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1 VI. 2 6

2 ! 50! 76! 44! 70! 56! 115! 108! EFZDFZEFZEEF 3 1 =180-{35+75}= =70 =180-{40+90}= =50 2 ABZ=DEZBZ= EFZAZ= DFZ ABZ=DEZBZ= EFZB= E BZ=EFZB= E = F 3 A B 1 B= x=70! B= x= 1 2 \{180!-80!}=50! B= x=180!-2\52!=76! B= x=180!-2\68!=44! =180!-110!=70! /x==70! =180!-118!=62! /x=180!-2=180!-2\62!=56! = 1 2 \{180!-50!}=65! /x=180!-=180!-65!=115! = 1 2 \{180!-36!}=72! /x =180!-=180!-72!=108! `cm90! 6`cm27! 1 4`cm90!70! 60! 60!10`cm10`cm `cm 19`cm 35`cm 1 BDZ= 1 2 \BZ= 1 2 \8=4{cm} 1 ABZ=AZ x=13 ABZ=AZ x=8 ABZ=AZ x=13 2 AZ=ABZ=9`cm 6+2\9=24{cm} 5+2\7=19{cm} 15+2\10=35{cm} ABZ=AZBAD=ADADZ\BZ /ADB =90! DZ= 1 2 \BZ= 1 2 \12=6{cm} ABDADB=90! BAD=180!-{63!+90!}=27! DZ=BDZ=4{cm} ABZ=AZBAD=ADADZ\BZ /ADB=90! ADAD=90! =180!-{20!+90!}=70! 2

3 =B=60! ABA=180!-{60!+60!}=60! BZ=2\BDZ=2\5=10{cm} AB ABZ=BZ=10{cm} ADADZAZ 3 DBDB 4 115! 27! 15! 12! 100! 36! 111! 75! 5 62!31!59!28! 24! 34! 6 GFEGEF53! 65! 64! 124! 55! 1 60! 90! 1 B=ABABZ=AZ /x=2 B=180!-{70!+55!}=55!B= ABABZ=AZ x=7 =180!-{50!+65!}=65!A= ABBAZ=BZ x=4 B+65!=130!B=65! /B= ABABZ=AZ x=10 B=180!-125!=55!B= ABABZ=AZ x=6 =180!-130!=50! ABA=180!-{80!+50!}=50! /A= ABBAZ=BZ x=5 2 ABZD ABDAD B= BAD= AD yy 180! ADB=AD yy ADZ yy ABD+ADASA /ABZ= AZ 3 ABABZ=AZ B= BDZDZB DB= 1 2 B DB = 1 2 /DB= DB DB DB 4 ABABZ=AZ AB= 1 2 \{180!-50!}=65! BDBZ=BDZ BD=BD=65! /x=180!-65!=115! ABABZ=AZ AB= 1 2 \{180!-42!}=69! ABDDAZ=DBZ DBA=DAB=42! /x=ab-dba=69!-42!=27! ABABZ=AZ AB= 1 2 \{180!-70!}=55! ADAZ=DZ DA=AD=70! /AD=180!-2\70!=40! /x=ab-ad=55!-40!=15! ABABZ=AZ AB=AB=64! BDBZ=BDZ BD=BD=64! /DB=180!-2\64!=52! /x=ab-db=64!-52!=12! ABABZ=AZ BA=180!-2\70!=40! ABDDAZ=DBZ 3

4 ABD=BA=40! /x=180!-{40!+40!}=100! ABDDAZ=DBZ DBA=DAB=x BD=DAB+DBA=x+x=2x BDBZ=BDZ BD=BD=2x ABABZ=AZ AB=BD=2x /x+2x+2x=180! 5x=180! /x=36! ABABZ=AZ AB=AB=74! DB= 1 2 AB= 1 2 \74!=37! /x=db+db=37!+74!=111! ABABZ=AZ AB= 1 2 \{180!-40!}=70! AD= 1 2 = 1 2 \70!=35! /x=da+ad=40!+35!=75! 5 ABABZ=AZ AB= 1 2 \{180!-56!}=62! AB=AB=62! /DB= 1 2 AB= 1 2 \62!=31! AE=180!-62!=118! /DE= 1 2 AE= 1 2 \118!=59! DB x=de-db=59!-31!=28! ABABZ=AZ AB=AB= 1 2 \{180!-48!}=66! /DB= 1 2 \56!=28! AE=180!-56!=124! /DE= 1 2 \124!=62! DB x=de-db=62!-28!=34! 6 x=gfe x=gef GEF x= 1 2 \{180!-74!}=53! x=efg x=feg GEF x= 1 2 \{180!-50!}=65! FE=GEF=58! GFE=FE=58! GEF x=180!-58!\2=64! FE=GFE=62! GEF=FE=62! GEFx=62!+62!=124! GE=110! GEF=FE /FE= 1 2 \110!=55! /x=fe=55! 1 ABABZ=AZ AB=AB=30! /x=ab+ab=60! ADAZ=DZ AD=180!-2\60!=60! /y=180!-{ab+ad} =180!-{30!+60!}=90! /DB= 1 2 \66!=33! AE=180!-66!=114! /DE= 1 2 \114!=57! 5 DB x=de-db=57!-33!=24! ABABZ=AZ AB=AB= 1 2 \{180!-68!}=56! 1 180E 2 AB+DEF{RHS} AB+FED{RHA} AB+FDE{RHS} 4

5 DEDEBZ 6 AE 6`cm3`cm 9`cm ABDEF AZDFZ AB+AE= 180!ABE ABZ=DEZ yy B= E yy AB+DEFRHA 2 ABDEF ABZ=DEZAZ=DFZ AB+DEFRHS ABFED AZ=FDZA=F AB+DEFRHA ABFDE ABZ=FDZBZ=DEZ AB+FDERHS x=bz=efz=4 DEF x=bz=efz=edz=8 5 ABDE AZ=EZ yy AB= DE =90! yy BA+AB=90! DE+AB=90! BA= DE yy AB+DERHA /ABZ+DEZ=DZ+ BZ=BDZ 6 ABDAE ABZ=AZ D=E=90! DAB+DBA=90! DAB+EA=90! DBA=EA /ABD+AERHA AEZ=BDZ=6`cmDAZ=EZ=3`cm DEZ=DAZ+AEZ=3+6=9{cm} DBE= 1 2 \{6+3}\9=81 2 AB= \ 1 2 \3\6=45 2 ABD+AE AEZ=BDZ=3`cmDAZ=EZ=5`cm /DEZ=DAZ+AEZ=5+3=8{cm} DBE= =H=90!ABZ=GIZ A=90!-30!=60!=G AB+GIHRHA E=J=90!DFZ=KLZ DEZ=KJZ DEF+KJLRHS =N=90!ABZ=MOZ A=M AB+MONRHA F=P=90!DEZ=QRZ FEZ=PRZ DEF+QRPRHS 4 x=az=dfz=7 x=abz=dez=9 /AB=32-2\ 1 2 ABD+AE AEZ=BDZ=8`cmDAZ=EZ=6`cm /DEZ=DAZ+AEZ=6+8=14{cm} DBE= 1 2 /AB=98-2\ 1 2 ABD+AE AEZ=BDZ=8`cmDAZ=EZ=12`cm /DEZ=DAZ+AEZ=12+8=20{cm} DBE= 1 2 /AB=200-2\ 1 2 5

6 6 1 OPZPOB POAPOB PAO=PBO=90! yy OPZ yy POA= POB yy POA+POBRHA /PAZ=PBZ 2 EBD=BDDEZ=DZ /x=5 EBD=BDBEZ=BZ=6`cm /x=abz-bez=10-6=4 AB=90!-40!=50! DEZ=DZEBD=BD x!= 1 \50!=25! /x=25 2 AB ABZ=AZx=5 4 AOP=BOPAOP+BOP RHA PAZ=PBZx=4 PAZ=PBZAOP+BOPRHS OAZ=OBZx= OZOZEZ 2 OBZOZ LZ OAL OL AB=90!-48!=42! DEZ=DZEBD=BD x!= 1 \42!=21! /x= x=70 x=30y= {RHS}{RHA} {RHA} ABABZBZO OABZBZ OAZ=OBZOBZ= OZ /OAZ= OZ yy OAZE OEA=OE=90! yy OEZ yy OAE+OE{RHS} /AEZ= EZ OEZAZ O 1 x!= 1 \{180!-40!}=70! /x=70 2 =B=60! ADZA x!= 1 2 \60!=30! AB BZ=ABZ=3`cm /y=3 /x=30 2 B=AB ABZ=AZx=3 =180!-{120!+30!}=30! 2 OAZ= OBZ= OZ ALZ= LZ OL= OAL OAL+ OL {RHS} 3 ADZ=BDZ /x=8 OAZ=OZ /x=5 OBZ=OZOB x!=180!-2\25!=130! /x=130 6

7 2 1 20! 33! 29! 34! 15! 68! 2 70! 72! 65! 26! 112! 36! 55! 60! `cm 1 x+30!+40!=90! /x=20! x+32!+25!=90! /x=33! x=ob x+28!+33!=90! /x=29! x=oa x+24!+32!=90! /x=34! OA=40! x+40!+35!=90! /x=15! OAZ OAB=48!OA=20! /x=48!+20!=68! 2 x= 1 2 \140!=70! x= 1 2 BO= 1 2 \144!=72! OB=OB=25! BO=180!-2\25!=130! /x= 1 2 BO= 1 2 \130!=65! BO=2\64!=128! OB=OB /x= 1 2 \{180!-128!}=26! OA=OA=20! A=36!+20!=56! /x=2a=2\56!=112! BO=180!-2\35!=110! /x= 1 2 BO= 1 2 \110!=55! OA=OA=30! AO=180!-2\30!=120! /x= 1 2 AO= 1 2 \120!=60! 3 OBZ=OZ=6`cm /x=6 OAZ=OBZ=OZ=5`cm /x=oaz+obz=5+5=10 OAZ=OBZ=OZ= 1 2 \16=8{cm} /x=8 OB=OB=35! x!=ob+ob=35!+35!=70! /x=70 OB=OB=x! AO=OB+OB 80!=x!+x! x!=40! /x=40 OB=OB=24! x!=ob+ob=24!+24!=48! /x=48 OB=OB=62! x!=ob+ob=62!+62!=124! /x=124 1 OB=OB=30! AO=90!-30!=60! AO=30!+30!=60! AO /OAZ=AZ=3`cm OAZ=OBZ=OZ=3`cm /ABZ=OAZ+OBZ=3+3=6{cm} 3 1 IEZIEZ 2 IFZ FAI IF A= 1 2 \132!=66! OA=A-BAO=66!-30!=36! /x=oa=36! OB=OB=35! 1 ABABI IABZBZAZDE F IAB 7

8 IDZ=IFZIDZ= IEZ /IFZ= IEZ IEZFZ IE=IF IZ I IAZ 1 2 \76!+x+20!=90! /x=32! 2 x=90!+ 1 2 \70!=125! 2 IDZ=IEZ= IFZ DAI= FAI x=90!+ 1 2 AB IE+ IF {RHA} =90!+ 1 2 \86!=133! 3 IB=IBA x!=34! /x=34 IAIA=180!-{118!+30!}=32! x!=ia=32! /x=32 x=4 116!=90!+ 1 2 x 26!= 1 2 x /x=52! 120!=90!+ 1 2 x 30!= 1 2 x 1 x+20!+30!=90! ! 32! 27! 28! 64! 32! 2 125! 133! 52! 60! 132! 22! 16! 16! 3 BIEIDBZ 4 4`cm 6`cm 10`cm 30`cm 21`cm 25`cm 24`cm 1 13`cm /x=40! IB=IBA 26!+x+32!=90! /x=32! IB=IBA=27! x+36!+27!=90! /x=27! IA=IB=x 34!+28!+x=90! /x=28! IZ 33!+25!+ 1 2 x=90! 1 2 x=32! /x=64! /x=60! AB=2\42!=84! /x=90!+ 1 2 \84!=132! BI=90!+ 1 2 \76!=128! /x=180!-{128!+30!}=22! AI=90!+ 1 2 \68!=124! /x=180!-{40!+124!}=16! AIB=90!+ 1 2 \96!=138! ABI=BI=x x=180!-{138!+26!}=16! 3 IAB DBI=BIEI= BI yy DEZ BZ DIB=BIEI=BI yy DIB=DBIEI= EI DIZ= DBZEIZ=EZ /DEZ=DIZ+EIZ=DBZ+EZ 4 DIZ=DBZ=4`cm EIZ=EZ=6`cm DEZ=DIZ+EIZ=4+6=10{cm} {ADE} =ADZ+DEZ+EAZ= =30{cm} 8

9 DIZ=DBZ=3`cmEIZ=EZ=4`cm DEZ=DIZ+EIZ=3+4=7{cm} /{ADE}=6+7+8=21{cm} DIZ=DBZ=6`cmEIZ=EZ=4`cm DEZ=DIZ+EIZ=6+4=10{cm} /{ADE}=9+10+6=25{cm} DIZ=DBZ=5`cmEIZ=EZ=3`cm DEZ=DIZ+EIZ=5+3=8{cm} /{ADE}=10+8+6=24{cm} 1 {ADE} =ADZ+DEZ+EAZ =ADZ+DIZ+EIZ+EAZ =ADZ+DBZ+EZ+EAZ =ABZ+AZ =5+8=13{cm} 35= 1 2 r\30 35=15r /r= 7 3 {cm} 60= 1 2 r\40 60=20r /r=3{cm} 3 r`cm AB= 1 2 6= 1 2 \r\{5+3+4} 6=6r /r=1{cm} AB= = 1 2 r{ } `cm 7 `cm 3`cm 3 3 1`cm 4 7`cm 8`cm `cm 4`cm 7`cm `cm `cm 1 AB= 1 2 AB= 1 2 AB= r`cm 84= 1 2 r\42 84=21r /r=4{cm} 96=24r /r=4{cm} AB= = 1 2 r{10+6+8} 24=12r /r=2{cm} 4 ADZ=AFZ=7`cm BDZ=15-7=8{cm} BEZ=BDZ=8`cm /x=8 FZ=EZ=4`cm AFZ=8-4=4{cm} ADZ=AFZ=4`cm /x=4 AFZ=ADZ=2`cm FZ=6-2=4{cm} EZ=FZ=4`cm /x=4 BDZ=BEZ=5`cm AFZ=ADZ=ABZ-BDZ=9-5=4{cm} FZ=EZ=7`cm AZ=4+7=11{cm} /x=11 9

10 AFZ=ADZ=4`cm EZ=FZ=8-4=4{cm} BEZ=BDZ=6`cm /BZ=BEZ+EZ=6+4=10{cm} /x=10 FZ=EZ=6`cm ADZ=AFZ=10-6=4{cm} BDZ=BEZ=7`cm /ABZ=4+7=11{cm} /x=11 AFZ=ADZ=x`cm EZ=FZ=11-x{cm} BEZ=BDZ=15-x{cm} BZ=17`cm {11-x}+{15-x}= x=17 /x= 9 2 BDZ=BEZ=x`cm AFZ=ADZ=7-x{cm} FZ=EZ=9-x{cm} AZ=8`cm {7-x}+{9-x}=8 16-2x=8 /x=4 ADZ=AFZ=x`cm BEZ=BDZ=12-x{cm} EZ=FZ=9-x{cm} BZ=9`cm {12-x}+{9-x}=9 21-2x=9 /x=6 1 ADZ=x`cm AFZ=ADZ=x`cm EZ=FZ=10-x{cm} BEZ=BDZ=12-x{cm} BZ=15`cm {10-x}+{12-x}= x=15 /x= 7 2 {cm} 1 124! 43! 59! 64! 2 31! 139! 32! 72! OB=OB=28! OB x=180!-2\28!=124! OAZ OAB=OBA=23!OA=OA=20! /x=oab+oa=23!+20!=43! A= 1 2 BO= 1 2 \156!=78! OAB=OBA=19! /x=a-oab=78!-19!=59! OB=OB=26! ABx=180!-{90!+26!}=64! 2 x=iba=31! x=90!+ 1 2 B=90!+ 1 2 \98!=139! IAB=IA=x 122!=90!+ 1 2 \2x /x=32! AIZIAB=IA= 1 2 x 1 2 x+29!+25!=90! 1 2 x=36! /x=72! 3 ADZ=AFZ=4`cm BEZ=BDZ=8-4=4{cm} EZ=FZ=3`cm /BZ=4+3=7{cm} /x=7 BDZ=BEZ=x`cm AFZ=ADZ=5-x{cm} FZ=EZ=8-x{cm} AZ=7`cm {5-x}+{8-x}=7 13-2x=7 /x=3 10

11 `cm ! 6 114! 7 15`cm `cm ! `cm 1 ABZ=AZB= x+x=72! /x=36! 2 B==52! x!=180!-{90!+52!}=38! /x=38 BMZ=MZ BZ=BMZ+MZ=3+3=6{cm} /y=6 /x+y=38+6=44 3 A=AZ\BDZ ABABZ=BZ /AZ=2DZ=2\5=10{cm} 4 AD=A=68! AD=180!-2\68!=44! = 1 2 \{180!-68!}=56! /x=-ad=56!-44!=12! x=oa=48!-18!=30! 11M /AMZ=BMZ=MZ=1`cm x=iba=25! 14IAB= 1 2 A= 1 2 \50!=25! 25!+30!+x=90! /x=35! 15 BDZ=BEZ=3`cm AFZ=ADZ=11-3=8{cm} EZ=FZ=13-8=5{cm} /BZ=BEZ+EZ=3+5=8{cm} 16 r`cm AB= = 1 2 r{ } 96=24r /r=4{cm} 5 ABDBDZ=ADZ ADB=180!-2\52!=76! ADADZ=DZ x+x=76! /x=38! 6 FE=GEF GFE=FE /GEF=GFE=57! GEF x=57!+57!=114! 7 ABD+AE{RHS} ADZ=EZ=5`cm AEZ=BDZ=10`cm /DEZ=5+10=15{cm} 8 9 OB=OB=31! x+31!+43!=90! /x=16! 10 OAZ OAB=OBA=18! 01 PBZ BOP ! 11

12 2 1 ABZ DZx=70! ADZ BZy=45! ABZ DZx=39! ADZ BZy=28! ABZ DZx=72! ADZ BZy=35! 1 2 x=55!y=45!x=40!y=50! 3 x=90!y=35! 4 AZ 2 x=55!y=45! x=40!y=50! 3 ABABZ=AZ ADZ\BZx=90! A=180!-{55!+55!}=70! y= 1 2 \70!=35! 2 ADZ BZAB=AD=40! OB x+30!+40!=180! /x=110! ABZ DZAD=AB=33! OD x+33!+80!=180! /x=67! ADZ BZDB=ADB=27! AB 58!+25!+27!+x=180! /x=70! 01 3 ABDA ABDA ABZ DZ 1 1 x=70!y=45! x=39!y=28! x=72!y=35! 2 110! 67! 70! 3 DADADZDAZ 4 x=3y=4 x=9y=11 x=7y=4 x=5y=6 x=6y=4 5 BAAZASADD x=7y=9 6 x=109!y=71!x=45!y=135! x=70!y=110!x=125!y=55! x=32!y=96! x=50!y=92! 7 ODODDZOD 8 x=4y=5 x=4y=3 x=2y=1 x=8y=6 x=7y=8 x=5y= x=9y=125 x=4y=110 x=5y=75 x=6y=84 10AEB AEBDF EM BA= DA yy ADZ BZ BA= DA yy AZ yy AB+DAASA /ABZ= DZBZ= DAZ 4 ABZ=DZx=3 ADZ=BZy=4 ABZ=DZx=9 ADZ=BZy=11 ABZ=DZ x-1=6 /x=7 ADZ=BZ 2y+1=92y=8 /y=4 ABZ=DZ 4=x-1 /x=5 ADZ=BZ y+6=2y /y=6 ABZ=DZ x+2=2x-4 /x=6 ADZ=BZ 12

13 y+1=3y-72y=8 /y=4 ABZ=DZ y+3=3x-9 /3x-y=12 yy ADZ=BZ 2x+2=x+y /x-y=-2 yy - 2x=14 /x=7 x=7 7-y=-2 /y=9 5 ABDA ABDA ABZ DZ BA=DA yy ADZ BZ BA =DA yy AZ yy AB+DA ASA B= D A=BA+DA=DA+BA= /A= B= D 6 A=x=109! B=Dy=71! B=Dx=45! B+=180! y=180!-45!=135! A+D=180! x=180!-110!=70! A=y=110! A+B=180! x=180!-55!=125! A=y=55! ADZ BZx=ADB=32! B+=180!B=52!+32!=84! y=180!-84!=96! ADZ BZx=BA=50! A+D=180! A=38!+50!=88! y=180!-88!=92! 7 ABDABD O OABOD yy OAB= OD yy OBA= OD yy ABZ= DZ OAB+ OD {ASA} /OAZ=OZOBZ=ODZ 8 OAZ=OZx=4 OBZ=ODZy=5 OAZ=OZx=4 OBZ=ODZy=3 OAZ=OZ 3x+2=83x=6 /x=2 OBZ=ODZ y+5=6 /y=1 OAZ=OZx=2\4=8 OBZ=ODZy=6 OAZ=OZx=7 OBZ=ODZy= 1 2 \16=8 OAZ=OZx= 1 2 \10=5 OBZ=ODZy= 1 2 \15= ADZ=BZx=9 A=y!=125! /y=125 ABZ=DZx=4 B+=180! y!=180!-70!=110! /y=110 OBZ=ODZx=5 A+B=180! y!=180!-105!=75! /y=75 OAZ=OZx= 1 2 \12=6 ABZ DZy!=DB=84! /y=84 10DAE=AEB ABE BEZ=BAZ=4 BZ=ADZ x=bz-bez=7-4=3 DAE=AEB ABE BEZ=BAZ=3 13

14 BZ=ADZ=6 x=bz-bez=6-3=3 DAE=AEB ABE x=bez=bz-ez=adz-ez=12-5=7 DAE=AEB ADF=DF ABEDF BEZ=BAZ=7 FZ=DZ=7 BZ=ADZ=10 x={bez+fz}-bz={7+7}-10=4 DAE=AEB ADF=DF ABEDF BEZ=ABZ=6 FZ=DZ=6 BZ=ADZ=8 x={bez+fz}-bz={6+6}-8=4 DAE=AEB ADF=DFE ABEDF BEZ=BAZ=8 FZ=DZ=8 BZ=ADZ=13 x={bez+fz}-bz={8+8}-13=3 11BMZ=MZABM=EM AMB=EM /ABM+EMASA EZ=BAZ x=dz+ez=8+8=16 BMZ=MZABM=EM AMB=EM /ABM+EMASA EZ=BAZ=3 x=dz+ez=3+3=6 BMZ=MZABM=EM AMB=EM /ABM+EMASA EZ=BAZ=DZ=6 x=dz+ez=6+6= SSSDADA 3 x=4y=4 x=2y= BZDZ 5 x=45!y=68! x=75!y=6! 6 ODDZBZ 7 x=4y=6 x=12y=8 8 DADZ 9 x=66y=5 x=5y= DQQZQZ 13OZQOZ 14NZAMZBZ 15QZRQZRSZ 1 A D A D B B A D A D O B B A D B 2 ABZ=DZADZ=BZABDA ABDA ABZ=DZBZ=DAZAZ /AB+DA SSS BA= DA ABZ DZ yy BA= DA ADZ BZ yy ABD 14

15 3 ABZ=DZ 3x=12 /x=4 ADZ=BZ 3y+1=13 /y=4 ABZ=DZ 3x=6 /x=2 ADZ=BZ 12=2y+x12=2y+2 /y=5 4 A=B=DABD A+B++D=360! A+B= 180! yy BAZE EAD+DAB=180! yy EAD=B ADZ BZ yy ABZ DZ yy ABD 5 A= 67!+x=112! /x=45! y=180!-112!=68! A= 2x=150! /x=75! 5y=180!-150!=30! /y=6! 6 ABD O OABOD OAZ=OZOBZ=ODZAOB=OD /OAB+ OD SAS OAB=OD ABZ DZ yy OAD+OBSAS OAD=OB ADZ BZ yy ABD 7 OAZ=OZx=4 OBZ=ODZy=6 OAZ=OZ 4y= 1 \64=32 /y=8 2 8 ADZ BZADZ=BZABD A ABDA BZ=ADZAB=ADAZ AB+ DA SAS /ABZ= DZ ABD 9 ABZ DZx!=66! /x=66 ABZ=DZy=5 ABZ=DZ3x+5=20 /x=5 ABZ DZy!=57! /y=57 10ABZ=DZADZ=BZ A+B=120!+60!=180!ADZ BZ ADZ=BZ=4 =360!-{130!+50!+50!}=130! A=B=D OAZ=OZ DZ=4 11ABZ DZABZ=DZ ADZ BZADZ=BZ A=B=D OAZ=OZOBZ=ODZ ABZ=DZADZ=BZ 12ABPDQ APB=QD=90!ABZ=DZ ABP=DQ ABP+ DQ RHA /APZ= QZ APQ=QP=90! yy APZ QZ yy APQ 2x= 1 \48=24 /x=12 2 OBZ=ODZ 13ABQ OAZ= OZ yy 15

16 BPZ=DQZ POZ=QOZ yy APQ 14ADZ BZ OAB= 1 4 ABD= 1 4 OB= 1 4 ABD= 1 4 OAB+OD= 1 4 ABD+ 1 4 ABD AMZ NZ ADZ=BZ AMZ= 1 2 ADZ= 1 2 BZ=NZ yy yy = 1 2 ABD = 1 2 ANM 15APSRQ A= OB+ODA= 1 4 ABD+ 1 4 ABD = 1 2 ABD = 1 2 APZ= 1 2 ABZ= 1 2 DZ=RZ ASZ= 1 2 ADZ= 1 BZ= QZ 2 APS+RQSAS /PSZ= RQZ BQP+DSRSAS yy /PQZ= RSZ yy PQRS 4 PAB+PD= 1 2 ABD = 1 2 PB+PDA= 1 2 ABD = PDA=36 PAB+22= ANM ANM=ANM+MN = 1 2 ABNM+ 1 2 MND = 1 2 {ABNM+MND} = 1 2 ABD = AB= 1 2 ABD= 1 2 BD= 1 2 ABD= x=7y=4 2 x=75y=75 x=5y=7 3 x=5y=10 x=110y=70 x=3y=8 x=60y=3 4 16

17 1 ABZ=DZ 6=x-1 /x=7 ADZ=BZ y+8=3y2y=8 /y=4 2 x!=180!-105!=75! /x=75 y!=x!=75! /y=75 OAZ=OZx=5 OBZ=ODZy=7 3 ADZ=BZ 2x-1=9 /x=5 ABZ=DZ 2x=y /y=10 A= x!=69!+41!=110! /x=110 y!=180!-110!=70! /y=70 2 ABO x=oab=42! OB=90!-30!=60! OB x=ob=60! OB=OB=43! OBx=43!+43!=86! 2 1 DZDB 2 90 A BDZ OAZOZ OAZ=OZx= 1 2 \6=3 OBZ=ODZy=2\4=8 A=180-D x!+50!=180!-70!x!=60! /x=60 ABZ=DZ 4=3y-5 /y=3 4 OB+ODA= 1 4 ABD+ 1 4 ABD = 1 2 ABD = ABDABD ABDB AZ=BDZABZ= DZBZ AB+DBSSS /AB= DB ABD A=B=D /A=B= =D ABD 2 A= 90! A=B==D=90! 02 A=BB= A A=B==D=90! AZ= BDZ ! 60! 86! OBZ= OAZOBZ= OZ AZ=BDZ 1 BDZ=AZ x=7 AZ=BDZ x=5 BDZ=AZ=2OZ x=2\8=16 1 A=90! A=B==D=90! AZ= 6 `cmaz=bdz 17

18 x=9y=63 x=8y=29 x=6y=58 x=3y=90 1 ABZ=BZ x=11 OBZ=ODZ x=7 AZ\BDZ x!=90! /x=90 AZ\BDZBO=90! OBx!+50!+90!=180! x!=40! /x=40 2 BZ=ABZ x=9 DA=AB y!=63! / y=63 BZ=DZ x=8 AB y!=29! / y=29 BZ=ABZ x=6 ODy!+32!+90!=180! y!=58! / y=58 ABZ=DAZ 2x-3=4x-92x=6 /x=3 AZ\BDZ y!=90! / y= AZDABDZ 2 BZDAZ BDZ ABD ABZ=BZ=DZ=DAZ ABAD ABZ=ADZBZ=DZ AZ AB+ADSSS /BA= DA AZABDA BD /AZ\ BDZ 2 ABZ= BZABZ= DAZ AZ\ BDZ AOB= 90! AZ\BDZ 1 ABZ=ADZ AOD=90!AZ\BDZ DZ=ADZ x=9 AZ=BDZ x=2\8=16 BDZ=AZ x= 1 2 \10=5 AZ\BDZ x!=90! /x=90 x!= 1 \90!=45! /x=45 2 BAE=90!-25!=65! x=2y=45 x=10y=90 ABE= 1 2 \90!=45! ABE 65!+45!+x!=180! x!=70! /x=70 1 OAZ=ODZx=2 18

19 ABDA=90! y!= 1 2 \90!=45! /y=45 DAZ=DZx=10 AZ\BDZ y!=90! /y=90 ABZ=BZ=DZ= DAZ yy OABOBODODA OAB=OBA=OB=OB =OD=OD=ODA DAZ =OAD= 45! A=B==D= 90! yy ABD 1 AOB=90!AZ\BDZ 1 x=13daz=dz x=90az\bdz 2 x=3az=bdz x=6\2=12az=bdz x=90 3 AOB=AODAZ\BDZ 4 DAB=ABDAB=AB=90! OAZ=OBZAZ=BDZ 5 ABDABDO OAB+OB+OD+ODASAS 7 1 DZ DBZ DA OB OZ DZBZ DEDEDZDEZ `cm 2 51`cm 1 ABZ= DZ AZ= DBZ B= ABD+DASSS ABD= DA B=ABD=DA OB= OB OBOB=OB OBZ= OZ 19

20 A=DB= A+B= 180! 2 ABDB ABZ= DZB= BZ AB+DBSAS /AZ=DBZ 3 DZ=ABZ x=4 DBZ=AZ x=13 DBZ=AZ x+13=15 /x=2 =B x!=55! /x=55 B=180!-A=180!-105!=75! =Bx!=75! /x=75 DB=ADB=40! B=ABD+DB=30!+40!=70! =B x!=70! /x=70 AB=DA=45! B= 70!=x!+45!x!=25! /x=25 OB=OB=x!BO=AOD=98! OB x!+x!+98!=180!2x!=82! /x!=41! /x=41 D=180!-66!=114! DA=DA AD DA= 1 2 \{180!-114!}=33! =B=66! AB=-DA x!=66!-33!=33! /x=33 AD=BDA=44! OAD x!=44!+44!=88! /x=88 4 ABDDABZ BZE ABZ DEZ B= DE DE DE = DEZ= DZ yy ABED ABZ= DEZ yy ABZ=DZ 5 ABE+DF A 6 D RHA /BEZ=FZ=x EFZ=ADZ=6 x B E x+6+x=142x=8 14 F /x=4 ABF+DE A 10 D RHA /BFZ=EZ=4 FEZ=ADZ=10 4 B E F x=4+10+4=18 x ABED BEZ=ADZ=11 BEZ+EZ=BZ 11+x=19 /x=8 6 B=B=DE DE==60! DE ABED DEZ=ABZ=10 DE EZ=DEZ=10 DEDZ=DEZ=10 BEZ=BZ-EZ=14-10=4 ABED ADZ=BEZ=4 1 ABZF ABF+DERHA /FEZ=ADZ=9`cm A 9`cm D BFZ=EZ EZ= 1 2 {17-9}=4{cm} /BEZ=BZ-EZ B F E 17`cm =17-4=13{cm} 2 DABZBZ E ABED BEZ=ADZ=9`cmDEZ=ABZ=11`cm 20

21 B=B=DE A 9`cm DE==60! 11`cm DE 60! B E /DZ=EZ=DEZ=11`cm ABD ABZ+BEZ+EZ+DZ+DAZ D A B A D D = =51{cm} B 8 A D 1 2 B A D B A D 10 1 DBADOAB AE DE ABE 4 5 AB AE AB 1 1 ADZ BZABDB /AB=DB ADZ BZABDAD /ABD=AD AB=DBOB OD=OAB B A 2 DB=OB+OD=14+11=25 AB=DB=25 AD=ODA+OD=6+11=17 ABD=AD=17 B D OAB=ABD-OAD=17-6=11 ABD=OAB+OB+OD+ODA = =42 21

22 3 AZ DEZ AD=AE AED=DE ABD=AB+AD =AB+AE =ABE 5 ADZ BZDB=AB ADZ BZDE=AE ABE+DE=ABE+AE =AB 1 ADZ BZ DM= 1 2 DB= 1 2 AB = 1 2 AB= 1 2 \16\12=96 ABP= \96=36 AP= \96=60 ABPAP=3660=35 3 AD= 1 2 ABD= 1 2 \60=30 /PD= 1 2 AD= 1 2 \30=15 DB= 1 2 \ABD=30 /DP= 2 3 DB= 2 3 \30=20 ABD= 1 2 \ABD=30 /ABP= 2 3 ABD= 2 3 \30=20 ABD= 1 2 \ABD=30 /ABP= 1 4 ABD= 1 4 \30= : : : AB= \30=10 AD= \30=20 AB= \30=12 AD= \30=18 4 OAZOZ=23 OADOD=23 4OD=23 /OD=6 ABD=AD OAB=OD=6 OABOB=23 6OB=23 /OB=9 ABD=OAB+OB+OD+ODA = =25 5 OAB=ABD-AOD=8-3=5 /OD=OAB=5 ODZOBZ=OADOAB=35 ODOB=ODZOBZ=35 5OB=35 /OB= AB= 1 2 \8\6=24 BD=OB+OD= =40 3 ABP= \24=9 AP= \24=15 ABPAP=915=35 22

23 1 x=6y=55 x=9y=40 x= 11 2 y=45 x=14y= x=oz= 1 2 BDZ= 1 2 \12=6 OBA=90!-35!=55! OAB y!=oba=55! /y=55 OBZ=ODZ x=9 AB y!=40! /y=40 OBZ= 1 2 AZ x= 11 2 ABB=90! y!=45! /y=45 AZ=DBZ x=14 AB=DA=34! B= y!=34!+38!=72! /y= OAZOZ=25 OADOD=25 OAD60=25 OABOB=OAZOZ=25 60OB= `cm A+B=180! A= \180!=100! /=A=100! 3 ADZ BZ DAE=AEB ABE BEZ=ABZ=7 BZ=7+3=10 ABD 2\{7+10}=34 4 ABZ=DZ x+6=3x-42x=10 /x=5 /BZ=3x+5=3\5+5= PAB+PD=PB+PDA PAB+13= OAZ=OBZ= 1 2 \12=6`cm OAB x=60! y=60!+60!=120! /x+y=60!+120!=180! 8 9 OAD OAD=180!-{90!+24!}=66! /AB=OAD=66! 23

24 10ABZ=ADZ=AEZABE /AEF=ABE=20! ABE BAE=180!-{20!+20!}=140! EAD=BAE-BAD =140!-90!=50! ADE EDF= 1 2 \{180!-50!}=65! 11DABZ A 5`cm D BZ 120! E 8`cm ABED B E BEZ=ADZ=5`cmDEZ=ABZ=8`cm B=180!-120!=60! B=B=DE /DE==60! DE EZ=DEZ=8`cm /BZ=BEZ+EZ=5+8=13{cm} ABEBZEZ=72 ABAE=72 AE= ODZOBZ=12 OADOAB=12 5OAB=12 OAB=OD ODZOBZ=12 ODOB=12 10OB=12 /DB=OD+OB 24