ABI+34˘+20˘=90˘ ABI=36˘
ABC=2 ABI=2_36˘=72˘
72˘
34˘
20˘
A
B C
I x
32˘
A
B C
68˘
I
329
35˘+ x+28˘=90˘ x=27˘ 27˘
330
33˘+ OCD+25˘=90˘ OCD=32˘
ODC x=180˘-(90˘+32˘)=58˘
331
OBC OB”=OC”
OBC= OCB=32˘
BAO+32˘+14˘=90˘ BAO=44˘
OCA OA”=OC”
OAC= OCA=14˘
BAC= BAO+ OAC=44˘+14˘=58˘ 58˘
332
AOC=2 B=2_42˘=84˘
OCA OA”=OC”
x=;2!;_(180˘-84˘)=48˘ 48˘
333
OAB OA”=OB”
OAB= OBA=30˘
BAC= OAB+ OAC=30˘+36˘=66˘
x=2 BAC=2_66˘=132˘ 132˘
30˘+ OCB+36˘=90˘ OCB=24˘
OBC OB”=OC”
x=180˘-2_24˘=132˘
334
OC”OCB= OBC=25˘
OCA= OAC=44˘
x= OCB+ OCA
=25˘+44˘=69˘
y=2 x=2_69˘=138˘
x+ y=69˘+138˘=207˘ 207˘
335
BOC=360˘_ =120˘ yy
BAC=;2!; BOC=;2!;_120˘=60˘ yy 60˘
3 4+3+2
A
B
O 25˘ C
44˘
x y
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346
132˘=90˘+;2!; ACB ACB=84˘
x=;2!; ACB=;2!;_84˘=42˘
347
IBC= IBA=32˘ ICB= ICA=23˘
IBC y=180˘-(32˘+23˘)=125˘
125˘=90˘+;2!; x x=70˘
x+ y=70˘+125˘=195˘ 195˘
348
B=180˘_ =60˘
x=90˘+;2!; B=90˘+;2!;_60˘=120˘ 120˘
349
ABC BIC=90˘+;2!; A=90˘+;2!;_40˘=110˘
IBC BI'C=90˘+;2!; BIC=90˘+;2!;_110˘=145˘
350
ABC r cm
;2!;_r_(13+15+14)=84 21r=84 r=4
ABC 4 cm 4 cm
351
;2!;_2_(AB”+BC”+CA”)=24
AB”+BC”+CA”=24(cm) 24 cm
352
ABC r cm
ABC=;2!;_r_(5+4+3)=6r(cm¤ ) ABC=;2!;_4_3=6(cm¤ ) 6r=6 r=1
ABC 1 cm 1 cm
353
ABC r cm
ABC=;2!;_r_(15+12+9)=18r(cm¤ ) yy 4
3+4+5
ABC=;2!;_12_9=54(cm¤ )
18r=54 r=3 yy
IBC=;2!;_12_3=18(cm¤ ) yy 18 cm¤
354
AD”=x cm AF”=AD”=x(cm) BE”=BD”=7-x(cm) CE”=CF”=6-x(cm)
BC”=BE”+CE” 9=(7-x)+(6-x)
2x=4 x=2
AD”=2 cm 2 cm
355
AF”=AD”=3(cm)
CE”=CF”=AC”-AF”=10-3=7(cm) BE”=BD”=5(cm)
BC”=BE”+CE”=5+7=12(cm) 12 cm
356
ABC AB
BC CA D E F
IECF
CE”=CF”=IEÚ=2(cm) yy AD”=AF”=AC”-CF”=6-2=4(cm)
BE”=BD”=AB”-AD”=10-4=6(cm) yy
BC”=BE”+CE”=6+2=8(cm) yy
8 cm
357
AD”=AF” BD”=BE” CE”=CF”
ABC =2(AD”+BD”+CF”)=2(AB”+9)=40
AB”+9=20 AB”=11(cm) 11 cm
358
I ABC DBI= IBC
DE” BC” DIB= IBC
DBI= DIB DBI DB”=DIÚ
EIC EC”=EIÚ
ADE =AD”+DE”+EA”
=AD”+(DIÚ+IEÚ)+EA”
=(AD”+DB”)+( EC”+EA”)
=AB”+AC”
=13+10=23(cm) 23 cm 10 cm
6 cm
2 cm A
B C
I
E F
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D364
OBC OB”=OC”
BOC=180˘-2_42˘=96˘ yy
A=;2!; BOC=;2!;_96˘=48˘ yy BIC=90˘+;2!; A
BIC=90˘+;2!;_48˘=114˘ yy 114˘
365
BOC=2 A=2_40˘=80˘
OBC OB”=OC”
OBC=;2!;_(180˘-80˘)=50˘
ABC AB”=AC”
ABC=;2!;_(180˘-40˘)=70˘
I ABC
IBC=;2!; ABC=;2!;_70˘=35˘
x= OBC- IBC
=50˘-35˘=15˘ 15˘
366
ABC R cm
R=;2!;AB”=;2!;_5=;2%;
ABC r cm
;2!;_r_(5+4+3)=;2!;_4_3 6r=6 r=1
ABC ;2%; cm
1 cm
;2%;+1=;2&;(cm) ;2&; cm
367
ABC R cm
R=;2!;B’C’=;2!;_10=5
ABC r cm
;2!;_r_(8+10+6)=;2!;_6_8 12r=24 r=2
=
-=p_5¤ -p_2¤
=21p(cm¤ )
359
I ABC DBI= IBC
DE” BC” DIB= IBC
DBI= DIB DBI DB”=DIÚ
EIC EC”=EIÚ
DI”=DB”=10(cm) EI”=EC”=8(cm)
DE”=DI”+EI”=10+8=18(cm) 18 cm
360
BIÚ CIÚ I ABC
DBI= IBC
DE” BC” DIB= IBC
DBI= DIB DBI
DB”=DIÚ
EIC EC”=EIÚ
ADE =AD”+DE”+EA”
=AD”+(DIÚ+IEÚ)+EA”
=(AD”+DB”)+( EC”+EA”)
=AB”+AC”=2AC”
2AC”=24 AC”=12(cm) 12 cm
361
BIÚ CIÚ I ABC
DBI= IBC
DE” BC” DIB= IBC
DBI= DIB DBI
DB”=DIÚ
EIC EC”=EIÚ
ABC =AB”+BC”+CA”
=(AD”+DB”)+BC”+(AE”+EC”)
=AD”+DI”+BC”+AE”+EI”
=AD”+(DI”+EI”)+BC”+AE”
=(AD”+DE”+AE”)+BC”
=18+7=25(cm) 25 cm
362
BOC=2 A 100˘=2 A A=50˘
BIC=90˘+;2!; A=90˘+;2!;_50˘=115˘ 115˘
363
BOC=2 A=2_38˘=76˘
BIC=90˘+;2!; A=90˘+;2!;_38˘=109˘
BIC- BOC=109˘-76˘=33˘ 33˘
A
B C
D I E
7 cm A
B
D E
C I
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368
ABC I D
E F B’C’=x cm AC”=y cm IECF
CE”=CF”=IEÚ=2(cm) BD”=BE”=x-2(cm) AD”=AF”=y-2(cm)
AB”=2 OB”=2_5=10(cm) (x-2)+(y-2)=10 x+y=14
ABC=;2!;_2_(10+x+y) ABC=;2!;_2_24=24(cm¤ )
5 cm
2 cm A
B C
D I F O
E
369 370
8 cm371
100˘372
10 cm373
18˘374 375
70˘376
27p cm¤377 378
100˘379 380
26˘381
192˘382 383
201˘384 385
9p cm¤386
(4-p) cm¤387
:¡2¡: cm388
12 cm389 390
4 cm391
392
116p cm¤실력콕콕 67 69
369
370
ABC r cm
2pr=10p r=5 OA”=OB”=OC”=5(cm)
OBC 18 cm OB”+BC”+OC”=18
5+BC”+5=18 BC”=8(cm) 8 cm
371
O ABC OA”=OB”=OC”
OAB= OBA=35˘+10˘=45˘
BAC= x OCA= OAC= x-45˘
ABC x+35˘+( x-45˘-10˘)=180˘
2 x=200˘ x=100˘
BAC=100˘ 100˘
O ABC OA”=OB”=OC”
OAB= OBA=35˘+10˘=45˘
OAC= x OCA= OAC= x
ABC (45˘+ x)+35˘+( x-10˘)=180˘
2 x=110˘ x=55˘
BAC= OAB+ OAC=45˘+55˘=100˘
372
O ABC OA”=OB”=OC”
ABC A=180˘-(30˘+90˘)=60˘
AOC OA”=OC” OCA= A=60˘
AOC OA”=OC”=AC”=5(cm)
OB”=OA”=5(cm)
AB”=2OA”=2_5=10(cm) 10 cm
373
M ABC MA”=MB”=MC”
MAC= C=36˘
AMC AMH=36˘+36˘=72˘
AHM x=180˘-(90˘+72˘)=18˘ 18˘
374
OAB OA”=OB”
OAB=;2!;_(180˘-140˘)=20˘
OCA OA”=OC”
OCA= OAC=50˘
20˘+ x+50˘=90˘ x=20˘
375
OAB+ OBC+ OCA=90˘
OAB=90˘_ =40˘
OBC=90˘_ =30˘
OAB OA”=OB”
OBA= OAB=40˘
ABC= OBA+ OBC=40˘+30˘=70˘ 70˘
376
BOC=2 A=2_60˘=120˘
OBC =p_9¤ _;3!6@0);
OBC =27p(cm¤ ) 27p cm¤
377
OAB OA”=OB”
OBA= OAB=12˘
ABC= OBA+ OBC=12˘+40˘=52˘
x=2 ABC=2_52˘=104˘
3 4+3+2
4 4+3+2
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384
BI'C=90˘+;2!; BIC
148˘=90˘+;2!; BIC BIC=116˘
BIC=90˘+;2!; A
116˘=90˘+;2!; x x=52˘
385
ABC r cm
36=;2!;_r_24 r=3
=p_3¤ =9p(cm¤ ) 9p cm¤
386
ABC r cm
ABC=;2!;_r_(10+6+8)=12r(cm¤ ) ABC=;2!;_6_8=24(cm¤ ) 12r=24 r=2
= IECF - IEF
=2_2-;4!;_p_2¤ =4-p(cm¤ ) (4-p) cm¤
387
BD”=x cm BE”=BD”=x(cm)
AF”=AD”=13-x(cm) CF”=CE”=10-x(cm) AC”=AF”+CF” 12=(13-x)+(10-x) 2x=11 x=:¡2¡:
BD”=:¡2¡: cm :¡2¡: cm
388
IFÚ IECF
CE”=CF”=IEÚ=2(cm) AD”=AF”=AC”-CF”
=5-2=3(cm)
BE”=BD”=AB”-AD”=13-3=10(cm)
BC”=BE”+EC”=10+2=12(cm) 12 cm
389
I ABC DBI= IBC
DE” BC” DIB= IBC DBI= DIB
B C
E I
D A
F5 cm 2 cm
13 cm
378
ABC O BC” BAC=90˘
ABO OA”=OB” OAB= B=40˘
OAC=90˘-40˘=50˘
O' AOC
x=2 OAC=2_50˘=100˘ 100˘
379
380
I ABC
IBC= IBA= x ICB= ICA=27˘
IBC x=180˘-(127˘+27˘)=26˘ 26˘
381
BCE x=;2!; ABC+68˘
ADC y=;2!; BAC+68˘
BAC+ ABC=180˘-68˘=112˘
x+ y={;2!; ABC+68˘}+{;2!; BAC+68˘}
x+ y=;2!;( BAC+ ABC)+136˘
x+ y=;2!;_112˘+136˘=192˘ 192˘
382
I ABC
IAB+20˘+ ICA=90˘
IAB+ ICA=70˘
AIC
x=180˘-( IAC+ ICA)
=180˘-( IAB+ ICA)
=180˘-70˘=110˘
I ABC
ABC=2 IBC=2_20˘=40˘
x=90˘+;2!; ABC=90˘+;2!;_40˘=110˘
383
IBC= IBA=25˘ IBC y=180˘-(25˘+28˘)=127˘
127˘=90˘+;2!; x x=74˘
x+ y=74˘+127˘=201˘ 201˘
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DBI DB”=DI”
ECI= ICB EIC= ICB ECI= EIC
EIC EI”=EC”
390
ABC AB”=AC”
B= C I
DBI= IBC= ECI= ICB
IBC= ICB IBC
IBÚ=ICÚ
DE” BC” DIB= IBC EIC= ICB DBI™ ECI ASA
EC”=DB”=AB”-AD”=8-6=2(cm)
DE”=DIÚ+EIÚ=DB”+EC”=2+2=4(cm) 4 cm
391
IBC= ABI=38˘ ICB= ACI=32˘
IBC BIC=180˘-(38˘+32˘)=110˘
BIC=90˘+;2!; A
110˘=90˘+;2!; A A=40˘
BOC=2 A=2_40˘=80˘
392
ABC R cm
R=;2!;AB”=;2!;_20=10
=p_10¤ =100p(cm¤ )
ABC r cm
;2!;_r_(20+12+16)=;2!;_12_16 24r=96 r=4
=p_4¤ =16p(cm¤ )
100p+16p=116p(cm¤ ) 116p cm¤
6 cm
8 cm A
B C
D I E
393
BAM=90˘_ =50˘
M ABC MÚAÚ=MÚBÚ=MÚCÚ
2단계
5 1단계 5+4
393
80˘394
72˘395
8 cm396
10 cm397
150˘398
120˘술형 70 서 콕콕
ABM MÚAÚ=MÚBÚ ABM= BAM=50˘
ABM AMB=180˘-2_50˘=80˘ 80˘
394
MCA=90˘_ =54˘ yy
M ABC MÚAÚ=MÚBÚ=MÚCÚ
AMC MÚAÚ=MÚCÚ
MAC= MCA=54˘ yy
AMC AMC=180˘-2_54˘=72˘ yy 72˘
395
AF”=AD”=AB”-BD”=13-7=6(cm) BE”=BD”=7(cm)
CF”=CE”=BC”-BE”=9-7=2(cm)
AC”=AF”+CF”=6+2=8(cm) 8 cm
396
CE”=CF”=AC”-AF”=10-4=6(cm) yy
AD”=AF”=4(cm)
BE”=BD”=AB”-AD”=8-4=4(cm) yy
BC”=BE”+CE”=4+6=10(cm) yy
10 cm
397
ABC ACB=180˘-(70˘+90˘)=20˘
I ABC
ICB=;2!; ACB=;2!;_20˘=10˘
O ABC OA”=OB”=OC”
OBC OB”=OC”
OBC= OCB=20˘
PBC BPC=180˘-(20˘+10˘)=150˘
150˘
398
ABC ABC=180˘-(50˘+90˘)=40˘
I ABC
IBC=;2!; ABC=;2!;_40˘=20˘ yy
O ABC OA”=OB”=OC”
OBC OB”=OC”
OCB= OBC=40˘ yy
PBC
BPC=180˘-(20˘+40˘)=120˘ yy 120˘
3단계 2단계 1단계 3단계 2단계 1단계
3 3+2 3단계
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1. 평행사변형
Ⅲ. 사각형의 성질
399
AD” BC”x= ADB=30˘ y= DAC=50˘
x= D=75˘
B+ C=180˘ y=180˘-75˘=105˘
A+ D=180˘ x=180˘-110˘=70˘
y= A=110˘
AD” BC” x= ADB=26˘
ABD A= C=120˘
y=180˘-(120˘+26˘)=34˘
x=30˘ y=50˘ x=75˘ y=105˘
x=70˘ y=110˘ x=26˘ y=34˘
400
BC”=AD”=5(cm) x=5 AB”=DC”=4(cm) y=4
OD”=;2!;BD”=;2!;_8=4(cm) x=4 OC”=OA”=2(cm) y=2
x=5 y=4 x=4 y=2
401
OA”=OC” OB”=OD”
ABD ADB
OAB OCD
OA”=OC” OB”=OD” AOB= COD OAB™ OCD SAS
402
DC” BC” DC” BC” A B
OC” OD” AB” AB”” AD” AD”
403
= ABD=;2!; ABCD
=;2!;_12=6(cm¤ )
= AOD=;4!; ABCD
=;4!;_12=3(cm¤ )
개념콕콕 73
= PDA+ PBC=;2!; ABCD
=;2!;_12=6(cm¤ )
= PAB+ PCD=;2!; ABCD
=;2!;_12=6(cm¤ )
6 cm¤ 3 cm¤ 6 cm¤ 6 cm¤
404
BCO= ABO=5(cm¤ )
ABD=2 ABO=2_5=10(cm¤ ) ABCD=4 ABO=4_5=20(cm¤ )
5 cm¤ 10 cm¤ 20 cm¤
405
AB” DC” ABD= CDB=46˘
ABC x+(46˘+28˘)+ y=180˘
x+ y=106˘
406
AD” BC” 125˘+ D=180˘ D=55˘
AED 30˘+ x+55˘=180˘
x=95˘
405 406 407
40˘408
DCA DAC AC” ASA409 410 411
x=9 y=100412
105˘413 414
14415
416 417 418 419
2 cm420 421 422
90˘423
30˘424
125˘425 426 427
50˘428
120˘429 430 431
432
COD SAS OCD BC”433
360 180 B AD”434 435 436 437
438
x=2 y=110439
x=45˘ y=70˘440
10441 442 443
OC” OD” OB” OF”444
DF” AB” DC”445
446 447 448
449 450
28 cm451 452
12 cm¤453
6 cm¤454
52 cm¤455
12 cm¤456
7 cm¤457
40 cm¤458
5 cm¤459
20 cm¤유형콕콕 74 82
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407
AB” DC” y= ABD=30˘ yy
OCD x=100˘- y=100˘-30˘=70˘ yy
x- y=70˘-30˘=40˘ yy
40˘
408
DCA DAC AC” ASA