, A ABEACD(SAS ) DC =EB, DBF= ECF DBFECF DB =EC, DBF= ECF, DFB= EFC DBF ECF ASA 26

ABC AB =AC B= C=64, DBC=;2!; ABC, DCB=;2!; ACB DBC= DCB=32 DBC BDC=180 -( DBC+ DCB) DBC BDC=180 -(32 +32 ) DBC BDC=116 CBD= ABC=35 ACB= CBD=35 ABC x=180 -(35 +35 )=110 AB =AC ABC= ACB=66, DBC=;2!; ABC=33, DMB=90 - DBM DMB=90-65 =25 ODAOEA DAO= EAO, ODA= OEA=90, OA ODA OEA RHA DOA= EOA yy OFC OEC RHA FOC= EOC yy, AOC= EOA+ EOC=;2!; DOF DBFO DOF=360 -(90 +62 +90 )=118 AOC=;2!; DOF=;2!;_118 =59 59 ACE=180-66 =114 ACD=;2!; ACE=57 DBC BDC=180 -( DBC+ ACB+ ACD) DBC BDC=180 -(33 +66 +57 ) DBC BDC=24 Q uestion Bank 11 12 13 14 15 16 17 18 19 10 57 11 12.5 cm 12 98 cm RHA ASA ASA,, ACMBDM AM =BM, ACM= BDM=90, AMC= BMD ACM BDM RHA CM =DM =7 cm ABC AB =AC DBM= ECM=;2!;(180-50 )=65 A=180 -(96 +42 )=42, CAB CA =CB x=5 B= CABC AB =AC., AD BC, BAD= CAD ABDACD BD =CD, ABD= ACD, ADB= ADC=90 ABD ACD(ASA ) 27

AB =AC ABC=70 A= ABD=180 -(70 +70 )=40, DBC=70-40 =30 BCD BDC=180 -(30 +70 )=80 DBFECF DB =EC, BDF= CEF=90, DFB= EFC DBF ECF ASA FB =FC, FBC, BFC= DFE=108 AB =BD BAD=;2!;(180-56 )=62 FCB=;2!;(180-108 )=36 ABC BAC=62 +20 =82 B=56 C=180 -(82 +56 )=42 CED CD =CE EDC=;2!;(180 - C) EDC=;2!;(180-42 )=69 CA =CD DAC= ADC=66, BDC=66 +48 =114 DBC BD =DC ABC AB =AC B= C ABDACE AB =AC, BD =CE, B= C ABDACE SAS AD =AE, ADE AD =AE, DBC=;2!;(180-114 )=33 AD BC, DC =;2!; BC =3(cm) ADC=;2!; DC AD =;2!; AC DE ;2!;_3_4=;2!;_5_DE DE =2.4cm EFC CEF= AED=53 ECF=37 ABC AB =AC ABC= ECF=37 DAE= B+ C DAE=37 +37 =74 ADFE DFE=108 AB =AC B= C=66 BEDCFE BD =CE, BE =CF, B= C BED CFE SAS DE =EF, CEF= BDE=26 DEB=180 -(66 +26 )=88 DEF=180 -(88 +26 )=66 DEF ED =EF EDF=;2!;(180 - DEF) EDF=;2!;(180-66 )=57 57 AC =BC DBE= DAC=45 DBE DBE= DEB=45 DBE DB =DE ADEACE AD =AC, ADE= ACE=90, AE ADE ACE RHS 28

DE =CE, DB =DE =CE =5 cm ABC =2(6+4+5)=30(cm) DBE=;2!;_5_5=12.5(cm ) 12.5 cm OABC A ABDCAE AB =CA, DAB= ECA, ADB= CEA=90 ABDCAE(RHA ) DA =EC =6 cm, AE =BD =8 cm DBCE=;2!;_(6+8)_14=98(cm ) 98 cm OAB= OBA=35, OAC= OCA=13, BAC=48 BOC=2 BAC=2_48 =96 B 13 35 35 O 13 C OABC OAB+ OBC+ OCA=90 OB =OC OBC= OCB=;2!;(180-100 )=40, x+40 +35 =90 x=15,, x+23 +40 =90 x=27 OA OAB= OBA= a, OAC= OCA= b, OBC= OCB= c 2 a+2 b+2 c=180 a+ b+ c=90 a+ b=65 c=25 x=180 -(25 +25 )=130 27 130 ABC A M =B M =C M =3 cm, ABC 3cm EICFIC IEC= IFC=90, E I =F I, IÆC EIC FIC RHS, x=2 A=2_65 =130 OABC AD =BD =6cm, BE =CE =4cm, AF =CF =5cm x+36 +26 =90 x=28 x=90 +;2!; A=90 +;2!;_46 =113 28 113 29

IBC= ABI=30 BIC=180 -(30 +27 )=123 x=123 BIC=90 +;2!; A 123 =90 +;2!; A A= y=66 x+ y=123 +66 =189 BIC=119 119 =90 +;2!; A A=58 BOC=2 A=2_58 =116 OCB=;2!;(180 - BOC) OCB=;2!;(180-116 )=32 32 CE =CF AF =AC -CF =7-4=3(cm) x=3 AF =AD BD =AB -AD =6-3=3(cm) BD =BE BE =3cm y=3 x+y=3+3=6 AOB=2 C=2_53 =106 OAB= OBA=37 O'O O'ABO BO'O=2 BAO=2_37 =74 AO'O=2 ABO=2_37 =74 AO'B=74 +74 =148 IABC DIB= CBI= DBI DB =DI EI =EC DE =BD +CE ADE =AD +DE +EA ADE =AD +(BD +CE )+EA ADE =AB +AC ADE =8+6=14(cm) IABC DBC=34, ACB=180 -(52 +34 +34 )=60 ICB=30 I'DBC I'BC=;2!; IBC=;2!;_34 =17 II'B= I'BC+ I'CB=17 +30 =47 5cm ABC= AIB+ BIC+ CIA 57=;2!;{AB +BC +CA }_3 AB +BC +CA =38(cm) 38cm S =5_5_p=25p(cm ) DC S =2_2_p=4p(cm ) S -S =25p-4p=21p(cm ) 21p cm ABC DABC AB =AC B= C=;2!;(180-32 )=74 DBC= DCB=26 x=26 DABC DCA= DCB=30 y=30 x+ y=26 +30 =56 BAO= CAO=16 I ABI= IBC=37 O ABO= BAO=16 OBI= ABI- ABO=37-16 =21 21 30

11 12 13 14 15 16 17 18 19 10 11 12 9 Question Bank BAC=180 -(64 +58 )=58 ABI=;2!; ABC=;2!;_64 =32 IAB=;2!; BAC=;2!;_58 =29 AID=32 +29 =61 AOBBOCCOA=4 2 3 COA=360 _;9#;=120 ABC=;2!; COA=;2!;_120 =60 OABC OBC= OCB=40, BOC=180 -(40 +40 )=100 y+43 +34 =90 y=13 OA =OC OAC=43 x=180 -(43 +43 )=94 x+ y=94 +13 =107 A=;2!; BOC=50, AB =AC ACB=;2!;(180-50 )=65 ACO= ACB- OCB =65-40 =25 AM =B M =CM MCB=48 HBC CHB=90 HCB=42 MCH= MCB- HCB=48-42 =6 DIB DE //BC DIB= IBC IABC DBI= IBC DIB= DBI, DIB DB =D I EIC E I =EC DE =DB +EC ADE =AD +DE +AE ADE =AD +DB +EC +AE ADE =AB +AC ADE =7+5=12(cm) DC =xcm EC =xcm, AF =AE =(12-x)cm, BF =BD =(10-x)cm, AB =AF +FB 11=(12-x)+(10-x) 2x=11 x=5.5 ABC A rcm 15cm ABC= AIB+ BIC+ CIA 12cm F rcm rcm ;2!;_9_12=;2!;_15_r I E rcm B C D +;2!;_9_r+;2!;_12_r 9cm 18r=54 r=3(cm) 31

ABC AB =AC B= C=54 IABC IBC=;2!; B=27 OABC BOC=2 A=2_72 =144 OB =OC A rcm 13cm rcm rcm 5cm rcm I ABC= AIB+ B 12cm C BIC+ CIA ;2!;_12_5=;2!;_13_r+;2!;_12_r+;2!;_5_r 15r=30 r=2(cm) OBC=;2!;(180-144 )=18 IBC=;2!;_12_2=12(cm ) IBO= IBC- OBC IBO=27-18 =9 9 Q uestion Bank 11 12 13 35 14 15 16 17 18 19 10 129 ABC OA =OB =OC OC =;2!;AB =;2!;_10=5(cm) ABC =p_5 =25p(cm ) B 10cm O 8cm A 6cm C 11 24 12 11 cm BOC=2 A=2_55 =110 OABC OB =OC OBC=;2!;(180-110 )=35 35 DE //BC A DIB= IBC, I ABC D 6cm 9cm I DBI= IBC B 26cm DIB= DBI E 7cm C DBI DB =D I ECI E I =E C, DE =DB +EC =9+7=16(cm) DBCE=;2!;_(16+26)_6=126(cm ) 34 + x+ y=90 x+ y=56 A I =12-4=8(cm), A I, ABC 16cm AOC=2 B=2_65 =130 A D OACD AOD=2 ACD, 65 O COD=2 CAD B C, AOC=2( CAD+ ACD) 130 =2( CAD+ ACD) CAD+ ACD=65 ACD ADC=180 -( CAD+ ACD) ACD ADC=180-65 =115 32

OABC OCB= OBC=34 IABC PCB=;2!; OCB=;2!;_34 =17, PBC BPC=180 -( PBC+ PCB), PBC BPC=180 -(34 +17 ), PBC BPC=129 129,,,, IBC=30, ICB=22 IBC BIC=180 -(30 +22 )=128 BIC=90 +;2!; A 128 =90 +;2!; A A=76 BOC=2 A=2_76 =152 BOC- BIC=152-128 =24 24 AB // ID ABI= BID A IABC 9cm 10cm ABI= IBD I BID= IBD B D E C BID BD =IÆDÚ 11cm CIE IÆE =CE IDE =IÆDÚ+DE +E IÆ IDE =BD +DE +EC IDE =BC =11(cm) 11cm EBC= ECBEBC EB =EC ABC= DCB, EBC= ECB ABE= ABC- EBC ABE= DCB- ECB= DCE ABEDCE EB =EC, ABE= DCE, AEB= DEC ABE DCE(ASA ) AE =DE AB =AC ABC=68 BC =BD BDC=68, DBC=44 ABD= ABC- DBC ABD=68-44 =24 AB =AC B= C=62 BD =BE DEB=;2!;(180-62 )=59, CF =CE FEC=59 Q uestion Bank DEF=180 -(59 +59 )=62 62 11 12 13 14 15 16 62 17 18 2cm 19 10 11 12 13 3cm 14 189p cm ABC= CBEABD=46 ABC= CBE=;2!;(180-46 )=67 CBE= ACB ACB=67 33

ADCCEB AC =CB yy CDA= BEC=90 yy DAC+ ACD= ACD+ ECB=90 DAC= ECB yy,, ADC CEB(RHA ) CD =BE, AD =CE DE =CD -CE DE =BE -AD =8-6=2(cm) 2cm ABEECD AE =ED yy ABE= ECD=90 yy BAE+ AEB= AEB+ CED=90 BAE= CED yy,, ABE ECD(RHA ) AB =EC, BE =CD, BC =BE +EC =AB +DC ABCD=;2!;(DC +AB )_BC ABCD=;2!; BC _BC =;2!; BC ADEACE ADE= ACE=90, DAE= CAE, AE ADE ACE RHA, DE =CE =4cm ACE=;2!;_4_8=16(cm ) BI'C=90 +;2!; BIC BI'C=90 +;2!;_120 =150 rcm, a, b, c, =;2!;(a+b+c)r 51=;2!;_(13+11+10)_r 17r=51 r=3(cm) 3 cm ABC C r cm 30cm O ABC= AIB+ 24cm rcm BIC+ CIA A I 18cm B ;2!;_18_24 =;2!;_18_r+;2!;_24_r+;2!;_30_r 216=36r r=6(cm) ABC 15cm O- I =15_15_p-6_6_p=225p-36p =189p(cm ) 189p cm Q uestion Bank ADEC=2_16=32(cm ) OB =OC OBE= OCE=30 BOC=180 -(30 +30 )=120 11, 12 20cm 13 1 10 14 59 15 140 16 8.5 17 38 18 143 19, 10 75, A=;2!; BOC=;2!;_120 =60 IBC= ABI=36, ICB= ACI=24 BIC BIC=180 -(36 +24 )=120 I'IBC BD x BE =x, AF =AD =13-x, FC =EC =16-x B x A 13-x 13-x D P F I 16-x Q C x E 16-x 34

(13-x)+(16-x)=9, 2x=20 x=10cm BD =BE =10 cm PQ =PD +QE PBQ =BP +PQ +BQ =BP +PD +QE +BQ =BD +BE =10+10=20(cm) 20cm =;2!; AB =;2!;_13=6.5 r ;2!;_5_12=;2!;_(13+12+5)_r r=2, 2+6.5=8.5 8.5 AD =x (5-x)+(7-x)=8 x=2cm r IAD=;2!;_2_r=r D x x F 5-x 7-x B 5-x I E 7-x C OAB+ OBC+ OCA=90 OAB=20 OA =OB ABO=20 ABH=32 ABH BAH=90-32 =58 OAH= BAH- OAB OAH=58-20 =38 38 ABC= IAB+ IBC+ ICA ABC=;2!;_5_r+;2!;_8_r+;2!;_7_r ABC=10r IADABC=r 10r=1 10 1 10 BPRCQP B= C=62 BR =CP, BP =CQ BPRCQP(SAS ) BPR= CQP, BRP= CPQ, BRP+ BPR= CPQ+ BPR RPQ=62, PRQ PR =PQ PQR=;2!;(180-62 )=59 59 A=60 ABC+ ACB=120 EBC+ ECB=120 _;3!;=40 BEC=180-40 =140 140 ADC=68-38 =30 BA =BC BCA= BAC=68 ABC=180 -(68 +68 )=44 I I'ABCACD ABI=;2!; ABC=;2!;_44 =22 ADI'=;2!; ADC=;2!;_30 =15, BOD IOI'=180 -(22 +15 )=143 143,, ab=0 a=0 b+0, a+0, b=0 ab=0,, 35

ABCEBD BEF= BCH BEF=45 EBF= a, FBG= b CBH=90 - FBH= EBF= a BFGBHG FB =GB =HB BFG, BHG BFG= BGF, BGH= BHG FBG= HBG EBD= a+2 b=90 yy BFG BFG=45 + a b+2(45 + a)=180 2 a+ b=90 yy, a= b=30 GHB=45 +30 =75 E A F 45 a B b b a G D H 45 C 75 4 3 4_3_2 6 =4 4 6 6 12 6 (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) 5 12(6, 6) 1, ;3 6;=;6!; _ ;2!0);_;2!0);=;4!; 11 12 13 14 15 16 17 18 19 10 11 12 13 14 15 16 17 18 40 19 12 20 ;7$; 21 ;1 6; 22 6 6 18 23 25 24 120 25 {9-;4(;p} cm 1 =1- =1-;1ª0 0;_;9(9%;=1-;1!6%5@;=;1 6 5; 4_4_3=48 250 3 4 4_3_2=24, ;4@8$;=;2!; 3+2=5 5_4_3=60 3x+y{12 (x, y) (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), 36

(2, 5), (2, 6), (3, 1), (3, 2), (3, 3) 15, ;3!6%;=;1 2;,,,, IDA=81, IEA=96 DAE+ DIE=360 -(81 +96 )=183 DIE= BIC BIC=90 +;2!; DAE, DAE+ DIE= DAE+90 +;2!; DAE 183 =;2#; DAE+90 ;2#; DAE=93 DAE=62 AB =AC AB =AC ABC= ACB=66 ACB= BDC=66 DBC=180 -(66 +66 )=48 ABCCDE ABC= CDE=90, AC =CE ACB+ ECD= ECD+ CED=90 ACB= CED, ABC CDE RHA AB =CD, DE =BC BOC=2 BAC=2_24 =48 OB =OC OBC=;2!;(180-48 )=66 BIC=90 +;2!; BAC=90 +12 =102 IBC=180 -(102 +22 )=56 OBI= OBC- IBC=66-56 =10 A P 4, P B 10 A P B 4_10=40 40 ABDE=;2!;_(8+16)_24=288(cm ) AC =BC DBC= DAC=45 BDC=90 DCB= DCA=45, BD =CD =AD DBCDAC BOC=2 A=144 OB =OC OBC=;2!;(180-144 )=18., 3_2_1=6, 6_2=12 12 7_6 =21 2 4_3=12, ;2!1@;=;7$; ;7$; 37

A ;2!;_;8#;=;1 6; B ;2!;_;8@;=;8!;, ;1 6;+;8!;=;1 6; ;1 6; 6 6 18, CAB= x C E ACB= x 3x x x 2x 2x 100 CBD= CDB A B D F CBD=2 x(cba, DCE= DEC=3 x(acd ), EDF=4 x(eda ) 4 x=100 x=25 25 11 12 13 14 15 16 17 18 19 10 11 12 13 14 15 16 17 18 6 19 45 20 ;3!; 21 ;1!6#; 22AB =AC, AD BC BD =CD 23 57 24 14 cm 25 23 cm, 2,, 4,, 6 3 BACABCBCA=3 5 1 BAC=180 _;9#;=60 DA =DB =DC DABC BDC=2 BAC=2_60 =120 120 A 5, B A4, C A, B3, D A, C 3, E A, D3 5_4_3_3_3=540 r cm ABC= AIB + BIC+ CIA B A 15cm D F rcm 8cm I E C 17cm a5 4 5_4_3_2=120 ;2!;_15_8=;2!;_15_r+;2!;_17_r+;2!;_8_r 20r=60 r=3(cm) 90 =3_3-p_3 _ =9-;4(;p(cm ) 360 {9-;4(;p} cm 4 100 1,,,,,,,,,,,,,,,, ;1 6; 38

,,, ;1 6; A=180 -(57 +57 )=66, ;1 6;+;1 6;=;1 6; =;3@;_;5$;=;1 5; ABC= CBD, ACÍ// BDÍACB= CBD ABC= ACB=60, ABC BC =AC =5 cm ;8^;=;4#;, ;8^;=;4#;, ;4#;_;4#;=;1ª6; 4_4_3=48 3 0, 2, 4 0, 2, 7 2, 3, 4 2, 3, 7 0, 2, 4 2_2_1=4 0, 2, 7 2_2_1=4 2, 3, 4 3_2_1=6 2, 3, 7 3_2_1=6, 3 4+4+6+6=20 A=90 ABE=36 ABDEBD DAB= DEB=90, AB =EB, BD ABD EBD RHS ABD= EBD=18 ADB=90-18 =72 OBD O A BOC=180 -(29 +29 ) BOC=122 BAC=;2!; BOC BAC=;2!;_122 =61 B O 29 D C, ;4@8);=;1 2; c=0 a+b, AB // EC ABC= ECD, BAC= ACE ACB+ ACE+ ECD=180 ACB+ BAC+ ABC=180 BE =x cm A (14-x)cm (14-x)cm BD =x cm, D F CF =CE =(16-x)cm, xcm I (16-x)cm AF =AD =(14-x)cm B C xcm E(16-x)cm 12=(14-x)+(16-x), 2x=18 x=9(cm) BIC=90 +;2!; A 115 =90 +;2!; A ACB=57, AB =AC A=50 BOC=2 A=2_50 =100 39

4 (1, 5), (2, 6), (5, 1), (6, 2) 4 5 (1, 6), (6, 1) 2, 4+2=6 ;2!;_10_9=45 6 45 DCO FCO RHA EOA= DOA, DOC= FOC B=66 EOF=114 AOC= DOA+ DOC AOC=;2!; EOF=;2!;_114 =57 57 OABC OB =OA =OC ABO=90-30 =60 BAO= BOA=60, ABO OB =7 cm BC =OB +OC =14 cm 14 cm 10_9=90 6_5=30 ;9#0);=;3!; ;3!; ABC a, b, c, r ABC=;2!;r(a+b+c) =;4!; =1-;4!;=;4#; =;6!; =1-;6!;=;6%; =, +, =;4!;_;4#;+;4#;_;6%;=;1 6;+;8%;=;1!6#; ;1!6#; 23=;2!;_2_( ABC) ABC =23 cm 23 cm AB =AC, AD BC BD =CD EAODAO OEA= ODA=90, AO, EAO= DAO EAO DAO RHA 40

ADB= DBC=40 AOD AOD=180 -(50 +40 )=90 PH =8-3=5(cm) PF =10-4=6(cm) Q uestion Bank ABCDEBH= D=75 GPFD GP // DF, GD //PF GPFD GPF= D=75 FCH+ D=180 FCH=105 AD =BC =4cm A+ D=180 A=180-60 =120 PAB+ PCD= PAD+ PBC=;2!; ABCD PAB+12=30 PAB=18cm ADE=;2!;_70 =35, AD =BC 3x-1=2x+2 x=3 AB =DC 2y-2=4x-6 2y-2=6 y=4 OC =OA =3 y=3, OD =OB =4 x=4 x=3, y=4 x=4, y=3 AFD FAD=180 -(90 +35 )=55, BAD+ B=180 BAD=110 BAF= BAD- FAD=110-55 =55 AD // BC DAE= AEB, ABE BA =BE BE =BA =6cm AD =BC =BE +EC =6+2=8(cm) A+ B=180 AB=7 5 A=7 xb=5 x 7 x+5 x=180 x=15 C= A=7_15 =105 AB //CD ABE= CEB, BCE CB =CE CE =CB =8cm DE =CE -CD =8-5=3(cm) AB =DC =6 cm, AO =;2!; AC =4 cm BO =;2!; BD =6 cm AOB =AB +AO +BO =16(cm) AD //BC ADF= DFC, DCF CD =CF CF =DC =5cm BF =BC -CF =6-5=1(cm) 41

A+ B=180 CD OD =7 cm, OC =5 cm DOC =OD +OC +CD DOC =7+5+6=18(cm), AEHCGF AH =AD -DH =BC -BF =CF A= C, AE =CG AEH CGF(SAS ) EH =GF BFE DHG(SAS ) EF =GH, EFGH AD //BC DAC= ACB=45 ABD ABD+ BAD+ ADB=180 y+( x+45 )+35 =180 x+ y=100 A=3 xb=2 x, A+ B=180 5 x=180 x=36 D= B=2 x=2_36 =72 ABNM=;2!; ABCD, MPN=;4!; ABNM=;8!; ABCD MPNQ=2 MPN PAB+ PCD=;2!; ABCD ABCD=2( PAB+ PCD) =2(16+18)=68(cm ) MPNQ=;4!; ABCD=8(cm ) 8cm ABCD B= D=50 AB =BE ABE E= BAE=;2!;(180-50 )=65 Question Bank CFE= BAE=65, AB //DC 11 12 13 14 15 16 17 18 19 10 11 12 24 cm AD //BC EBC= AEB AEB= ABE, AE =AB =6 cm ED =AD -AE =8-6=2(cm) 42

ABC B=180 -(70 +45 )=65 ABCDD= B=65 Q uestion Bank ABCD AD //BC, BAE= DAE= AEB=50 BAD=2 BAE=100 BAD+ B=180 B=180-100 =80 D= B=80 11 12 13 14 15 16 16 cm 17 18 19 10 11 12, ABCD OA =OC yy OB =OD, BE =DF OE =OF yy, AECF AB //GH //DC, AD //EF //BC AEPG, GPFD, EBHP, PHCF GD =8-5=3(cm) PH =6-2=4(cm) EPG= EAG=110 PFC= GDC=180-110 =70 ADC=180-110 =70 ABEFCE ABE= FCE, BE =CE, AEB= FEC ABE FCE(ASA ), AB =FC =7cm DF =DC +CF =14(cm) ABCD AD =BC, AB =CD 2(AB +AD )=16 2(3+AD )=16 AD =5 cm ACD ADC=180 -(35 +70 )=75 ODC= OBA=48 ADB=75-48 =27 ABCFCB ABC= FCB, AB =FC, BC ABC FCB(SAS ) BC =CE, DC =CF BFED BFED=4_ FCB BFED=4_ ABC BFED=4_6=24(cm ) 24cm AD //BC DAE= AFB, ABF BF =AB =7 cm FC =BC -BF =10-7=3(cm) 43

x=180-70 =110 ABC B= C AB //RP, AC //QP B= RPC, C= QPB, B= QPB, C= RPC QB =QP, RC =RP ( AQPR) =AQ +QP +RP +R A =(AQ +QB )+(RC +RA ) =AB +AC =8+8=16(cm) yy yy 16 cm AGD DAG+ ADG=90, ABCD BAD+ ADC=180 BAG= DAG AD //BC DAG= EFG, ADG= FEG, ABFDEC AB =BF =DC =EC =8cm EF =BC -(BE +FC )=10-(2+2)=6(cm) AO =CO, AP =CR PO =RO yy BO =DO, BQ =DS QO =SO yy, PQRS A+ B=180 A=122 AD //BE DAE= AEC=35 DAC=70 BAC= A- DAC=122-70 =52 AB //DC ACD= BAC=52 AOECOF AO =CO, EAO= FCO, AOE= COF AOE COF ASA, AOE= COF EOD+ FOC= EOD+ AOE EOD+ FOC= AOD=;4!; ABCD EOD+ FOC=;4!;_60=15(cm ) A M //NC, A M =NC ANCM, AN //MÚC PN //MÚQ yy MÚD //BN, MÚD =BN MBND, MÚB //DN MÚP //QN yy, MPNQ ABCD AO =CO, BO =DO BE =DF EO =FO, AECF OA =OB =OC =OD x=12 ABC OCB=90-55 =35 OBC OB =OC OBC= OCB=35 DOC=35 +35 =70 BOC y=70 x+y=12+70=82,, 44

ABCD=2_{;2!;_12_6}=72(cm ) ABCDBAD+ ABC=180 EAB EAB+ EBA=;2!;( BAD+ ABC)=90, AEB= HEF=90 HGF= EFG= EHG=90, EFGH 90, ABCD BAD=90 DCB=90, AD //BC ABC= CDA=90, 90, ABCD DBC= ADB=35 BOC=90, OBC ACB=180 -(90 +35 )=55 ABNMMNCD PN =P M =QMÚ =QN, MPN= PNQ= NQM= QMP=90, MPNQ ( ABCD)=5_4=20(cm) ABCD ACB=;2!;_90 =45 EAC AE =CE, EAC= ECA=15, ACF ACB= EAC+ AFC AFC= ACB- EAC=45-15 =30 BD =2BO =6(cm) AC =BD x=6 OBC ACB=45 y=45 x+y=51 ABCD B= C, AD //BC A+ B=180, x= B=180 - A=65, ABCD ABC= DCB ABCD BO =;2!;AC =6(cm) ABCD=2 ABC ABCD=2_{;2!;_AC _BO } AD //BC ADB= DBC=35 ABD AB =AD ABD= ADB=35 45

, B= ABD+ DBC=70 C=70 DBC BDC=180 -(35 +70 )=75, A BC H' H 'H =8 cm, ABH' DCH RHA A 8cm D B H' H C 12cm CH =B H' =;2!;_(12-8) CH =B H' =2(cm) D AB A 6cm D BC E ABED 8cm DE =AB =8 cm, BE =AD =6 cm B 60 60 E C, DEC DEC= ABE=60 DEC, BC =BE +EC =6+8=14(cm) 90 90, AD //BC ABCDBC, BC DBC= ABC=10 cm A DC A BC E AECD, DC =AE =BE =AB B E ABEB=60 D C AD //BC ABC= DBC OBC= DBC- OCD OBC=42-14=28(cm ) l//mabc= DBC, M BC ABM=;2!; ABC=;2!; DBC ABM=;2!;_24=12(cm ),,, S,Q,P, S,R,P P Q S R, AC //DE ACD= ACE ABCD= ABC+ ACD ABCD= ABC+ ACE ABCD= ABE ABCD=;2!;_12_8=48(cm ) 46

BD =DC ABD= ACD AP PD =2 1ABPPBD=2 1 ABP=;3@; ABD=;3@;_;2!; ABC ABP=;3@; ABD=;3!;_30=10(cm ) BE =DE DBE= BDE ADB= DBE D=90 EDC=90 _;3!;=30 DEC=90-30 =60 AB //DC EBD= EBC AD //BC FCD= FBD EF //BD EBD= FBD AD //BC ACD= ABD=32 cm AOD= ACD- DOC =32-20=12(cm ) 11 12 13 14 15 Question Bank 16 17 18 19 10 11 cm 11 12 65 S;R=S Q'P=P S'P=P,,, 4 ABEBCF AB =BC, BE =CF, ABE= BCF=90 ABE BCF(SAS ) BAE= CBF ABE BAE+ AEB=90 CBF+ AEB=90 AOF= BOE=90 ABCD AB =AD ABD= ADB=32 AOD=90 CAD=180 -(90 +32 )=58 D AB BC E ABED BE =AD =3 cm, DE =AB =8 cm A3cmD 120 8cm 60 60 E BED= A=120 DEC=60 yy ABCD ABC= DCB=60 yy B C 47

, DEC EC =8 cm BC =BE +EC =3+8=11(cm) 11 cm CB =CD AD // BC AED= AEC ABED= ABE+ AED ABED= ABE+ AEC ABED= ABC BDC BDC=;2!;(180-128 )=26 APB= DPH=90-26 =64, ABED=;2!;_18_10=90(cm ) EADECD AD =CD, EDA= EDC=45, ED EADECD(SAS ) ECD=20, ECD BEC= EDC+ ECD=45 +20 =65 65 AD =DC, AD //BC DAC= ACB=36, DCA=36 DCB=72 ABCD B= DCB=72 BAC=180 -(72 +36 )=72 Q uestion Bank 11 12 13 14 15 16 17 18 19 10 11 12 12 cm,, ABCD,, ABCD,,,,,,, AOFAOECOECOF AF =FC =CE =EA, AFCE, OA =OB =;2!;AC =;2!;_20=10(cm), OA OB AOB=;2!;_10_10=50(cm ) EODFOB DO =BO, EOD= FOB=90, EDO= FBO EOD FOB(ASA ) OE =OF, ED =FB ED =FB ED // F B EBFD 48

, EBFD, ABCDCB B= C, AB =DC, BC ABC DCB(SAS ), DCO= ABO=15 cm ABCD= AOB+ BOC+ COD+ DOA ABCD=15+25+15+9=64(cm ) A=5 xb=4 x, A+ B=180 5 x+4 x=180, x=20 A=5 x=5_20 =100 ABF BF =BA =9 cm CF =BC -BF =3(cm) DCE CE =CD =9 cm BE =BC -EC =3(cm) EF =12-(3+3)=6(cm) AB //CD ACB= AOB, AOB =p_6 _;6!; =6p(cm ), x+y=2y-1 x-y+1=0 yy 2y-1=5x-2 5x-2y-1=0 yy, x=1, y=2 x=1, y=2 ABMACM=2 3, 8ACM=2 3 2 ACM=24 ACM=12 cm AD // EC ADE= ADC AMDE= AMD+ ADE = AMD+ ADC = ACM=12(cm ) 12 cm Q uestion Bank 11 12 13 14 x=1, y=2 15 16 17 18 19 10 11 12 13 15 14 15 16 15 cm, D= B=60 DAF= DFA=60, BAE= BEA=60 DAFABE AE =BE =10 cm, EC =BC -BE =4(cm) AE +EC =10+4=14(cm) AD //BC, AB // DC ABCD, AC BD ABCD,,,,, Q;R={} 49

APB+ CPD= APD+ BPC 16+27=24+ BPC BPC=19 cm Q uestion Bank A C APCD PAD=60 PAC=;2!; PAD=30 ABC BA =BC BAC=;2!;(180-64 )=58 BAP=58-30 =28 PBC ABP=90-60 =30 AB =PB ABP 11 12 32 13 16 cm 14 10 cm 15 235 16 10cm 17 2cm 18 25 19 70 10 ABEADF AEB= AFD=90 B= DBAE= DAF AE =AF ABE ADF(ASA ),AB =AD ABCD BAP=;2!;(180-30 )=75 DAP= A- BAP=15 15 BC F AD =;2!; BC AD =FC AD //BC AFCD, AB =AF =BF ABF AFB=60 FA =FC FAC= FCA FAC+ FCA=60 ACB=30 ADP= DEA- DPE = DEC- DPE = CEP DMC= DME+ DEC = DME+ DEA = DMEA B D ABF= DBF, BDC= EDC BDC- FDC= EDC- FDC DBF= FEC FEC=15 cm 15 cm ABC= AEP=64 BCD=180-64 =116 PF =FC =CG =PG =6 cm CGF CGF=;2!;(180-116 )=32 32 OBPOCQ OB =OC, OBP= OCQ=45, BOP=90 - POC= COQ OBPOCQ(ASA ) OPCQ= OBC=;4!; ABCD OPCQ=;4!;_8_8=16(cm ) 16 cm E F BFHG= BFE BFHG A E D = BFE G =;2!;_ ABFE H B F C =;4!;_ ABCD =;4!;_40=10(cm ) 10 cm GAD+ GDA=90 50

AGD=180-90 =90 DGF=90 ADC= ABF=70 CDG=35, DGFC 35 +90 + x+ y=360 x+ y=235 235 HEGD HD =EG =7cm FBEHEB FBE= HEB BE, BFE= EHB=90 FBE HEB(RHA ) BH =EF =3cm BD =BH +HD =3+7=10(cm) 10 cm CP PD =1 2 ACP=;3!; ACD=;3!;_;2!; ABCD ACP=;6!; ABCD=;6!;_40=;; 3º;;(cm ) AO =CO AOP=;2!; ACP=;2!;_;; 3º;;=;; 3º;;(cm ) AQ PQ =3 2 AOQ=;5#; AOP=;5#;_;; 3º;;=2(cm ) 2cm ABCD A D ABEBCF AB =BC, BE =CF, F G B= C=90 115 B ABE BCF(SAS ) E C, BAE= CBF, AEB= BFC BFC= AEB=180-115 =65 GBE=90 - BFC=90-65 =25 25 CD BP =DR R ABPADR AB =AD, BP =DR ABP= ADR=90 ABP ADR (SAS ) APQARQ AP =AR, AQ, PAQ=45, BAP= DAR BAP+ DAQ= DAR+ DAQ = RAQ=45 APQ ARQ(SAS ) AQR= AQP=180 -(45 +55 )=80 PQC=180 - PQD=180-80 _2=20 QPC=90 - PQC=90-20 =70 ABHDFH AB =DC, FD =DC AB =FD DFH= ABH BAH= FDH ABH DFH(ASA ) ABG ECG(ASA ) 45, BG =CG AB =BG 55 70, AB =AH =BG =HG ABGH ABGH, FPE=90 FPE=90 FPE A B P R D Q C 51

H 'G' 1:2 =2 HG h 4b:6b=2:3 2 : 3=8a : h, 2h=24a h=12a Q uestion Bank 12a C= F=50 E= A=180 -(50 +55 )=75 BAC= DEC ABCEDC BC :DC =9:6=3:2 DBE A ' D ' C' D' OA O A' =16 28=4 7 AC A 'C' =4 7 12 A 'C' =4 7 A 'C' =21cm 21cm A A' OA O A' =(18-10) 10=4 5 4 5 AB BC =A 'B' B 'C' 1:2 OB =O B' =1:2 OB =BB ' =7 cm OB ' =14 cm AB DE =AC DF 8 12=AC 15 AC =10 cm EFGH, a cm, b cm 7 a=5 6 3 b=5 6 a=: 5 :(cm) b=: 5 :(cm) 52

( EFGH)=2_{: 5 :+: 5 :}=24(cm) ABCª EDF AA AC :EF =BC :DF, 6:EF =4:5 ABCEBD ACB= EDB, B ABCª EBD AA AB EB =10 4=5 2 BC BD =5 2, (4+x) 5=5 2 2(4+x)=25 x=8.5cm EF =: 4º:=7.5(cm) ABCª EDF AA 7.5 cm AA, SAS AA, SAS ABCª HBA AA ABHª CAH AA AC =HC `BC ABCEDC ACB= ECD, CAB= CED ABCª EDC AA AB ED =20 15=4 3 x 9=4 3 x=12 16 y=4 3 y=12 x+y=24 12 =9(9+BH ), 144=81+9BH BH =7cm 8_6=10_AH AH =: 5 : cm BH =4_9=36 BH =6 cm ABCAED AB :AE =AC :AD =2:1, A ABCª AED SAS 2 1=BC 6 BC =12 cm ABC=;2!;_13_6=39(cm ) AH =BH CH 12 =16x x=9 AC =CH CB y =9_25=225 y=15 x+y=9+15=24 ABCD AB =DC =5 cm ABECFB A= C, ABE= CFB ABEª CFB AA AB :CF =AE :CB 5 : (5+x)=5 : 8, 5(5+x)=40 x=3 cm 3cm M BC A M =B M =C M =;2!; BC =5(cm) AG =BG CG AG =2_8=16 AG =4 cm, G M =B M -BG =5-2=3(cm) 4_3=5_GH GH =: 5 : cm 53

Question Bank AC =HC BC 5 =3_(3+y) y=: 3 : 11 12 13 14 15 AB =BH BC x =: 3 :_{: 3 :+3}={: 3º:}2 16 17 18 19 10 11 12 ;; 5 ;;(=5.6)cm x=: 3º: x+y=12, ABCª EDC AA AC :EC =BC :DC 9 : 3=BC :5 BC =15 cm BC :B 'C' =18 : 12=3 : 2 AB :A 'B' =3:2 15:A 'B' =3 : 2, 3A 'B' =30 A 'B' =10 cm C'=360 -(130 +70 +85 )=75 ABDª ACB AA AD :AB =BD :CB 8 : 10=BD :15 BD =12 cm A a BC 2a, 4a, a 2a 4a=1 2 4, ACDDBE C= B=60, ADB= CAD+60 =60 + BDE CAD= BDE ACDª DBE AA, CA DB =CD BE 12 9=3 BE BE =;4(; cm, B( B') CFEBED A OB B B' =1 1 C= B CEF=120 - CFE =120 - BED x D 7cm 12-x 12cm F CFE= BED B 4cm E 8cm C ABCª EFD AA CFEª BED AA a e=b f=c d, BD :CE =BE :CF (12-x) : 8=4 : 5 A=75, D=45 ABCFDE AA 5(12-x)=32 x=: 5 :(=5.6)cm : 5 :(=5.6)cm 54

Q uestion Bank 11 12 13 14 15 16 17 18 19 10 11 12 ABCDBA AB :DB =6 : 4=3 : 2, BC :BA =9:6=3:2, B ABCª DBA SAS, CA :AD =3:2 8:AD =3:2 AD =: 3 :cm AA ABCª EBDª AFDª EFC ABCDA'B'C'D' AB :A 'B' =8:6=4:3 CGC= G DAEBCA DAE= BCA, DEA= BAC DAEª BCA AA, AE :CA =ED :AB 6:8=3:AB AB =4 cm ABCDBE B, BCA= BED ABCª DBE AA, AB :DB =6:5 ABECDE AEB= CED, BAE= DCE ABEª CDE AA, 8 6=6 DE DE =;2(; cm ABDACE A, ADB= AEC=90 ABDª ACE AA, AB AC =AD AE 10 8=6 (10-x), 48=10(10-x) x=: 5 :cm AH =BH HC 4 =BH _2 BH =8cm ABH=;2!;_8_4=16(cm ) ABCAED A, ABC= AED ABCª AED AA, AC AD =AB AE 18 5=(5+x) 6, 108=25+5x x=: 5 :cm AFDCDE A= C, AFD= CDE AFDª CDE AA, AF :CD =AD :CE 6:4=9:CE CE =6 cm 55

6 9=5 y y=7.5 6 9=x 6 x=4 x+y=11.5 AD :AB =AE :AC =2:3 DE // BC 4 (4+2)=AE 4 AE =;3*; cm APDª FPE(AA ) AP FP =2 3 2 3=4 x x=6 4 5=x 6 x=: 5 : p 4 4 9=(y-4) 6 y=: 3º: 5x+3y=24+20=44 l m n 4 5 p p' 4 x y-4 y 6 6 10 APDª CPB(AA ) AP CP =2 5 2 5=4 y y=10 x+y=16 BF DG (=AF AG )=FC GE 3 4=FC 8 FC =6cm p 4cm 1 2=2 (x-4) x=8 l m n p' p 4cm 6cm 2cm xcm (x-4)cm ABCª FEC(AA ) BC EC =8 12=2 3 BFE BC BE =2 5 2 5=CD 12 CD =4.8cm 2 5=y 10 y=4 3 5=x 5 x=3 xy=12 BDEBAC BD DA =BE EC =1 1 DE //AC DE ABC AE AB =EG BC 2 3=EG 18 EG =12cm CAD CF CD =GF AD 1 3=GF 9 GF =3cm EG =12cm, GF =3cm 8 4=6 x x=3 9 6=x 4 x=6 BAD AE EB =2 1 EB AB =E M AD 1 3=E M 12 E M =4cm 56

ABC AE AB =E N BC 2 3=EN 18 EN =12cm MÚN =EN -E M =8(cm) IABCBAD= CAD, AB AC =BD CD 9 12=x (14-x) x=6cm AC EF P, ABC AE AB =EP BC 4 6=EP 12 EP =8cm ACD CF CD =PF AD 2 6=PF 6 PF =2cm EF =EP +PF =10(cm) A 4cm E 2cm B 6cm D P F C 12cm ABDACD BD CD ABDACD=BD CD BD CD =AB AC ABDACD=8 10=4 5 ABD E M AD =1 2 E M 8=1 2 E M =4cm EN =4+3=7(cm) ABC 1 2=7 BC BC =14cm AB :AC =BD :CD =9:6=3:2 ABD : ACD=3 : 2 24 : ACD=3 : 2ACD=16 cm AB AC =BD CD 4 3=(2+CD ) CD CD =6cm A DC AE AB =4 9 x (x+9)=4 9 x=: 5 : 5x=36 A 8cm D xcm 12cm E 4cm 8cm F 9cm 9cm 8cm B 17cm C AB AC =BD CD 15 12=25 CD CD =20cm, BC =5cm BC =;2 5;=;5!; BD APDª CPB AA AP PC =AD BC =10 12=5 6 ABC AP AC =EP BC 5 11=x 12 x=;1^1); 11x=60 DE =;2!; AC =;2(;(cm), FE =;2!; AB =;2&;(cm) DF =;2!;BC =4(cm) DEF =DE +FE +DF =12(cm) AB AC =BD CD 6 9=BD 6 BD =4cm EH =FG =;2!; BD =8(cm), HG =EF =;2!; AC =6(cm) EFGH =2_8+2_6=28(cm) 57

M N BD P M P =;2!;AD =1.5(cm), M N =5 cm PN =3.5cm, PN =;2!;BC 3.5=;2!;x x=7 B M A 3cm D P 5cm xcm N C Question Bank 11 12 13 14 15 ;; 3º;;cm 16 GF =4cm, BC =15cm 17 18 19 10 11 12 ABC M F =;2!; BC =5(cm) BAD M ÚE =;2!; AD =2(cm) x=5-2=3 7 3 12 : (12+DB )=6 : 8, 12+DB =16 DB =4 cm 12 : 4=AE :3 AE =9 cm M N =;2!;(AD +BC ), 5=;2!;(3+x) x=7 EF =;2!;(BC -AD ) x=;2!;(10-4)=3 ADG EF //DG, AE =ED 4 y=1 2 y=8 CBF BF //DG, BD =DC 8 (x+4)=1 2 x=12 x+y=20 DCE GF =;2!;DE 6 10=x 12 x=: 5 :, 6 10=8 y y=: 3º:, ABF DE =;2!; BF 3y-5x=4 GF =;2!;DE =;2!;_{;2!;BF }=3(cm) ABPª CDP AA BP :PD =6:9=2:3 AC A BF // DG G F CFB CG =GF =5cm, ADG E AD B E D BF //DG AF =FG =5cm 10cm G C BCD BQ :BC =BP :BD BQ :10=2:5 BQ =4 cm AOBª DOC(AA ) OA :OD =AB :DC 5:OD =6:18 OD =15 cm, OD :OE =CD :CF 15 : x=18 : 4, 18x=60 EG =;2!; AB, GF =;2!; DC x=: 3º:cm : 3º:cm EG +GF =;2!;(AB +DC )=;2!;_18=9(cm) EGF =9+7=16(cm) CAD CF CD =GF AD 58

4 12=GF 12 GF =4cm ABC EG BC =AG AC =DF DC 10 BC =8 12 BC =15cm GF =4cm, BC =15cm P, Q DB, DC BC =2 PQ =2_6=12(cm), M, N AB, AC BC EG EG =;2!; BC =;2!;_10=5(cm) GEF= CDF B EFG= DFC, A E G F 10cm C EF =DF EFG DFC ASA CD =EG =5cm D M N =;2!; BC =;2!;_12=6(cm) 10 AC =15 9 AC =6cm E, N AB, AC AD //EN //BC Q uestion Bank 11 12 13 14 15 16 17 18 19 10 11 : 3º:cm 12 16 cm BAD E M =;2!; AD =4(cm) ABC EN =;2!; BC =6(cm) x:3=8:2 x=12 6:8=y:10 y=7.5 MÚN =EN -E M =6-4=2(cm) x+y=12+7.5=19.5 2EG =GH EG GH =1 2 3AE =4 EB AE EB =4 3 BAD BE BA =EG AD 3 7=EG 14 EG =6cm, GH =2 EG =12cm EH =18cm ABC AE AB =EH BC 4 7=18 BC BC =31.5cm E, F, G, H AB, BC, CD, D A AG // EC, HB // DF ASD DS =2PH =4(cm) DRC DS =SR =4cm CRF APH RF =PH =2cm DF =DS +SR +RF =10(cm) DAE DF DA =FH AE 6 9=FH 9 FH =6cm FBG FD DB =FH HG 6 4=6 HG HG =4cm AE EB =AF FC FC =ED =8cm 3 4=x 8 x=6 BE BA =BD BC 4 7=6 y y=: 2 : xy=63 10 4=8 x x=: 5 :, 10 4=y 3 y=: 2 : : 5 : z=4 8 z=: 5 : y(x+z)=: 2 :_: 5 :=72 59

ABC AD DB =AE EC =2 1, AFC AB BF =AE EC =2 1 AB AC =BD CD, 6 5=BD (8-BD ) BD =;1$1*; cm 12 BF =2 1 BF =6cm PS =QR =;2!; BD, SR =PQ =;2!; AC A A 4cm D PQRS DC BC H AD =GF =HC =4cm EG =3cm B E G 7cm H F 4cm C =P S +QR +SR +PQ =2{;2!; BD +;2!; AC } =BD +AC =18(cm) ABH AE EB =3 2 AE AB =3 5, AE AB =EG BH 3 5=3 BH BH =5 cm BC =BH +HC =9(cm) ABPª CDP AA AP :CP =AB :CD =15 : 12=5 : 4, CAB AB :PH =CA :CP 15:PH =9:4 PH =: 3º:cm : 3º:cm ABC AE AB =E M BC 1 3=E M 15 E M =5cm AG AB =GN BC 2 3=GN 15 GN =10 cm CAD CH CD =N H AD 1 3=N H 9 N H =3cm CF CD =MÚF AD 2 3=MÚF 9 MÚF =6cm EF +GH =(E M +MÚF )+(GN +NH ) =(5+10)+(3+6)=24(cm) AODª COB AA AO :CO =DO :BO =12 : 24=1 : 2 ABC AO :AC =EO :BC 1 : 3=EO :24 EO =8 cm, CDA CO :CA =OF :AD 2 : 3=OF :12 OF =8 cm EF =EO +OF =8+8=16(cm) 16cm ABCD E, F AB, DC AD //EF //BC ABC EG =;2!; BC =3(cm) M BC ABMACM ABC=2 ABM=20(cm ) EG =GH =HF =3 cm EH =2 EG =6(cm), ABD AD =2 EH =12(cm) ABP=;2!; ABM=;2!;{;2!; ABC} ABP=;4!; ABC=;4!;_24=6(cm ) 60

ABD= ACD=;2!; ABC=;2!;_30=15(cm ) ABD=;2!;_BD _AH 15=;2!;_BD _6 BD =5 cm A M =B M =C M =9cm, GABC CG G M =2 1, C M :CG =3:2 9:CG =3:2 CG =6cm ABM= ACM PBM= PCM ABP= ACP, AMC=;2!; ABC=12(cm ), ACP= ABP=8cm PMC= AMC- APC=4(cm ) GABC AD :AG =3:2,AD :12=3:2 AD =18 cm CAD CF =AF, CE =DE EF =;2!; AD =;2!;_18=9(cm) AN NB =4 5ANMBNM=4 5 8BNM=4 5BNM=10cm ABC=2 ABM =2( ANM+ BNM) =36(cm ) PBQ=;3!; ABM=;3!; {;2!; ABC} BPQ=;6!; ABC=;6!;_30=5(cm ) D, E B M, C M DE =6cm ADE A G AD =A G AE =2 3, G G DE =2 3 G G 6=2 3 G G =4cm BD AC O A M P D BO =DO P, Q ABD, CBD O Q N 18cm B C GABC AG GD =2 1, 10 GD =2 1 GD =5cm PO =;3!; AO, QO =;3!; CO PQ =PO +QO =;3!;(AO +CO ) PQ =;3!; AC =6(cm) GD =;3!; AD =12(cm), G G' =;3@; GD =8(cm) EBDG= EBG+ DBG EBDG=;6!; ABC+;6!; ABC=;3!; ABC 61

ABC=3 EBDG=3_20=60(cm ) D, E AB, AC DE // BC, DE =;2!; BC GG'C=;3@; GDCGDC=6_;2#;=9(cm ), GDC=;3!; ADC 9=;3!; ADC ADC=27cm ADEª ABC(AA ) ADEABC=1 2 =1 4 5ABC=1 4 ABC=20cm ADC=;2!; ABC ABC=2_27=54(cm ) ABD=;2!; ABC=24(cm ) FE // BC AF FB =2 1 AFD=;3@; ABD=16(cm ) ADG=;2!; ABG, AEG=;2!; ACG ABG= ACG=;3!; ABC = ADG+ AEG =;3!; ABC =6(cm ) FACD FOCE=;3!; ACD=;3!; {;2!; ABCD} FOCE=;6!; ABCD FOCE=;6!;_30=5(cm ) 4 9=2 3 2 3 ABC 4+5+3=12(cm) 2 3=12 A'B'C' A'B'C' =18 cm ADBª ABC(AA ) 3 5 3 5 =9 25, 9 25=18ABCABC=50cm BDC= ABC- ABD=50-18=32(cm ) GABC GBC=;3!; ABC=;3!;_36=12(cm ), D, E AB, AC DE //BC, DE =;2!; BC, DGEª CGB(AA ) 1 2 1 2 =1 4 DGE=;4!; GBC=3(cm ) ADEª ABC(AA ) 6:10=3:5, ADE : ABC=3 :5 =9:25 ABCª ADE(AA ), AB AD =4 3 ABCADE=4 3 =16 9 DBCE : ABC=(25-9) : 25=16 : 25 DBCE 32 cm 32 : ABC=16 : 25 ABC=50 cm 50 cm 62

8 27=2 3 2 3, 2 3 =4 9 4:6=2:3 2 :3 =8:27 ;3!;_p_2 _4=: 3 :p(cm ) 8 : 27=: 3 :p : =18p(cm ) 18p cm 1 2 3 1 2 3 =1 8 27 1 (8-1) (27-8)=1 7 19, C xcm 3 x=1 19 x=57 5 26_5=130 130 = =;100 000;= 1 50000 =12cm 1 10000 1 10000 =1 100000000 =12_10000 =1200000000(cm ) =120000(m ) =0.12(km ) =5_25000=125000(cm) =1250(m)=1.25(km) 8 1 8 1 =512 1, 512 =2_12_200000 =4800000(cm) =48(km), ;6$0*;=0.8=48 9 16=3 4 3 4, 3 4 =27 64,27p=27 64 =64pcm ABCª A'B'C' AB A 'B' =BC B 'C' AB 4=10000 5 AB =8000cm=80m 4:12=1:3 1 :3 =1:27, 1 : (27-1)=1 : 26 240 m 6cm 6 cm : 240 m=6 cm : 24000 cm=1 : 4000, A, D x 1 : 4000=4.2 : x x=4.2_4000=16800(cm)=168(m) 168 m 63

Question Bank ABC=6 BGF=24(cm ) 11 12 13 14 15 16 17 18 19 10 11 12 AD, BE GABC GDEGAB=1 2 =1 4 GDE 36=1 4 GDE=9cm M GBC B M =C M =G M =5cm A M =3 G M =15(cm) BCD E, F BC, CD BD EF P, QABCADC AP AE =2 3 APQAEF=2 3 =4 9, APQPEFQ=4 5 28PEFQ=4 5PEFQ=35cm 2 1 G AG =8cm 8 12=GQ 6 GQ =4cm 1 2 3 1 2 3 =1 4 9, A, B, C 1 (4-1) (9-4)=1 3 5 BCD BD =2 MÚN =30(cm) BO =;2!; BD =15(cm) ABC P PO =;3!; BO =5(cm) P, Q 9:4=3 :2 3 2, 3 2 =27 8 27 8=216Q Q=64 cm QO =5cm PQ =PO +QO =10(cm) 1 500 AODª COB(AA ) 4:6=2:3 2 :3 =4:9 AOD 8cm 4 : 9=8 : COB COB=18cm 1 : 500, 1 : 500 =1 : 250000 = 10000_10000 250000 = 10000 =400(cm ) 25 64

Q uestion Bank 11 12 13 14 15 16 17 18 19 10 11 20 cm 12 57 cm GABC PF =;2!; AF =;2!;_18=9(cm) GF =;3!; AF =;3!;_18=6(cm) PG =PF -GF =9-6=3(cm) GABC AG G M =2 1 12 x=2 1 x=6 V, V' V : V'=2 :5 =8 : 125, 8 : 125=V : 250 V=16 cm AMC GN //MÚC, MÚC =B M =9cm AG A M =GN MÚÆC 12 18=y 9 y=6 x+y=12 GDE=;2!; GDC=;2!; {;6!; ABC} GDE=;1 2; ABC=;1 2;_60=5(cm ) O A' =4cmABCA'B'C' OA :O A' =6:4=3:2, 3 :2 =9:4 ADC AD =2 EF =18cm GABC G'BD=;3!; GBD=;3!;_{;3!; ABD} G'BD=;3!;_;3!;_{;2!; ABC} G'BD=;1 8; ABC G'BD=;1 8;_72=4(cm ) AG =;3@; AD =12(cm) AO, CO ABD, CBD P, QABD, CBD, =7_25000, =175000(cm), =1750(m) OQ =OP =;2!; AP =5(cm) ADEª ACB AA, G'GBC G G' GD =2 3, 4 GD =2 3 GD =6cm, GABC GD AD =1 3, 6 AD =1 3 AD =18cm AD :AC =8:16=1:2 ADE : ABC=1 :2 =1:4 ADE=;4!; ABC=;4!;_80=20(cm ) 20cm V :(V +V ):(V +V +V ) 1:2:3 65

1 :2 :3 =1:8:27 V :V :V =1 : (8-1) : (27-8)=1 :7:19 V 21 cm 7 : 19=21 : V V =57 cm 57 cm DC x cm 8 =(16-x)_16 x=12(cm) ABC CF CB =GF AB =6 9=2 3 Q uestion Bank, DBC BF :BC =1:3 1 : 3=7 : BC BC =21 cm 21 cm 11 12 13 16 cm 14 15 16 17 21cm 18 19 21cm 10 11 12 13 14 16 cm 15 112 cm AC ABC MÚP =;2!; BC =7(cm) A D 7cm P M 9cm 2cm N 16 2000 m PN =MÚN -MÚP PN=2(cm) B 14cm C,, ACD AD =2 PN =4(cm) AFD AP PD =AE EF 3 2=18 EF EF =12cm BCE BF FE =BD DC BF 12=2 3 BF =8cm AB AC =BD CD =7 6 ABDACD=7 6 ABD 18=7 6 ABD=21cm 21cm ABCDBA BCA= BAD, B ABCª DBA AA, AB DB =CB AB 6 2=(2+DC ) 6 DC =16cm 16cm AB :AC =BD :DC 8 : 6=BD : (7-BD ) BD =4 cm DC =3 cm AB :AC =BE :CE 8 : 6=(7+CE ) :CE CE =21 cm DE =DC +CE =3+21=24(cm) p p p' 2cm 3 7=3 (x-2) x=9 l 3cm 2cm 2cm m 5cm 4cm n xcm D BC AC G DG =;2!; BC =3(cm) DFGEFC B D A 6cm G F C E DF =EF, GABC x=2gd =6, y=dc =6 x+y=12 GFD= CFE, GDF= CEF DFG EFC ASA CE =DG =3cm 66

AGC=;3!; ABC=9(cm ), V, V GG'C=;3!; GBC=;3!;{;3!; ABC}=3(cm ) AG'C= AGC+ GG'C=12(cm ) V V =2 1 =8 1 V +V =144p V +;8!;V =;8(;V =144p V =;8!;V V =128pcm DBG=;6!; ABC=;6!; {;2!;_8_6}=4(cm ) ABCDEF=1 3 =1 9 DEF=8 1 2=8 1 =16cm 16cm 8cm 6cm 6cm 4cm 4:6:8=2:3:4 2 :3 :4 =8:27:64, (27-8) : (64-8)=19 : 56 xcm 19 : 56=38 : x x=112(cm ) 112 cm r pr _8=128 r=4cm 4cm PQ =a cm PS =2a cm APSª ABC(AA ) (8-a) 8=2a 16 a=4 QR =PS =8cm 8cm ABD AB //EG EGD=30 BCD GF //DC DGF=80 EGF= EGD+ DGF=110 110 ABCª BDC AA AC :BC =BC :DC 12:9=9:DC DC =: 4 : cm AD =12-: 4 :=: 4 : (cm), BE ABD BA :BD =AE :DE =4:3 DE =;7#;AD =;7#;_: 4 :=;4(; (cm) ;4(; cm =20_1000000 =20000000(cm ) =2000(m ) 2000m Q uestion Bank DBEECF B= C=60, BDE+ B= DEC= DEF+ CEF BDE= CEF DBEª ECF AA AF =EF =14cm AC =BC =20cm, BE CF =DE EF 2 3=DE 14, DE =;; 3 ;; cm 11 4cm 12 8cm 13 110 14 ;4(; cm 15 : 3 : cm 16 3cm 17 12 cm 18 30 cm 19 27 cm 10 45 cm AD =DE =;; 3 ;; cm ABQª PDQ AA BQ DQ =AB PD =5 3 ;; 3 ;; cm 67

BQ =5a, DQ =3a BD =8a BO =DO =4a, QO =DO -DQ =a AOQ=;4!; AOD=;4!;_;4!; ABCD AOD=;4!;_;4!;_48=3(cm ) 3cm DEFABC DEF= BAE+ ABE = CBF+ ABE= B DFE= CBF+ BCF = ACD+ BCF= C DEFª ABC AA, EF :BC =5:10=1:2 DE :6=1:2 DE =3 cm DF :8=1:2 DF =4 cm DE +EF +DF =3+5+4=12(cm) 12 cm ABC=;2!;_30_18=270(cm ) EBG=;3@; EBD=;3@;_{;3!; ABD} EBG=;3@;_;3!;_{;2!; ABC} EBG=;9!;_270=30(cm ) 30cm ADECBE 2:4=1:2 ADE : CBE=1 :2 =1:4 3: CBE=1 : 4 CBE=12 cm, ADE : ABE=DE :BE =1:2 1 : 2=3 : ABE ABE=6 cm DCE=6 cm, ABCD 3+6+12+6=27(cm ) 27 cm, EBC EFCASA EBC=;2!; FBCFBC=2 EBC, FADª FBC FA :FB =1:4 FAD : FBC=1 :4 =1:16 FAD=;1 6; FBC ABCD=;1!6%; FBC=;1!6%;_2 EBC ABCD=;1!6%;_2_24=45(cm ) 45 cm 11 12 13 14 15 16 17 18 19 10 11 12 13 14 15 16 17 18 11 cm 19 120 20 5 6 4 21 10 cm 22 23 5 cm 24 32 cm 25 196 cm A+ D=180 120 + x=180 x=60, y=ad =7 cm AOB COD AO =CO, BO =DO ABCD AB CD F E A F D AO =BO =CO =DO EBCEFC BCE= FCE, B EC, CEB= CEF C 68

ABCD =6_4=24(cm) x=36, y=90-36 =54 x+ y=36 +54 =90 AB // DC BE DE =AB CD =20 12=5 3 BE BD =5 8 EF // DC EF DC =BE BD EF 12=5 8 EF =7.5 cm PQRS Q;P=Q H P Q S R PQ =SR =;2!; AC, P S =QR =;2!; BD AC +BD =2(PQ +PS )=( PQRS =15(cm) AD // BC ABC= DBC COD= DBC- BOC = ABC- BOC =60-35=25(cm ) AP =PQ =QD ABP= PBQ= QBD ABD=3 BPQ=18(cm ) AC A'C' =3 2, AC =;2#;A'C' BG GE =2 1 8 x=2 1 x=4 y=;2!;ac =5 x+y=9 BC DC =10 5=2 1 AB ED =2 1, 12 ED =2 1 DE =6 cm 54 36=9 DC DC =6 cm DGEª CGB AA, DG GC =1 2 DGECGB=1 2 =1 4 GBC=4 DGE=16(cm ) ABE BD DE =BF FA ABC BF FA =BE EC =3 4 BD DE =3 4 4 9=x 18 x=8, 4 5=12 y y=15 x+y=23 MD // BN, MD =BN A M D MBND, AM // NC, AM =NC P Q ANCM B N C, MP // QN, PN // MQ MPNQ 69

ABNM=;2!; ABCD MPN=;4!; ABNM=;4!;_;2!; ABCD=;8!; ABCD MPNQ=2 MPN=;4!; ABCD MPNQ=;4!;_44=11(cm ) 11 cm D AB BC E A D ABED B E C, DE =AB BE =EC DECB= DEC=60 A=180 - B=120 120 D BC A DF D F M DF =;2!; BC =5(cm) B 10cm DMFEMC C E DM =EM, FDM= EMC, DMF= EMC DMF EMC ASA CE =DF =5 cm 5cm DEF =2GHI =16(cm) ABC =2DEF =32(cm) 32 cm DEF= BAE+ ABE = CBF+ ABE= B EDF= ACD+ CAD = BAE+ CAD= A ABCª DEF AA DE EF FD =AB BC CA =5 6 4 5 6 4,, 6 8 10=3 4 5 3 4 5 =27 64 125 =(125-27) (64-27) =98 37 98 37=74 =196 cm 10cm 6cm 196 cm ABEª DEF AA EF =FC =8-3=5(cm), EB FE =AB DE EB 5=8 4 EB =10 cm 10 cm ABC EH =;2!; BC EH //BC DBC FG =;2!; BC FG //BC, EH //FG EH =FG EFGH 11 12 13, 14 15 16 17 18 19 10 11 12 13 14 15 16 17 18 19 24 cm 20 9 cm 21 ;4%;S cm 22 ;; 5 ;;(=7.2)cm 23 ;;; 5 ;;(=5.6)cm 24 4cm 25 4 7 70

ABC B=180 -(70 +45 )=65 D= B=65, AB ED =AC EC 6 ED =4 5 ED =7.5 cm AD //BC AEB= DAE, ABE BE =BA =9 cm EC =BC -BE =6 cm, AF // EC, AE // FC AF =FC AECF FAE= ECF, BAE= DCF 3 DCF=90 AC, AC PQ O A 8cm ABC AP AB =PO BC 3 5=PO 12 PO =7.2 cm P B O 12cm CAD CQ CD =OQ AD 2 5=QO 8 QO =3.2 cm PQ =PO +QO =10.4(cm) DMC=;2!; DBC=;2!; ABC=9(cm ) D Q C BAE=;3!;_90 =30 AOCDOF AD // BC ADB= DBC=36 AC DF =OA OD =10 6=5 3 AB =AD ABD= ADB=36, B=36 +36 =72 C=72 ABC EN =;2!;BC =7(cm) BAD EM =;2!;AD =4(cm) MN =EN -EM =3(cm) ABCEDC ABC= EDC, C ABCª EDC AA AB ED =AC EC 12 6=8 EC EC =4 cm BC =2MN =14(cm) PQ =;2!;BC =7(cm) GM =;3!; AM =12(cm), G 'M =;3!;G M =4(cm) AB //DE ABCEDC BAC= DEC, ABC= EDC ABCª EDC AA AG' =AM -G 'M =36-4=32(cm) BE =ED =DF =FC =4 cm 71

EF =ED +DF =8(cm) AGG'AEF AG AE =AG ' AF =2 3, EAF, AGG'ª AEF SAS GG' EF =2 3 G G' 8=2 3 GG' =;; 3 ;; cm ABC S'cm ADEª ACB(AA ) S S'=2 3 =4 9 S'=;4(;S DBCE= ABC- ADE DBCE=;4(;S-S=;4%;S(cm ) ;4%;S cm ABC=6 BEG=30(cm ) 1 4 1 4 =1 64, 64 ABC AD A AB 8=6 4 AB =12 cm, AC //ED ABCª EBD(AA ), AB EB =BC BD 12 EB =10 6 EB =;; 5 ;;(=7.2)cm ;; 5 ;;(=7.2)cm BCPDCQ B= D, PC =QC, BPC= DQC=90 BCP DCQ ASA, BC =CD ABCD AD A 16 AC =8 6 AC =12 cm, BE B 16 14=(12-x) x x=;; 5 ;;(=5.6)cm ;; 5 ;;(=5.6)cm AC //DE C= DEB AB =AC B= C DEB= B, DBE DB =DE FEC FE =FC ADEF =AD +DE +EF +AF =AD +DB +FC +AF =AB +AC =24(cm) 24 cm AC // DE ACD= ACE ABCD= ABC+ ACD= ABC+ ACE ABCD= ABE=;2!;_6_3=9(cm ) 9cm GABC GDC=;6!; ABC=8(cm ) GE =EC GDE=;2!; GDC=4(cm ) 4cm AD AF =2 3 AD DF =2 1 AD DF FB =2 1 1 AD AF AB =2 3 4 ADEAFGABC=2 3 4 =4 9 16, ADE=4a FBCG= ABC- AFG=16a-9a=7a ADEFBCG=4a 7a=4 7 4 7 72