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TYT AYT Geometri Ders İşleyiş Modülleri 2. Modül Üçgenler

Published by Nesibe Aydın Eğitim Kurumları, 2019-08-21 02:06:05

Description: TYT AYT Geometri Ders İşleyiş Modülleri 2. Modül Üçgenler

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#VLJUBCOIFSIBLLTBLMESWF\":%*/:\":*/-\"3*OBBJUUJSTBZMZBTBOOIÐLÐNMFSJOF HËSFLJUBCOEÐ[FOJ NFUOJ TPSVWFõFLJMMFSJLTNFOEFPMTBIJ¿CJSõFLJMEFBMOQZBZNMBOB- NB[ GPUPLPQJZBEBCBõLBCJSUFLOJLMF¿PóBMUMBNB[ :BZO4PSVNMVTV $BO5&,÷/&- :BZO&EJUÌSÑ #JMJNTFM÷ODFMFNF ÷MIBO#&:\";5\"õ %J[HJ–(SBGJL5BTBSN *4#//P .VTUBGB:·$& :BZOD4FSUJGJLB/P #BTN:FSJ \"ZEO:BZOMBS%J[HJ#JSJNJ ÷MFUJöJN &SUFN#BTN:BZO-UEõUJr \":%*/:\":*/-\"3* JOGP!BZEJOZBZJOMBSJDPNUS 5FMr 'BLT 0533 051 86 17 aydinyayinlari aydinyayinlari * www.aydinyayinlari.com.tr ·/÷7&34÷5&:&)\";*3-*, %¸O¾P.DSDáñ ÜNİVERSİTEYE HAZIRLIK 2. MODÜL GEOMETRİ Alt bölümlerin Karma Testler ÜÇGENLER EDĜOñNODUñQñL©HULU KARMA TEST - 1 Üçgenler Modülün sonunda A tüm alt bölümleri ³ Açı ve Açı Türleri t 2 1. A ABC üçgen 4. L©HUHQNDUPDWHVWOHU | |AB =DN zy ³ Üçgende Açı t 11 | |AC =DN ³ Dik Üçgen t 30 | |18 12 BC =DN ³ İkizkenar Üçgen t 50 Bx C ³ Eşkenar Üçgen t 58 B 15 C \"#$ÀFöJULFOBSCJSÑÀHFOIx < hZ, n# < nCPM 5BSBM CÌMHFOJO ÀFWSFTJ DN PMEVôVOB HÌSF EVôVOBHÌSF XA XB XC BÀMBSOOTSBMBOöBöBô UBSBMPMNBZBOCÌMHFOJOÀFWSFTJLBÀDNEJS EBLJMFSEFOIBOHJTJEJS \" # $ % & ³ Açıortay t 67 6ñQñIð©LðĜOH\\LĜ \" WB > WA > XC # WA > WB > XC $ WA > XC > WB ³ Kenarortay t 76 %XE¸O¾PGHNL¸UQHN % XC > WA > WB & XC > WB > WA ³ Üçgenlerde·/E÷7ş&3l4i÷k5&:-&)B\";e*3n-*,ze2r.lMikODtÜL 85ÜÇGENLER www.aydinyayinlari.com.tr \"¦*7&\"¦*5·3-&3÷ 2. Peynir \\HUDOñU ÖRNEK 1 ³ Üçgende Merkezler t 104 TANIM ³ Üçgende Alan t 111 #BõMBOH¿OPLUBMBSPSUBLPMBOJLJõOOCJSMFõJN 3aCJSEBSBÀÌMÀÑTÑ iCJSHFOJöBÀÌMÀÑTÑJTF 45° 30° 5. A ABC bir üçgen LÐNFTJOFBÀEFOJS [AC] m [BC] ³ Karma Testler t 132 B i - a OO EFSFDF DJOTJOEFO en küçük ve FO CÑZÑL Beyaz Siyah UBNTBZEFôFSMFSJUPQMBNLBÀUS Fare Fare õFLJMEFLJ TJZBI GBSFOJO QFZOJSF VMBöNBL JÀJO 18 |BF| = |FD| ³ Yeni Nesil Sorular t 140 0° < 3a < 90° j 0° < a < 30° j 90° < 2i < 180° VRUXODUñQ©¸]¾POHULQH BMBDBô ZPMVO CFZB[ GBSFOJO QFZOJSF VMBöNBL | |D AB =DN <HQL1HVLO6RUXODU j 45°< i < 90°dir. j 15° < i - a <PMVS DNñOOñWDKWDX\\JXODPDVñQGDQ | |BF =DN A (i - a)min = 16° (i - a)max = 89° j 16° + 89° = 105° dir. XODĜDELOLUVLQL] JÀJOBMBDBôZPMBPSBOLBÀUS F2E | |FE =DN 0RG¾O¾QJHQHOLQGH\\RUXP \\DSPDDQDOL]HWPHYE C ÖRNEK 2 3 $< (21 m% 1 3( 6&m / 6258/$54 x EHFHULOHUL¸O©HQNXUJXOX 5ÑNMFSJLJBÀEBOCJSJOJOÌMÀÑTÑ EJôFSJOJOÑÀLBUO- # B VRUXODUD\\HUYHULOPLĜWLU EBO FLTJL PMEVôVOB HÌSF CV JLJ BÀOO ÌMÀÑMFSJ \" Üçgenler $\\UñFDPRG¾OVRQXQGD GBSLLBÀEFSFDFEJS 2 D WDPDPñ\\HQLQHVLOVRUXODUGDQ #\"$ B¿T [\"# WF [\"$ õOMBSOO CJSMFõJN LÐ- C ROXĜDQWHVWOHUEXOXQXU % ²MÀÑMFSJUPQMBNPMBOBÀMBSBUÑNMFSBÀMBSEJZPSV[ %% E \"ÀMBSEBOCJSJOJOÌMÀÑTÑaJTFEJôFSJOJOÌMÀÑTÑ- a m ( BAC ) = m ( CAD ) G NFTJEJS#\"$B¿TOOËM¿ÐTÐm ( BAC )õFLMJO- dir. 90° - a = 3a - 30° | |1. 5BOHSBNUBõ QMBTUJL UBIUB LºóUHJCJOFTOFMFSLVM- a =PMVS#VBÀOOUÑNMFSJJTFEJS#VJLJBÀOO 2. A EFHËTUFSJMJS ÌMÀÑMFSJGBSL- 30° = 30° dir. MBOMBSBLHFPNFUSJLQBS¿BÐ¿HFO :VLBSFE BWQFBS-JMFOMFSFHÌSF '$ =YLBÀDNEJS ±M¿ÐTÐJMFBSBTOEBPMBOB¿MBSBEBSBÀ SBMFMLFOBSCJSBSBZBHFUJSFSFL¿FõJUMJHFPNFUSJLõF- EFOJS LJMMFSPSUBZB¿LBSBOCJS[FLBPZVOVEV\"S # $ % & ±M¿ÐTÐPMBOB¿ZB1EJLBÀEFOJS 3. A ABC üçgen C ±M¿ÐTÐJMFBSBTOEBPMBOB¿MBSBge- B % DN OJöBÀEFOJS (CAB) m = 120° 180° E |BD| = |AC| F BD |AE| = |EB| ve BA C 6. #JSEJLÐ¿HFOEFEJLLFOBSMBSOV[VOMVLMBSDNWF CDN DNEDJNS [ED] m [AB] ±M¿ÐTÐPMBOB¿ZBEPôSVBÀEFOJS % %JLMJLNFSLF[JWFÀFWSFMÀFNCFSJONFSLF[JBSB PMEVôVOBHÌSF m (EDB) LBÀEFSFDFEJS ôFLJM* TOEBLJV[BLMLLBÀDNEJS 360° B ÖRNEK 3 $OW%¸O¾P7HVWOHUL \" # $ % & \" 17 # 17 $ 1&H27FOOFESKFJ%OÐ SFPUMNVõFBLO&J¿ JZOFMUEBFTóBJSSMNBOFBOOJO ÐJ¿T FBõóMBFNõLMBFõOUBSSN ÐB¿L- 1. D DN 5 3 TEST - 36#ÑUÑOMFSJLJBÀOOÌMÀÑMFSJGBSLPMEVôVOBHÌSF Her alt bölümün AC VRQXQGDRE¸O¾POHLOJLOL J¿JO\"# %&WF'(LFOBSMBSOBCJSCJSMFSJZMFLFTJõF- LÑÀÑLBÀOOUÑNMFSJLBÀEFSFDFEJS WHVWOHU\\HUDOñU ,FOBSPSUBZ \"LJG ±óSFUNFO TOGOEBLJ1 Ë3ó2SFODJMFSJ JMF UBOHSBN DFLõFLJMEFEPóSVTBM¿UBMBS¿BLBSBLZFMEFóJSNFOJ- ±M¿ÐTÐPMBOB¿ZBUBNBÀEFOJS 2. C 3. D 4. # 5. C 6O.JCTBóMBNMBõUSZPSWFôFLJM**PMVõUVSVMVZPS FULJOMJóJ ZBQNBL J¿JO ËóSFODJMFSJOF LºóU DFUWFM ±M¿ÐMFSJUPQMBN1.PMBOB¿MBSBUÑNMFSBÀMBS A (180° - a) - a = 30° j4a. = 75° dir. A NBLBTWFB¿ËM¿FSEBóUQBõBóEBLJUBOHSBNõBC- K EFOJS 90°- 75°= 15° MPOVOEBOHFPNFUSJLõFLMJLFTNFTJOJJTUFNJõUJS 15° ±M¿ÐMFSJ UPQMBN PMBO B¿MBSB bütünler BÀMBSEFOJS 12 16 AD N B DÖRNEKC 4 B AB ] m [ AD ] m % C C E \"#$Ð¿HFOJOEF [ (#DÑCUÑAO) M=FS1J5L°JBÀEBOCÑZÑôÑOÑOÌBMÀÑTÑOÑOZBSTLÑ-D B | | | |BD = 2 DAC PMEVôVOBHÌSF mÀ(ÑA%ôCÑBOÑ) O= UaÑNkaMFçSJOJO JLJ LBUOB FöJU PMEVôVOB HÌSF %BIBTPOSB\"LJG±óSFUNFOËóSFODJMFSJOEFOJLJLÐ- CÑZÑLBÀOOÌMÀÑTÑLBÀEF\"SF#D$FEÐJ¿SHFOJOEF [ AB ] m [ AC ] [ AD ]LFOBSPSUBZ ¿ÐLWFPSUBCPZÐ¿HFOJBMBSBLCVÐ¿HFOMFËODFEJL EFSFDFEJS CJSÐ¿HFOEBIBTPOSBJTFZJOFÐ¿Ð¿HFOMFCJSLBSF- LF EFOGBSLMEJLEËSUHFOZBQNBMBSOJTUJZPS AC | | | |[ BN ]B¿PSUBZ AB =DN AC =DNPMEV- GM \" # $ % & | |ôVOBHÌSF ND LBÀDNEJS #ÑZÑLBÀOOÌMÀÑTÑa CÑUÑOMFSJ- aPMTVO :BQMBO FULJOMJL TPOSBTOEB ÌôSFODJMFSJOJO PMVöUVSEVôVEJLÑÀHFOWFEJLEÌSUHFOJOÀFWSF #JS B¿Z ËM¿ÐMFSJ FõJU JLJ B¿ZB BZSBO õOB a = 2^ 90° - ^ 180° - a h h A) 35 43 45 50 MFSJOJOGBSLMBSOONVUMBLEFôFSJLBÀDNEJS 2 3a 8 B) C) D) E) 5 BÀPSUBZEFOJS a 10 11 11 % % = m ( DAC ) = - 180° + 2a j 180° = j 120° = a ô LJM ** m ( BAD ) 22 õFLJM**EFPMVöBO,-.ÑÀHFOJOJOBMBOOOõFLJM 2. \"#$CJSÐ¿HFO,WF.LFOBSPSUBOPLUBMBS(BóS- \" 4 - 2 2 # 8 - 4 2 $ 4 2 * EFLJ ÑÀHFOMFSJO BMBOMBS UPQMBNOB PSBO LBÀ MLNFSLF[JEJS US A 5. % 6 - 4 2 & 2 2 - 8 A 2 1. 105 2. 30° 3. 15° 4. 120° x \" # $ % & D K G G 10 B 16 L C BM C \"#$Ð¿HFOJOEF (BóSMLNFSLF[J [ AG ]B¿PSUBZ | | | | | |KL = LM [ AG ] m [ BG ]WF AB =DNPMEV- | | | | | | | |AD = DC BG =DN BC =DN | | | |ôVOBHÌSF GL + LM UPQMBNLBÀDNEJS | | :VLBSEBLJWFSJMFSFHÌSF AG =YLBÀDNEJS \" # $ % & \" # $ % & 1. # 144 2. \" 3. A 6. A 7 9 G G 8 BC B KD C \"#$CJSÐ¿HFO (BóSMLNFSLF[JE JS \"#$CJSÐ¿HFO (BóSMLNFSLF[JEJS | | | | | |AG =DN GC =DNWF BG =DN | | | |% | |:VLBSEBLJWFSJMFSFHÌSF \"# LBÀDNEJS m ( BGK ) \" # $ % & = m ( % ) AG = 3 BG KGD | | | |BC =DNPMEVôVOBHÌSF ,% LBÀDNEJS A) 3 B) 4 C) 3 2 % & 1. C 2. A 3. E 83 4. D 5. D 6. A

ÜNwİwVwE.ayRdinSyaİyTinlaEri.YcoEm.trHAZIRLIK ·/÷7&34÷5&:&)\";*3-*, GEOMETRİ 2. MODÜL ÜÇGENLER ³ Açı ve Açı Türleri t 2 ³ Üçgende Açı t 11 ³ Dik Üçgen t 30 ³ İkizkenar Üçgen t 50 ³ Eşkenar Üçgen t 58 ³ Açıortay t 67 ³ Kenarortay t 76 ³ Üçgenlerde Eşlik - Benzerlik t 85 ³ Üçgende Merkezler t 104 ³ Üçgende Alan t 111 ³ Karma Testler t 132 ³ Yeni Nesil Sorular t 140 1

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr \"¦*7&\"¦*5·3-&3÷ TANIM ÖRNEK 1 #BõMBOH¿OPLUBMBSPSUBLPMBOJLJõOOCJSMFõJN 3aCJSEBSBÀÌMÀÑTÑ iCJSHFOJöBÀÌMÀÑTÑJTF LÐNFTJOFBÀEFOJS i - a OO EFSFDF DJOTJOEFO en küçük ve FO CÑZÑL B UBNTBZEFôFSMFSJUPQMBNLBÀUS AC 0° < 3a < 90° j 0° < a < 30° j 90° < 2i < 180° j 45°< i < 90°dir. j 15° < i - a <PMVS (i - a)min = 16° (i - a)max = 89° j 16° + 89° = 105° dir. #\"$ B¿T [\"# WF [\"$ õOMBSOO CJSMFõJN LÐ- ÖRNEK 2 % 5ÑNMFSJLJBÀEBOCJSJOJOÌMÀÑTÑ EJôFSJOJOÑÀLBUO- NFTJEJS#\"$B¿TOOËM¿ÐTÐm ( BAC )õFLMJO- EBO FLTJL PMEVôVOB HÌSF CV JLJ BÀOO ÌMÀÑMFSJ GBSLLBÀEFSFDFEJS EFHËTUFSJMJS ²MÀÑMFSJUPQMBNPMBOBÀMBSBUÑNMFSBÀMBSEJZPSV[ ±M¿ÐTÐJMFBSBTOEBPMBOB¿MBSBEBSBÀ \"ÀMBSEBOCJSJOJOÌMÀÑTÑaJTFEJôFSJOJOÌMÀÑTÑ- a EFOJS dir. 90° - a = 3a - 30° a =PMVS#VBÀOOUÑNMFSJJTFEJS#VJLJBÀOO ±M¿ÐTÐPMBOB¿ZBEJLBÀEFOJS ÌMÀÑMFSJGBSL- 30° = 30° dir. ±M¿ÐTÐJMFBSBTOEBPMBOB¿MBSBge- ÖRNEK 3 OJöBÀEFOJS #ÑUÑOMFSJLJBÀOOÌMÀÑMFSJGBSLPMEVôVOBHÌSF 180° LÑÀÑLBÀOOUÑNMFSJLBÀEFSFDFEJS BA C (180° - a) - a = 30° j a = 75° dir. 90°- 75°= 15° ±M¿ÐTÐPMBOB¿ZBEPôSVBÀEFOJS 360° B A C ±M¿ÐTÐPMBOB¿ZBUBNBÀEFOJS ÖRNEK 4 ±M¿ÐMFSJUPQMBNPMBOB¿MBSBUÑNMFSBÀMBS EFOJS #ÑUÑOMFSJLJBÀEBOCÑZÑôÑOÑOÌMÀÑTÑOÑOZBSTLÑ- ±M¿ÐMFSJ UPQMBN PMBO B¿MBSB bütünler ÀÑôÑOÑO UÑNMFSJOJO JLJ LBUOB FöJU PMEVôVOB HÌSF BÀMBSEFOJS CÑZÑLBÀOOÌMÀÑTÑLBÀEFSFDFEJS B D AC #ÑZÑLBÀOOÌMÀÑTÑa CÑUÑOMFSJ- aPMTVO #JS B¿Z ËM¿ÐMFSJ FõJU JLJ B¿ZB BZSBO õOB a = 2^ 90° - ^ 180° - a h h BÀPSUBZEFOJS 2 a 3a % % = - 180° + 2a j 180° = j 120° = a m ( BAD ) = m ( DAC ) 22 2 1. 105 2. 30° 3. 15° 4. 120°

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, TANIM ÖRNEK 5 B ,ËõFMFSJWFCJSFS B E D [ AB // [ CE ] LPMMBSPSUBLPMBO 45° [ AE ] // [ CD D JLJB¿ZBLPNöV 45° 45° m ( B%AE ) = 45° BÀMBSEFOJS AC AC B%AD ve % :VLBSEBLJWFSJMFSFHÌSF m ( % = a LBÀEFSFDFEJS DAC LPNõVB¿MBSES ECD ) ,FTJõFO JLJ EPóSV- [\"#[$&PMEVôVOEBO B%AE % OVO PMVõUVSEVóV ile AEC JÀUFSTBÀMBSES B¿MBSEBOLPNõVPM- x NBZBO B¿MBSB UFST m ( B%AE ) = % = 45° [\"&[%$PMEVôVOEBO % yy BÀMBSEFOJS m ( AEC ) AEC x ile % iç terTBÀMBSES. % = % = a = 45° ECD m ( AEC ) m ( ECD ) 5FSTB¿MBSOËM¿ÐMFSJFõJUUJS ÖRNEK 6 d3 d // d2PMNBL Ð[FSF ba d1 A B [ AB // [ FG cd D F 20° b' a' d2 C d1 % c' d' 20° a E m ( BAC ) = 20° 40° 40° d2 m ( C%DE ) = 80° BJMFBhZËOEFõ B=Bh 80° d3 % = 30° EJMFChJ¿UFST Ch= d 40° m ( EFG ) BJMFDhEõUFST B=Dh BhJMFELBSõEVSVNMVB¿MBSES 40° % Bh+ d = 70° m ( DEF ) 30° 30° G = 70° % :VLBSEBLJWFSJMFSFHÌSF m ( ACD ) = aLBÀEFSFDFEJS [\"#E1E2E3['( **ZPM 20° + 80°+ 30°= a + 70° a = 20° + 40°= 60° a = 60° UYARI d1 d // d2JTF ÖRNEK 7 a a +C+D= EJS A B [ AB // [ CD b c d2 50° % m ( BAE ) a d1 d // d2JTF = 50° b a +C+D+ d = c EJS DC % = 150° m ( DCE ) d d2 d1 d // d2JTF d 150° a a 30° x a +C+D= x +Z b EJS E y c d2 :VLBSEBLJ WFSJMFSF HÌSF m( % = a kaç dereDF- AEC ) dir [\"#[%$Ej a + 30° = 50° j a = 20° 3 5. 45° 6. 60° 7. 20°

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 8 ÖRNEK 11 [ AB // [ CD BA [ AB // [ EF A B DC x + 54° m ( D%CE ) = 2x 140° 40° C d1 % 90° m ( BAC ) = 140° 2x x m ( C%EA ) = x % = 120° m ( CDE ) d 180°–2x° 126°–x° 12900°° 30° E % = x + 54° 150° D d2 % m ( EAB ) m ( DEF ) = 150° :VLBSEBLJWFSJMFSFHÌSF YLBÀEFSFDFEJS FE :VLBSEBLJWFSJMFSFHÌSF m % = a kaç dereDFEJS ( ACD ) E[%$[\"# [\"#E1E2[EF x + 180°- 2x + 126°– x = 180° j x = 63° dir. a = 40° + 90° = 130° dir. ÖRNEK 9 ÖRNEK 12 A B [ AB // [ DE 30° A B [ AB // [ FG ] // [ CD d 30°a C 30° 70° m ( B%AC ) = 30° [ FE ] // [ CG ] 110° % 30° E % = 140° m ( CDE ) 40° d m ( DCG ) = 110° F 40° ED G 40° % 140° ACD ) :VLBSEBLJWFSJMFSFHÌSF m( = a LBÀEFSFDFEJS DC :VLBSEBLJWFSJMFSFHÌSF m ( A%EF ) = a LBÀEFSFDFEJS [\"#[DE ['([CD j m ( F%GC ) = 40° a = 30° + 70° = 100° dir. [FE][CG] j % = 40° m ( EFG ) [\"#['(EPMEVôVOEBOj a = 40°+ 30° = 70° dir. ÖRNEK 10 ÖRNEK 13 A B [ AB // [ DE BD [ AB // [ CD 110° % ) = 110° d m % = 40° C a 70° m ( CAB ( BAE ) 40° d % = 140° C F% 140° m ( CDE ) 70° 70° 40° m ( CEA ) = 70° 40° A EK DE :VLBSEBLJWFSJMFSFHÌSF m ( % ) = a kaç dereDFEJS DCE :VLBSEBLJWFSJMFSFHÌSF m ( % ) = a LBÀEFSFDFEJS \" & ,EPôSVTBM [\"#[$%E ACD B%AK ile F%EK BÀMBSZÌOEFö m ( B%AK ) = m ( F%EK ) = 40° E[\"#[DE] j a = 70° + 40°= 110° dir. \" & , EPôSVTBM % = 70° % ile % BÀMBS m ( CEF ) DCE CEF LBSöEVSVNMVPMEVôVOEBO m ( % ) = 110° dir. DCE 8. 63° 9. 100° 10. 110° 4 11. 130° 12. 70° 13. 110°

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 14 ÖRNEK 16 d [ AB // [ FG K F B G % m ( BAC ) = 100° 100° A B x+10° A 80° E % = 120° C 80° 20° m ( CDE ) x + 1100°2° E 60° 120° m ( D%EF ) = 80° d 2x – 40° D M % m ( EFG ) = 20° F D 2x – 40° C :VLBSEBLJWFSJMFSFHÌSF m( % = a LBÀEFSFDFEJS ACD ) G E[\"#['(PMTVO [ AB // [$% m ( % ) = 102° m ( F%AB ) = x + 10° %% % FEG KCA ile CAB LBSöEVSVNMVm ( KCB ) = 80° dir. m ( D%CG ) = 2x - 40° % + m ( D%EF ) = % + % m ( MCD ) m ( CDE ) m ( EFG ) :VLBSEBLJWFSJMFSFHÌSF YLBÀEFSFDFEJS m ( % ) + 80° = 120° + 20° MCD [\"#[CD]EPMTVO % = 60° m ( MCD ) x + 10° + 2x - 40° = 102° j x = 44° dir. , $ .EPôSVTBM a + 80° + 60° = 180° j a = 40° dir. ÖRNEK 17 ÖRNEK 15 B K [ CA // [ DG ] // d 74° C D A 74° G [ DB // [ FK E 42° A D x % = 74° 74° 42° m ( ACB ) 59° dM FN 59° % = 42° m ( EGF ) 121° 118° % :VLBSEBLJWFSJMFSFHÌSF m ( EFG ) = x kaç dFSFDFEJS EB CF % % % [$\"[DG]EPMEVôVOEBO DAB BAC ACF [ AD // EF m ( ) = m ( ) m ( ) = 118° % % % ACB, DEK MFK :VLBSEBLJWFSJMFSFHÌSF m ( A%BE ) = a kaç dereDFEJS ve BÀMBSZÌOEFö m ( A%CB ) = m ( D%EK ) = m ( M%FK ) = 74° [%\"[CF j % = % = 118° [DG]EPMEVôVOEBO % BÀTJMF % BÀTJÀUFST m ( DAC ) m ( ACF ) EGF GFN m ( D%AB ) = m ( B%AC ) = 59° %% D%AB BÀTJMF A%BE BÀTLBSöEVSVNMV m ( EGF ) = m ( GFN ) = 42° . ' /OPLUBMBSEPôSVTBM + x + 42° = 180° j x = 64°dir. a = 180°- 59° = 121° dir. 14. 44° 15. 121° 5 16. 40° 17. 64°

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 18 A d1 ÖRNEK 20 d3 d // d2 E3 // d4 // d5 mk D d4 E d2 m( % = 40° m d2 d1 A 30° ABC ) F 40° C 140° 40° d5 m( % = 30° B B K ACB ) . n M nt C d// % = %% = m ( B%CD ) :VLBSEBLJWFSJMFSFHÌSF a + b + i UPQMBNLBÀEF- d2 m ( EAB ) m ( BAD ) m ( BCF ) SFDFEJS % = 140° d1E2 ve d3E4PMEVôVOEBOa ile i ve b ile iJÀUFST m ( ADC ) BÀMBSPMVQÌMÀÑMFSJFöJUUJS :VLBSEBLJWFSJMFSFHÌSF m( % = a kaç dereDFEJS m (Wa) = m (Vi) = m (Vb) ABC ) d3E4E5PMEVôVOEBO d1E2 m ( A%BC ) = m ( B%CK ) = 40° ÷ÀUFST k + t = 140° 2m + 2n = 220° % = % = i ÷ÀUFST m ( BAC ) m ( ACM ) m + n = a j a = 110° dir. , $ .EPôSVTBMPMEVôVOEBO+ 30° + i = 180° j i = 110° dir. a b = 110° a + b + i = 330° ÖRNEK 21 ÖRNEK 19 [AK // [$. [AB] // [$5 [$/ % B¿TOOB¿PSUBZ BCM [ AB // [$% m ( % ) = m ( % ) m ( % ) = m ( % ) m ( B%AK ) = 140° m % ) = 24° BAD CAD ACE ECD ( NCT A B A PK 140° 140° m m 90° E Ba N 90° T 24° D n 64° n 52° 40° C CM % :VLBSEBLJWFSJMFSFHÌSF m ( C%ED ) = aLBÀEFSFDFEJS 7FSJMFOMFSFHÌSF m ( ABC ) = aLBÀEFSFDFEJS [\",[CM [\"#][CT]PMEVôVOEBO [\"#[CD % = % = 140° j % % m ( BAK ) m ( CPK ) CPK ile PCM 2m + 2n = 180° j m + n = 90° dir. LBSöEVSVNMVBÀMBSESm ( % ) = 40° dir. [$/ % PCM BCM % = m + n = 90° dir. BÀTOOBÀPSUBZPMEVôVOEBO m ( % ) = 64° m ( AEC ) BCN \" & %EPôSVTBM j = 90°dir. j a = 40° + 52°= 92° dir. 18. 110° 19. 90° 6 20. 330 21. 92

\"ÀWF\"À5ÑSMFSJ TEST - 1 1. aWFi UÐNMFSJLJB¿ES 5. [ AC ]å[ KL ] [ DB ]å[ FK ] a=1 m ( D%BK ) = 2m ( A%BD ) = 3m ( K%BE ) = 6m ( E%BC ) i4 PMEVôVOBHÌSF i - aGBSLLBÀEFSFDFEJS F L \" # $ % & x K D E AB C 2. a WFb CÐUÐOMFSJLJB¿ES :VLBSEBLJWFSJMFSFHÌSF m ( F%KL ) = x kaç de- SFDFEJS 3a - 2b = PMEVôVOB HÌSF LÑÀÑL BÀOO UÑNMFSJ LBÀ EFSF \" # $ % & DFE JS \" # $ % & 3. C ôFLJMEF 6. A [ BC // [ DE B % 140° % ( BAC ) B m ( ABC ) = 140° m = 72° C m ( A%DE ) = 70° 70° 72° m % ) = 40°EJS ED 40° ( CAD A D :VLBSEBLJWFSJMFSFHÌSF #\"%BÀTOOBÀPSUBZ :VLBSEBLJ WFSJMFSF HÌSF m( % = a kaç de- JMF$\"%BÀTOOBÀP SUBZBSBTOEBLJBÀOOÌM- BAD ) ÀÑTÑLBÀEFSFDFEJS SFDFEJS \" # $ % & \" # $ % & 4. B A [ AB // [ DE 7. A B [ AB // [ EF C % = a m ( A%CD ) = 155° m ( BAC ) % C 155° % = m ( ACD ) = i m ( CDE ) 125° a + i 125° % = D 140° m ( DEF ) 140° DE EF :VLBSEBLJ WFSJMFSF HÌSF % = b kaç de- :VLBSEBLJWFSJMFSFHÌSF % = a kaç de- m ( CDE ) m ( BAC ) SFDFEJS SFDFEJS \" # $ % & \" # $ % & 1. D 2. # 3. D 4. # 7 5. # 6. A 7. C

TEST - 2 \"ÀWF\"À5ÑSMFSJ 1. B [ AB // [ CD ] 4. A B [ AB // [ LK ] C 80° % = m % ) 40° [ DE ] // [ FG ] m ( BAC ) ( CAD 45° C A % = 80° D 20° % = 40° m ( ACD ) m ( BAC ) E % F m ( ACD ) = 45° L G K % = 20° m ( CDE ) a % :VLBSEBLJWFSJMFSFHÌSF m ( FGK ) = a kaç de- reDFEJS D % \" # $ % & ADC :VLBSEBLJ WFSJMFSF HÌSF m ( ) = a kaç de- SFDFEJS \" # $ % & 5. B A 2. B A [ AB // [ CD EF m ( B%EA ) = 70° DC 70° % [ AB // [$% m ( % ) = m ( % ) m ( BAC ) = a BAE EAF E % m ( BDC ) = i a - i = % = m ( % ) m ( % ) + m % = 165° CD m ( FCE ) ECD AEC ( AFC ) :VLBSEBLJWFSJMFSFHÌSF iLBÀEFSFDFEJS :VLBSEBLJ WFSJMFSF HÌSF m ( % ) LBÀ EFSFDF- \" # $ % & AEC EJS \" # $ % & 3. B A 6. B A [AB // [CD 65° [CL // [EF 105° C F L m ( B%AE ) = 65° DE F 70° K m ( A%EF ) = 70° [ BA // [%& 4m ( A%BF ) = 3m ( % ) E FBC % = 3m ( % ) m ( % ) = 105° DC 4m ( FDE ) FDC BCD :VLBSEBLJWFSJMFSFHÌSF m ( B%FD ) = a kaç de- :VLBSEBLJWFSJMFSFHÌSF m ( % ) = a kaç dere- SFDFEJS DCL DFEJS \" # $ % & \" # $ % & 1. A 2. E 3. D 8 4. D 5. C 6. #

\"ÀWF\"À5ÑSMFSJ AF TEST - 3 d1 1. E 4. 140° 30° 40° D C d2 40° B :VLBSEBLJöFLJMEFWFSJMFOMFSFHÌSFa + i + b UPQMBNLBÀEFSFDFEJS % %% % \" # $ % & d // d m ( EAB ) = m ( BAD ) m ( DAC ) = m ( CAF ) % = 40° m ( ABC ) :VLBSEBLJ WFSJMFSF HÌSF m ( A%CB ) = a kaç de- reDFEJS \" # $ % & 5. B A 2. K [ AB // [ CD E [ LK ] // [ AC ] Ea G Fi 70° L A B % = 70° 100° m ( LEM ) % = 100° m ( CAB ) DC C [ AB // [$% m ( B%AE ) = m ( % ) = m ( % ) D EAG GAF M % = % = m( % m ( DCE ) m ( ECG ) GCF ) % :VLBSEBLJ WFSJMFSF HÌSF m ( DCM ) = a kaç de- 15° < a <JTFiOOBMBCJMFDFôJFOCÑZÑL ve reDFEJS en küçükUBNTBZEFôFSMFSJOJOUPQMBNLBÀEF SFD FEJS \" # $ % & \" # $ % & 3. A [ CD // [ FE % x m ( ABC ) = 10° % = 30° 6. H [ DE // [ BC m ( BCD ) A m ( H%DE ) = 130° m ( E%FK ) = 50° 60° N E C F % = 25° 130° m ( H%NB ) = 60° 10° 30° 50° 25° m ( FKA ) D C B K D E a B :VLBSEBLJWFSJMFSFHÌSF m ( B%AK ) = x kaç dere- 7FSJMFOMFSFHÌSF m ( % ) = a LBÀEFSFDFEJS DFEJS NBC \" # $ % & \" # $ % & 1. C 2. # 3. D 9 4. A 5. E 6. A

TEST - 4 \"ÀWF\"À5ÑSMFSJ 1. A B 4. A D DE B 140° M 64° H N C a C E F K [BA // [&) m ( % ) = m ( % ) [AD // [$& m ( B%AK ) = m ( K%AD ) ABC CBF m ( C%EF ) = m ( F%EH ) m ( C%DF ) = 64° % = m ( % ) m ( % ) = 140° m ( BCM ) MCE ABC :VLBSEBLJ WFSJMFSF HÌSF m ( % ) + m ( % ) :VLBSEBLJWFSJMFSFHÌSF m ( % ) = a kaç de- BCE BFE AKM UPQMBNLBÀEFSFDFEJS SFDFEJS \" # $ % & \" # $ % & 2. A B a C 5. C [BA // [FH 2a A 170° % H ABC ) Mi 140° m( = 140° 120° D B % F m ( CDE ) = 160° 2b 100° 120° D 160° E b m ( E%FH ) = 120° HF [BA // [') m ( M%BC ) = 2m ( M%BA ) E m ( M%FE ) = 2m ( H%FM ) m ( % ) = 170° :VLBSEBLJ WFSJMFSF HÌSF m ( % ) + m ( % ) BCD BCD DEF % 120° m ( F%ED ) UPQMBNLBÀUS m ( CDE ) = = 100° :VLBSEBLJWFSJMFSFHÌSF m ( B%MF ) = i kaç dere- \" # $ % & DFEJS \" # $ % & 3. [DE // [BC A % ) = 80° m ( BAF A 6. 40° F m ( A%BC ) = 10° a 80° DE m ( A%BF ) = % % m ( FBC ) m ( BCD ) = 60° % = % C E % m ( ADF ) m ( FDE ) m ( CDE ) 10° % = 40° 60° 10° = 20° m ( BAD ) F % B 20° m ( EFA ) = 10° BC D :VLBSEBLJ WFSJMFSF HÌSF % ) = a kaç de- :VLBSEBLJWFSJMFSFHÌSF m ( D%EF ) = a kaç dere- m ( BFD DFEJS SFDFEJS \" # $ % & \" # $ % & 1. A 2. # 3. C 10 4. D 5. # 6. A

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, %m/*m ÜÇGENDE AÇI ÖRNEK 3 x' A A [CA m[ CG ] x C 20° D B 70° 85° 95° [ CF m [ DG ] m ( A%BE ) = 95° z z' 75° 105° m ( B%EF ) = 105° C EF By y' 20° \"#$Ð¿HFOJOEFY Z [J¿B¿MBSOYh Zh [hEõ G B¿MBSOËM¿ÐMFSJEJS :VLBSEBLJWFSJMFSFHÌSF % =a LBÀEFSFDFEJS #JSÐ¿HFOJOJ¿B¿ËM¿ÐMFSJUPQMBN m ( CGD ) x +Z+[=EJS & ÑÀHFOJOJOJLJEöBÀTWFJTFJLJJÀBÀT #JSÐ¿HFOJOEõB¿ËM¿ÐMFSJUPQMBN CBE % Yh+Zh+[h=EJS BCE 85°vePMVS0IBMEF m ( ) = 20° PMVS #JS Ð¿HFOJO CJS Eõ B¿TOO ËM¿ÐTÐ LFOEJTJOF LPNõVPMNBZBOJLJJ¿B¿OOËM¿ÐMFSJUPQMBNOB % = 70° a = 20° FõJUUJS m ( DCG ) ÖRNEK 1 ÖRNEK 4 #JS ÑÀHFOJO JÀ BÀMBS TSBTZMB WF TBZMBS JMF A \"#$Ð¿HFO PSBOUMJTFFOLÑÀÑLEöBÀTLBÀEFSFDFEJS % = 20° ·ÀHFOJOJÀBÀMBSOOÌMÀÑTÑY Z [PMTVO m ( ABF ) xyz % ) = 45° = = = k JÀJO Y=L Z=L [= 4k dir. m ( ADF 234 x +Z+[= L= L= 20°dir. 20° 45° #JSÑÀHFOEFFOLÑÀÑLEöBÀJMFFOCÑZÑLJÀBÀCJSCJSJOJO CÑUÑOMFSJEJS&OCÑZÑLJÀBÀ[= 4k =PMEVôVOEBOFO B D E CF LÑÀÑLEöBÀEJS m ( B%AD ) = m ( D%AE ) = % PMEVôVOBHÌSF m ( EAC ) % + m ( % ) UPQMBNLBÀEFSFDFEJS m ( AEF ) ACF m ( B%AD ) = m ( D%AE ) = % = a m ( EAC ) m ( A%BD ) + m ( B%AD ) = a + 20° = 45° j a =PMVS m ( A%EC ) = 25° + 45° = 70° m ( A%CF ) = 70° + 25° = 95° & m ( A%EF ) + m ( A%CF ) = 165° ÖRNEK 2 . A 180°–3a \"#$Ð¿HFO ÖRNEK 5 \"#$Ð¿HFOJOEF 3a <\"%>B¿PSUBZWF m ( D%AC ) = 3a A m (WB ) - m (XC ) = 28° m ( A%CE ) = 4a m ( D%BE ) = 5a mm B 180°–4a 4a % n+28° a= 104° n D 5a CE m ( ACB ) = i B DC :VLBSEBLJWFSJMFSFHÌSF % ) = i LBÀEFSFDFEJS oMEVôVOBHÌSF m ( % ) =a LBÀEFSFDFEJS m ( ACB ADC #JSÑÀHFOJOEöBÀÌMÀÑMFSJUPQMBNEJS % = n, m ( B%AD ) = % = m PMTVO 180° - 3a + 4a + 5a = 360° j a = 30° m ( BCA ) m ( DAC ) i = 180°- 4a = 180° - 120° = 60° dir. 2n +28° + 2m = 180° j m + n =PMVS m + n + a =PMEVôVOEBOa = 104° dir. 1. 100° 2. 60° 11 3. 20° 4. 165° 5. 104°

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 6 \"#$Ð¿HFO %m/*m A \"#$% J¿ CÐLFZ a EËSUHFOJOEF A m( % ) = % b i x = a + b + iES ABF m ( CEF ) B C D D x 95° E m ( B%DF ) = 95° n n a–n B a F C :VLBSEBLJWFSJMFSFHÌSF m ( % = a kaç EFSFDFEJS A #JS Ð¿HFOEF JLJ J¿ ACB ) B¿PSUBZOPMVõUVSEV- óVHFOJõB¿OOËM¿Ð- m ( A%BF ) = % = n olsun. m( CEF ) I TÐ m ( % ) = a - n PMVS BC BFD m (WA) %#'ÑÀHFOJOEFJÀBÀÌMÀÑMFSJUPQMBNPMEVôVOEBO a = 90° + n + 95° + a - n = 180° j a = 85° dir. 2 ÖRNEK 7 \"#$Ð¿HFO A #JS Ð¿HFOEF JLJ Eõ A % = % B¿PSUBZOPMVõUVSEV- m ( BAD ) m ( ACB ) óVEBSB¿OOËM¿ÐTÐ mn n B C m (WA) m ( D%AE ) = % a = 90° - m ( EAC ) 2 % = 80° m ( ABC ) 80° a=n+ma m B DE C :VLBSEBLJWFSJMFSFHÌSF m ( A%EB ) = aLBÀEFSFDFEJS m ( B%AD ) = m ( A%CB ) = m m ( D%AE ) = m ( E%AC ) = n I PMTVON+ 2n = 100° j a = m + n = 50°dir. A #JS Ð¿HFOEF CJS ÖRNEK 8 2a J¿B¿PSUBZJMFCJS Eõ B¿PSUBZO A \"#$Ð¿HFO I PMVõUVSEVóV EBS a nn % = m( % B¿OO ËM¿ÐTÐ m ( BAD ) DAC ) BC E m ( A%BE ) = m ( E%BC ) m (WA) 96° a = EJS % = 84° a m ( ADC ) 2 DC 84° m % = 96° #JS Ð¿HFOEF JLJ Eõ m m ( BEC ) I B¿PSUBZJMFCVB¿MB- B A SB LPNõV PMNBZBO B :VLBSEBLJWFSJMFSFHÌSF % =a LBÀEFSFDFEJS CJS J¿ B¿PSUBZ BZO m ( ACB ) OPLUBEBLFTJõJS % % % % C m ( BAD ) m ( DAC ) ABE m ( EBC ) = = n m ( ) = = m 2n + m = N+ n = N+ 3n = N+ n =PMVS a + 2m + 2n =PMEVôVOEBOa = 60°dir. 6. 85° 7. 50° 8. 60° 12

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 9 ÖRNEK 11 A \"#$Ð¿HFO E <#%>WF<$%>J¿ A 64° B¿PSUBZ 3x+5° a % = 64° m ( BAC ) D B C b i a b i b i x+10° b i B C :VLBSEBLJ WFSJMFSF HÌSF % ) = a kaç deSFDF- D m ( BDC EJS \"#$Ð¿HFOJOEF[ BD ]WF[ CD ]EõB¿PSUBZ # \" &dPó- I. Yol: 2b + 2i + 64° = 180° j b + i = 58° %% SVTBM m ( EAC ) = 3x + 5° m ( BDC ) = x + 10°EJS a + b + i = 180°j a = 122° dir. :VLBSEBLJ WFSJMFSF HÌSF m ( % ) =a LBÀ EFSFDF- BAC % EJS % m ( BAC ) 64 II. Yol: m ( BDC ) = 90° + = 90° + = 122° dir. 22 % % m ( BAC ) a m ( BDC ) = - Y+ 10° = 90° - 90° 22 a x = 80° - dir. a + 3x + 5° =PMEVôVOEBO 23a a + 240° - + 5° = 180° & a = 130° 2 ÖRNEK 10 A ÖRNEK 12 A ii 2x–10° D BC Ba C E \"#$Ð¿HFOJOEF [ AD ]WF[ CD ]J¿B¿PSUBZ 28° % m ( ADC ) = 2x - 10°EJS :VLBSEBLJ WFSJMFSF HÌSF Y JO BMBCJMFDFôJ FO CÑZÑL D WFFOLÑÀÑLUBNTBZEFôFSMFSJOJOUPQMBNLBÀEFSF- \"#$Ð¿HFOJOEF [ BD]WF[ CD]EõB¿PSUBZ DFEJS % m ( ADC ) % = 28° % m ( ABC ) m ( ADC ) = a = + % 90° 2 dir. :VLBSEBLi verilere gÌSF m ( ABC ) = a kaç dereDFEJS 0IBMEF< a < 180° j 90° < 2x - 10° < 180° j 100° < 2x < 100° j 50° < x < YJOEFSFDFDJOTJOEFO #JS ÑÀHFOEF JLJ Eö BÀPSUBZ JMF CV BÀMBSO LPNöV PMNB- BMBCJMFDFôJFOLÑÀÑLUBNTBZEFôFSJ FOCÑZÑLUBN ZBOCJSJÀBÀPSUBZBZOOPLUBEBLFTJöJS TBZEFôFSJEJS+ 94°= 145° dir. m ( B%AD ) = m ( D%AC ) m ( A%DC ) = m ( A%BC ) dir. a 2 28° = 2 j a = 56°dir. 9. 122° 10. 145° 13 11. 130° 12. 56°

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 13 ÖRNEK 14 A A \"#$Ð¿HFO D 50° [ AB] m [ DF] a F % m ( BAC ) = 50° a E B 40° |EC|å= |CD| 3a c ib b E c i 40° 40° B C CD \"#$ Ð¿HFOJOEF [ BD ] WF [ CE ] J¿ B¿PSUBZ [ CD ] Eõ :VLBSEBLJWFSJMFSFHÌSF m ( % ) = a kaç dereDFEJS ABD B¿PSUBZWFm ( % ) = 3.m ( % )EJS m ( A%EF ) = 40° &$%JLJ[LFOBSÑÀHFO BEC BDC %% :VLBSEBLJWFSJMFSFHÌSF % kaç dereDFEJS m ( CED ) = m ( CDE ) = 40° m ( BAC ) % = % = 3a PMTVOi + 2b = 180° %'#ÑÀHFOJOEF a = 50° dir. m ( BEC ) 3.m ( BDC ) i + b = 90° j 3a = 90° + a j a = 45°dir. c + i = 45° j 2c + 2i =PMEVôVOEBO m ( % ) = 90° ES BAC :BEBEJôFSCJSZPMMB m ( % ) = % = 2a = 90° dir. BAC 2.m ( BDC ) ÷LJ[LFOBSWF&öLFOBS·ÀHFO %m/*m öLJLFOBSV[VOMVóVFõJUPMBOÐ¿HFOFJLJ[LFOBS ÖRNEK 15 üçgen EFOJS 6[VOMVLMBS FõJU PMBO JLJ LFOBSO CJSMFõUJóJ LËõFOJO B¿TOB UFQF B¿T UFQF B¿- (FPNFUSJ EFSTJOEF ZBQMBO CJS FULJOMJL J¿JO BõBóEBLJ TOOLBSõTOEBLJLFOBSBUBCBOLFOBS UBCBO BENMBSJ[MFONJõUJS LFOBSJMFFõJUV[VOMVLUBLJLFOBSMBSOPMVõUVSEV- óVB¿MBSBUBCBOBÀMBSEFOJS A 5BCBOB¿MBSËM¿Ð- MFSJCJSCJSJOFFõJUUJS | | | | | |r \"#$Ð¿HFOJJ¿JOEF AD = DC = BC PMBDBLõF- % UFQFB¿T LJMEFCJS%OPLUBTJõBSFUMFOJZPS BAC |AB| = |AC| r 4F¿JMFO%OPLUBTJ¿JOm ( D%AB ) = 15° % ) = 60°EJS m ( DCB BC #VBENMBSJ[MFOFSFLZBQMBOÀJ[JNJÀJOm ( A%DC ) kaç EFSFDFEJS % ve % UBCBOB¿MBSm ( % ) = % A ABC ACB ABC m ( ACB ) A ¶¿ LFOBS V[VOMV- 15° óV EB CJSCJSJOF 15° D 60° FõJU PMBO Ð¿HFOF 60° 60° FöLFOBS ÑÀHFO C B EFOJS &õLFOBS % = 150° Ð¿HFOJO J¿ B¿MBS m ( ADC ) 60° 60° EJS BC 13. 90° 14 14. 50° 15. 150°

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 16 ÖRNEK 18 A \"#$Ð¿HFO A \"#$EJLÐ¿HFO 70° | AB | = | AC | D [AB] m [ AC] 60° D |BE| = |EC| bE |BD| = |BF| Ea i |FC| = |CE| m ( % ) = 70° 180°–2b b a i 180°–2i BAC B FC 50° a/2 a/2 m ( % ) = 60° :VLBSEBLJ WFSJMFSF HÌSF % = a LBÀ EFSFDF- ADB m ( DFE ) B C EJS :VLBSEBLJWFSJMFSFHÌSF % =a LBÀEFSFDFEJS m ( B%DF ) = m ( D%FB ) = b m ( % ) = % = i m ( DEC ) CEF m ( EFC ) %% a % % % = 180° - 2b m ( % ) = 180° - 2i m ( EBC ) = m ( ECB ) = ABC m ( ACB ) m ( ABC ) BCE 2 m ( ) = = 55° b + i = 135° j a + b + i = 180° j a = 45° dir. a 50° + = 55° & a = 10° dir. 2 ÖRNEK 17 ÖRNEK 19 A \"#$Ð¿HFOJOEFm (WB) = 105°, m (XC) = 60° a D; [ AB]Ð[FSJOEF &[ AC]Ð[FSJOEFTF¿JMFOOPLUBMBS 24° | | | | | |DE = EC = BC PMEVóVOBHËSF m(A%DE)BÀTLBÀ EFSFDFEJS a–24 a a–24 A [&#]ÀJ[JMJSTF &%$FöLFOBS B D C 15° ÑÀHFOPMVS % 135° BAD D |DE| = |#&| | | | | | |\"#$Ð¿HFO AB= = m ) = 24° 45° AC DC ( m ( D%BE ) = m ( E%DB ) = 45° E m ( A%DE ) = 135° dir. 60° :VLBSEBLJWFSJMFSFHÌSF m ( D%AC ) = a kaç dereDF- EJS 45° 60° % = % = a m ( % ) = % = a - 24° 60° m ( DAC ) m ( ADC ) ABC m ( ACB ) B C 3a - 24° = 180° j 3a = 204° j a = 68°dir. 16. 10° 17. 68° 15 18. 45° 19. 135°

TEST - 5 ·ÀHFOEF\"À 1. B 4. A 50° 5x 2x C 80° F 3x 4x D x 3x EK ôFLJMEF m ( % ) = 50° m ( % ) = 80° :VLBSEBLJZME[MöFLJMEFWFSJMFOBÀÌMÀÑMFSJOF ABE CDF HÌSF aLBÀEFSFDFE JS % = % = m ( D%AE )EJS \" # $ % & m ( BAC ) m ( CAD ) A 5. :VLBSEBLJWFSJMFSFHÌSF m ( D%EK ) = x kaç de- SFDFEJS \" # $ % & 92° B E 48° C 2. A [ AE ] m [ DC ] D B [ DF ]WF[ AF ] D 50° B¿PSUBZMBS E 40° % = 40° [ AB ] // [$% m ( % ) = m ( % ) m ( % ) = 92° m ( ACD ) BAE EAC AEC C % = 50° m ( B%CD ) = 48° m ( AED ) F % :VLBSEBLJ WFSJMFSF HÌSF m ( ACB ) = a kaç de- % SFDFEJS AFD :VLBSEBLJWFSJMFSFHÌSF m ( ) = a kaç dere- \" # $ % & DFEJS \" # $ % & 6. A 68° 3. B [ AB ] m [ KE ] FK F E A [ CD ] m [ FH ] E 2x–20° m ( B%FH ) = 2x - 20° D m ( E%KD ) = x + 50° x BC G \"#$Ð¿HFOJOEF [ FC ] m [ AB ] [ BK ]åm [ AC ]å x+50° % = 68° m ( E%BD ) = % m ( BAC ) m ( DBC ) C HK D % = % m ( ECD ) m ( DCB ) :VLBSEBLJ WFSJMFSF HÌSF % = a kaç de- :VLBSEBLJWFSJMFSFHÌSF % = x kaç dere- m ( EGH ) m ( BDC ) SFDFEJS DFEJS \" # $ % & \" # $ % & 1. A 2. # 3. C 16 4. # 5. A 6. E

·ÀHFOEF\"À TEST - 6 1. A % ) = % 4. A m ( DBE m ( FBE ) 50° % = % m ( DCE ) m ( ECG ) D B 120° % ) = 50° m ( FAG C % m ( BDC ) = 120° 70° 2a D HC F G a E B % \"#$Ð¿HFOJOEF [ AD ]J¿B¿PSUBZ [ AH ] m [ BC ] :VLBSEBLJ WFSJMFSF HÌSF m ( BEC ) = a kaç de- SFDFEJS %% m ( ADC ) = 70° m ( ACB ) = 2a \" # $ % & :VLBSEBLJ WFSJMFSF HÌSF m ( A%BC ) = a kaç de- SFDFEJS \" # $ % & 2. A 120° D [ AE ] m[ AB ] E 70° [ ED ] m[ DC ] B m ( A%ED ) = 120° 5. K \"#$Ð¿HFOJOEF AD % = 70° B <#%>J¿B¿PSUBZ m ( ABC ) 38° C CM [ CD ]EõB¿PSUBZES % % = 38° DCB m ( BDC ) :VLBSEBLJWFSJMFSFHÌSF m ( ) = a kaç de- SFDFEJS \" # $ % & :VLBSEBLJWFSJMFSFHÌSF m ( K%AD ) = a kaç de- SFDFEJS 3. %\"#$Ð¿HFOJOJOEõB¿PSUBZMBSOOLFTJNOPLUBT \" # $ % & & #%$ Ð¿HFOJOJO J¿ B¿PSUBZMBSOO LFTJN OPLUBT WFm ( % ) = 20°EJS 6. F BAC A a+70° A 20° BC E a Da E BC D \"#$Ð¿HFOJOEF [#&WF[ CD ]J¿B¿PSUBZ % %% m ( BEC ) m ( FAC ) = a + 70° WF m ( CDE ) = aES :VLBSEBLJ WFSJMFSF HÌSF = a kaç de- % BDC SFDFEJS :VLBSEBLJWFSJMFSFHÌSF m ( ) LBÀEFSFDFEJS \" # $ % & \" # $ % & 1. E 2. # 3. A 17 4. E 5. # 6. C

TEST - 7 ·ÀHFOEF\"À 1. A \"#$Ð¿HFO 4. A |AB| = |AD| = |DC| m ( B%AC ) = 72° B DC 40° d BD C :VLBSEBLJ WFSJMFSF HÌSF m ( D%AC ) = a kaç de- SFDFEJS | | | |[ AB ]E [ AC ] mE AD = % \" # $ % & AC m ( ABC ) = 40° :VLBSEBLJ WFSJMFSF HÌSF m ( % ) LBÀ EFSFDF- BAD EJS \" # $ % & 2. A D 81° 5. A \"#$Ð¿HFO 100° EB C B |AB| = |AD| E \"#$Ð¿HFOJOEF & # $EPóSVTBM m ( % ) = 81° |BE| = |ED| ABE |AB| = |BD| = |DC| EJS D % = 100° m ( BAC ) 130° :VLBSEBLJ WFSJMFSF HÌSF m ( % ) kaç EFSFDF- x % = 130° ADB C m ( EDC ) EJS :VLBSEBLJWFSJMFSFHÌSF Y LBÀEFSFDFEJS \" # $ % & \" # $ % & 3. A DE 6. A \"#$Ð¿HFO D |AD| = |DE| E 70° a % = 35° B C m ( DFB ) m ( A%CB ) = 80° | | | | | |\"#$Ð¿HFO [ DE ] // [ BC ] AD = AE = DC 80° 35° B CF % = 70°EJS m ( ABC ) :VLBSEBLJWFSJMFSFHÌSF m ( A%BF ) = a kaç dere- DFEJS % :VLBSEBLJ WFSJMFSF HÌSF m ( DCB ) = a kaç de- SFDFEJS \" # $ % & \" # $ % & 1. D 2. C 3. C 18 4. # 5. C 6. D

·ÀHFOEF\"À \"#$Ð¿HFO TEST - 8 1. A |AE| = |DE| 4. ö[DJMJLLBNQOEBJ[DJMFSFQVTVMBZOBTMLVMMBOBDBL- |EF| = |EC| D MBS ËóSFUJMNFLUFEJS ¶¿ GBSLM OPLUBZB LVSVMBDBL E LBNQMBSEBOCJSCJSMFSJOFHJEFSLFOQVTVMBMBSOOBTM LVMMBONBMBSHFSFLUJóJËóSFUJMJSLFOCJSLºóEBLBNQ- x F C MBSO ZBQMBDBó ZFSMFS \" # $ JMF JTJNMFOEJSJMJQ \"# B LFOBS#$LFOBSOBFõJUPMBOCJS\"#$Ð¿HFOJOLËõF OPLUBMBSPMBSBLõFLJMEFLJHJCJJõBSFUMFOJZPS :VLBSEBLJWFSJMFSFHÌSF aOOYUÑSÑOEFOFöJ- UJBöBôEBLJMFSEFOIBOHJTJEJS B \" +Y # -Y $ + x A C % -Y & + 2x 2. (FPNFUSJ EFSTJOEF &SFO ±óSFUNFO ZBQUó FULJO- \"EBO#ZFHJEFSLFOWF#EFO$ZFHJEFSMFSLFOQV- TVMBOO LV[FZJ HËTUFSFO JCSFTJ JMF J[MFEJóJ ZPM BSB- MJLUF BõBóEBLJ BENMBS J[MFZFSFL HFPNFUSJL ¿J[JN TOEBLJB¿ZCJSLºóEBBõBóEBLJHJCJ¿J[NJõMFSEJS ZBQUSZPS r m ( B%AC ) = 120°PMBDBLõFLJMEF\"#$Ð¿HFOJ¿J- [JQCVÐ¿HFOJOJ¿B¿PSUBZMBSO¿J[JOJ[ B 80° r m ( % )B¿TOOB¿PSUBZ#$ZJ%OPLUBTOEB Kuzey C BAC 130° A LFTJZPS Kuzey B % r m ( ABC )B¿TOOB¿PSUBZ\"$ZJ&OPLUBTOEB LFTJZPS r m ( % )B¿TOOB¿PSUBZ\"#ZJ'OPLUBTOEB ACB LFTJZPS #VOBHÌSF m ( F%DE )BÀTLBÀEFSFDFEJS \" # $ % & &óJUJN BMBO J[DJMFSEFO JTF $ EFO \" ZB HJUNFL J¿JO QVTVMBMBSOOHËTUFSFDFóJEVSVNVLºóEB¿J[NFMF- SJOJJTUFNJõMFSEJS 3. 4FMJN B¿ËM¿FS LVMMBOBSBL õFLJMEFLJ Ð¿HFOJO JLJ J¿ #VOBHÌSF QVTVMBOOEPôSVHÌTUFSJNJBöBôEB- LJMFSEFOIBOHJTJEJS B¿TOOËM¿ÐTÐOÐIBUBT[PMBSBLËM¿ÐZPS A) A 5°K B) A 10°K C) A 25° K CCC D) A 30° E) A 50° K K #VOBHÌSF CVÑÀHFOJOEJôFSJÀBÀTLBÀEFSF- CC DFEJS \" # $ % & 1. D 2. C 3. E 19 4. C

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr \"¦*,&/\"3#\"ó*/5*-\"3* \"#$Ð¿HFO m (WA ) = 95°WF %m/*m ÖRNEK 3 |AC| > |AB| #JS Ð¿HFOEF CÐZÐL B¿OO LBSõTOEBLJ LFOBS A V[VOMVóV EJóFS LFOBS V[VOMVLMBSOEBO CÐZÐL- UÐS%PMBZTZMBCÐZÐLLFOBSOLBSõTOEBLJB¿- 95° OOËM¿ÐTÐEFEJóFSMFSJOEFOCÐZÐLUÐS ÖRNEK 1 BC A :VLBSEBLJ WFSJMFSF HÌSF $ BÀTOO FO CÑZÑL tam TBZEFôFSJLBÀEFSFDFEJS 40° 10° d a 90° D % % e c m ( ABC ) m ( ACB ) |AC| > |\"#| j > dir. 65° 80° m % + % = 85° B 75° ( ABC ) m ( ACB ) bC m ( A%CB ) OJO EFSFDF DJOTJOEFO BMBCJMFDFôJ FO CÑZÑL :VLBSEBLJ ÑÀHFOMFS BÀMBSB VZHVO PMBSBL ÀJ[JMTFZEJ UBNTBZEFôFSJEJS FOV[VOLFOBSIBOHJLFOBSPMVSEV \"$% ÑÀHFOJOEF FO V[VO LFOBS \"$ LFOBS \"#$ ÑÀHF- OJOEFFOV[VOLFOBS\"#LFOBSES D< d <F C< e < a ÖRNEK 4 A ÖRNEK 2 3 a D \"#$Ð¿HFOJOEFWFSJMFOJ¿B¿MBSBWFLFOBSMBSBHËSF A d 13 3a 86 cb be c B 4E 8C 4a a 2a | | | |\"#$WF#%&Ð¿HFOMFSJOEF AD =DN BD =DN B C | | | | | | | |AC =DN BE =DN DE =DN EC =DN | | | | | |C-D + D- a + a -C ifBEFTJOJOFöJUJOJCVMVOV[ :VLBSEBWFSJMFOMFSFHÌSF \"#$WF#%&ÑÀHFOMFSJOJO JÀBÀMBSOEBOFOCÑZÑLPMBOIBOHJTJEJS 4a > 3a > 2a j b > a >D \"#$ÑÀHFOJOEF C> a >D |b -D| + |D- a| + |a - b| = b -D-D+ a - a + b #%&ÑÀHFOJOEFF> b >EPMEVôVOEBO m ( D%EB ) PMVS = 2b -D 1. \"#2. CmD 20 3. 42° 4. m ( D%EB )

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ·ÀHFO&öJUTJ[MJôJ ÖRNEK 7 D Y Z`;PMNBLÑ[FSF %m/*m A6 x + Z UPQMBNOO FO #JSÐ¿HFOEFIFSIBOHJCJSLFOBSOV[VOMVóVEJóFS 10 y küçük ve FO CÑZÑL JLJLFOBSOV[VOMVLMBSUPQMBNOEBOLÐ¿ÐLUÐS x UBN TBZ EFôFSMFSJ #JS Ð¿HFOEF IFSIBOHJ JLJ LFOBSO V[VOMVLMBS LBÀUS GBSLOONVUMBLEFóFSJÐ¿ÐODÐLFOBSOV[VOMV- óVOEBOLÐ¿ÐLUÐS B8 C #JSÐ¿HFOJOLFOBSV[VOMVLMBSB C DPMNBLÐ[F- SF | |a -C <D< a +CEJS ÖRNEK 5 3x – 2 \"#$Ð¿HFO 10 - 6 < x < 10 + 6 j 4 < x < 16 YJOFOLÑÀÑLUBNTBZEFôFSJ A | |AB =DN YJOFOCÑZÑLUBNTBZEFôFSJ | |BC =DN 10 - 8 <Z< 10 + 8 j 2 <Z< 18 7 | |AC = 3x -DN ZOJOFOLÑÀÑLUBNTBZEFôFSJ ZOJOFOCÑZÑLUBNTBZEFôFSJEJS x +ZOJOFOLÑÀÑLEFôFSJ FOCÑZÑLEFôFSJEJS B 6C :VLBSEBLJ WFSJMFSF HÌSF x in alabilFDFôJ UBN TBZ EFôFSMFSJOJOUPQMBNLBÀUS 1 < 3x - 2 < 13 ÖRNEK 8 3 < 3x < 15 1<x<5 D 5 YJOBMBCJMFDFôJEFôFSMFSUPQMBNEVS 2 AC ÖRNEK 6 37 A B y | | | |õFLJMEFWFSJMFOMFSFHÌSF AC + #% UPQMBNOOBMB- 7 9D CJMFDFôJFOCÑZÑLWFFOLÑÀÑLUBNTBZEFôFSMFSJOJO 5 GBSLLBÀUS Bx C | |\"#%ÑÀHFOJOEF- 2 < %# < 3 + 2 | |%#$ÑÀHFOJOEF- 5 < %# < 5 + 7 õFLJMEFWFSJMFOMFSFHÌSF Y+ZUPQMBNOOBMBCJMFDF- | |0IBMEF< %# < 5 ôJFOCÑZÑLWFFOLÑÀÑLUBNTBZEFôFSMFSJLBÀUS | |\"#$ÑÀHFOJOEF- 3 < AC < 7 + 3 | |ADC üçgeninde 5 - 2 < AC < 5 + 2 9 - 7 < x < 9 + < x < 16 | |0IBMEF< AC < 7 9 - 5 <Z< 9 + <Z< 14 6 < |AC| + |%#| < 12 6 < x +Z< 30 x +ZOJOFOLÑÀÑLUBNTBZEFôFSJ 11 - 7 = 4 tür. x +ZOJOFOCÑZÑLUBNTBZEFôFSJEVS 5. 9 6. \\ ^ 21 7. \\ ^ 8. 4

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 9 ÖRNEK 11 D \"#$%CJSEËSUHFO A \"#$Ð¿HFO 11 a3 | |DC =CS % % C | |BC =CS m( BAC ) = m ( DBC ) 9 | |AB =CS a+b D | |AB =DN 6 | |AD =DN a | |BD =YDN B b A7 B C | |:VLBSEBLJ WFSJMFSF HÌSF AD UBN TBZ PMBSBL :VLBSEBLJ WFSJMFSF HÌSF Y JO BMBCJMFDFôJ UBN TBZ EFôFSMFSJUPQMBNLBÀUS en çokLBÀCJSJNPMBCJMJS ·ÀHFOFöJUTJ[MJôJOEFO | |11 - 9 < #% < 11 + 9 6-3<x<6+3 2 < |#%| < 20 3 < x <PMVS |AD| < |\"#| + |%#| \"ZSDB\"#%ÑÀHFOJOEFa + b > a PMEVôVOEBOY<ES |AD| < 27 0IBMEF< x <ES | |AD OOFOCÑZÑLUBNTBZEFôFSJES x ` { } + 5 =EVS ÖRNEK 10 ÖRNEK 12 \"#$Ð¿HFO ±OZÐ[ÐTBS BSLBZÐ[ÐNBWJSFOLMJPMBOÐ¿HFOCJ¿JNJO- A | |AC =DN EFLJ\"#$LºóEõFLJMEFHËTUFSJMNJõUJS#VLºóU#LË- | |AB = ( 2x + DN õFTJ \"LËõFTJOJOÐ[FSJOFHFMFDFLCJ¿JNEFõFLJMEFLJHJ- 2x+1 | |BC = ( 3x + DN CJLBUMBONõUS AA 75° 6 E 40° 65° B D C B 3x+2 C B C ôFLJM | |:VLBSEBLJWFSJMFSFHÌSF \"# OJOBMBCJMFDFôJFOCÑ- ôFLJM ZÑLWFFOLÑÀÑLUBNTBZEFôFSMFSJOJOUPQMBNLBÀ- | | | | | |#VOB HÌSF AC AE ve #% V[VOMVLMBSOO EPôSV US TSBMBOöOCVMVOV[ ·ÀHFOFöJUTJ[MJôJOEFO A (3x + 2) - (2x + 1) < 6 < (3x + 2) + (2x + 1) 40° 35° x + 1 < 6 < 5x + 3 E 3 40° 50° 65° <x<5 B 80° C 5 11 D < 2x + 1 < 11 |#%| = |DA| |ED|< |AE| < |AD| < |AC| 5 |AE| < |AD| < |AC| j |AE| < |#%|< |AC| 3 + 10 =PMVS 9. 26 10. ]\"&]]#%]]\"$] 22 11. 9 12. 13

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 13 ÖRNEK 15 \"#$WF\"%&Ð¿HFO [DE] // [BC] IOPLUBT\"%$Ð¿HF- A | |OJOJOJ¿B¿PSUBZMBSOOLFTJNOPLUBT BC =DNEJS 2x – 5 x –1 A B 9C ac :VLBSEB\"#$Ð¿HFOJWFLFOBSV[VOMVLMBSWFSJMNJõUJS D b Id E \"#$JLJ[LFOBSCJSÑÀHFOPMEVôVOBHÌSF YJOBMBCJ- bd MFDFôJEFôFSMFSUPQMBNLBÀUS B 11 C | | | | | | | |·ÀHFOJLJ[LFOBSJTF \"# = AC ZBEB AC = #$ ZBEB :VLBSEBLJWFSJMFSFHÌSF \"%&ÑÀHFOJOJOÀFWSFTJUBN |\"#| = |#$| olabilir. TBZPMBSBLFOÀPLLBÀDNEJS \"ODBLCVFöJUMJLMFSÑÀHFOFöJUTJ[MJôJOJTBôMBNBMES | | | |\"#$ÑÀHFOJOEF [#$]< \"# + AC | | | |\"# = AC j 2x - 5 = x - 1 j x =PMVS 11 < a + b +D+ d | | | | | |\"ODBLY= 4 için \"# + AC < #$ PMEVôVOEBOCVEF- \"%&ÑÀHFOJOJOÀFWSFTJB+ b +D+EPMEVôVOBHÌSF \"%&ÑÀHFOJOJOÀFWSFTJFOB[DNEJS ôFSBMOBNB[ | | | |\"# = #$ j 2x - 5 = 9 j x =PMVS | | | |·ÀHFOFöJUTJ[MJôJOJTBôMBS #$ = AC j x - 1 = 9 x =PMVS·ÀHFOFöJUTJ[MJôJOJTBôMBS0IBMEFYJOBMB- CJMFDFôJEFôFSMFSUPQMBN+ 7 = 17 dir. ÖRNEK 14 %m/*m b B C DUBNTBZPMNBLÐ[FSF #JS\"#$Ð¿HFOJOEF \"#$Ð¿HFOJOJOLFOBSV[VOMVLMBSBDN CDNWFDDNEJS A a2 - b2 =PMEVôVOBHÌSF \"#$ÑÀHFOJOJOÀFWSFTJ FOÀPLLBÀDNPMBCJMJS c a2 - b2 = 13 B aC (a - b) (a + b) = 13 tür. a + b = 13 m (WA) = 90°JLFOa = b2 + c2 ·ÀHFOFöJUTJ[MJôJOEFOD< a + b 1JTBHPSUFPSFNJ D< 13 tür. ¦FWSF \"#$ OJOFOCÑZÑLEFôFSJ | |m (WA) < 90°JTF C- D < a < b2 + c2 13 + 12 =DNEJS m (WA) > 90°JTF b2 + c2 < a < b + c EJS 13. 17 14. 25 23 15. 12

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 16 %m/*m A A \"#$Ð¿HFO 6 | |8 AB =DN cb B ha nA Va | |AC =DNWF m (WA ) 2 90° C B HN D C | |:VLBSEBLJ WFSJMFSF HÌSF #$ OJO BMBCJMFDFôJ LBÀ a GBSLMUBNTBZEFôFSJWBSES ¥FõJULFOBSCJS\"#$Ð¿HFOJOEFIa BLFOBS- OBBJUZÐLTFLMJLOA \"B¿TOBBJUB¿PSUBZ 7a | |#$ =YDNPMTVO BLFOBSOBBJULFOBSPSUBZPMNBLÐ[FSF m (XA) > 90°PMEVôVOEBO Ia < nA < Va Ib < n# < Vb 2 + 2 < x < 8 + 6 ID < nC < VD EJS 8 6 #JS\"#$Ð¿HFOJOEFBCDJTF 10 < x < 14 IaIbID nA > n# > nC x ` { ^ Va > Vb > VD EJS | |#$ OJOBMBCJMFDFôJGBSLMEFôFSWBSES ÖRNEK 17 ÖRNEK 18 x A A \"#$Ð¿HFO 10 5 | AD | = | AC | =DN B HN DC | |BD =DN 5 ba a | | | |\"#$¿FõJULFOBSÐ¿HFO <\")>m <#$> BD = DC C B3 D % NAC | |% = ) = m ( BAN ) m ( AN | |:VLBSEBLJWFSJMFSFHÌSF \"# =YJOBMBCJMFDFôJUBN | | | |AH = ( x + DN AD = ( 3x - DN TBZEFôFSMFSJOJOUPQMBNLBÀUS :VLBSEB WFSJMFOMFSF HÌSF Y JO BMBCJMFDFôJ UBN TBZ EFôFSMFSJUPQMBNLBÀUS a < b > 90° \"#$ÑÀHFOJOEF#$LFOBSOBBJUZÑLTFLMJL BÀPSUBZWFLF- 34 < x < 8 OBSPSUBZBSBTOEBIa< n < VaTSBMBNBTWBSES x ` { ^ A YJOBMBCJMFDFôJUBNTBZEFôFSMFSJUPQMBN Ia < nA jY Y 16 nA< Va j 10 < 3x - 3 < x PMVS OIBMEFYJOCVMVOEVôVFOLÑÀÑLUBNTBZBSBMô 16 < x < 8 inBMBCJMFDFôJUBNTBZEFôFSMFSUPQMBNUÑS 3 16. 3 17. 13 24 18. 13

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 19 ÖRNEK 20 \"#$Ð¿HFO V\"[#V$OMV¿FóõVJ UL\"F$OBLSFOÐB¿HSFOOBJOBEJUFZ Ð#LT$FLLMFJóOJBOSVO[BVOBMJVUóLVFOWBFSPA%SCUBBZ A | |AB =DN B¿TOOJ¿B¿PSUBZV[VOMVóVCJSCJSMFSJOFFõJUUJS #VOB HÌSF ÑÀHFOJO JÀ BÀMBS BSBTOEBLJ TSBMBOö- 4 x | |BC =DNWF OCVMVOV[ m ( % ) 1 60° ABC B6 C \"#$ÑÀHFOJOEF7a=Ib = nC dir. | |:VLBSEBLJWFSJMFSFHÌSF AC =YJOBMBCJMFDFôJLBÀ ¦FöJULFOBSÑÀHFOJOEF GBSLMUBNTBZEFôFSJWBSES Ia < na < Va Ib < nb < Vb ·ÀHFOFöJUTJ[MJôJOEFO ID < nD < VDTSBMBNBTWBSES 6-4<x<6+4 0IBMEF 2 < x < 10 (I) \"ZSDBLPTJOÑTUFPSFNJOEFOm (XB) < 60°PMEVôVOEBO Va=Ibj Va < Vb j a > b x2< 42 + 62 -DPT Va= nDj Va < VD j a >D x2< 16 + 36 - 24 Ib = nDj nD < nb jD> b x2< 28 j x < 2 7 PMVS ** a >D>CPMVS 0IBMEF*WF**FöJUTJ[MJLMFSEF< x < 2 7 ES x ` { }YJOBMBCJMFDFôJEFôFSWBSES 6[VOLFOBSLBSöTOEBCÑZÑLBÀPMBDBôOEBO % > m % > m ( % ) PMVS m ( BAC ) ( ACB ) ABC ÖRNEK 21 \"#$Ð¿HFO A | |AB =DN | |AC =DN 6 % 16 E m ( BAC ) > 90° x |BD| = |DC| 86 B DC | |:VLBSEBLJWFSJMFSFHÌSF AD =YJOBMBCJMFDFôJLBÀ GBSLMUBNTBZEFôFSJWBSES ,PTJOÑT5FPSFNJ [DE][\"#]ÀJ[FMJN %m/*m AB ,FOBSV[VOMVLMBSB C DPMBOCJS\"#$Ð¿HFOJO- |DE| = 2 |AE| = |EC| EF a2 =C2 +D2 -CDDPT\" m ( A%ED ) < 90° C2 = a2+D2 -BDDPT# 2 < x < 14 (I) D2 = a2 +C2 -BCDPT$ 2<x< 6 2 + 2 (II) 8 2 < x <PMVS *WF**FöJUMJLUFOYJOBMBCJMFDFôJEFôFSJWBSES %%% 25 20. 3 21. 7 19. m ( BAC ) > m ( ACB ) > m ( ABC )

TEST - 9 \"À,FOBS#BôOUMBS 1. A \"#$Ð¿HFO 4. #JS\"#$ÑÀHFOJOJOÑÀLFOBSV[VOMVLMBSDN % DNWF Y+ DNPMEVôVOBHÌSF YJOBMBCJ- m ( ABC ) = 50° MFDFôJLBÀUBNTBZEFôFSJWBSES c b % = 60° m ( ACB ) | |BC =BDN \" # $ % & | |AC =CDN 50° a 60° | |AB =DDN B C :VLBSEBLJWFSJMFSFHÌSF | a |-C + | |C-D + | C+D- a | 5. A UPQMBNOOEFôFSJBöBôEakilerden IBOHJTJEJS 24° 18° zy A) a +C # C $ D-C % D-C & B-C+D 66° BD x E C 2. A | |AB =DN \"#$Ð¿HFOJOEF m ( % ) = 62° m ( % ) = 66° BAC ABC 4 3 % = 24° m ( % ) = 18°EJS B6 | |D BC =DN m ( BEC ) EAC | |CD =DN :VLBSEBLJWFSJMFSFHÌSF Y Z [V[VOMVLMBSJÀJO | |2 AD =DN BöBôEBLJMFSEFOIBOHJTJEPôSVEVS C A) x >Z>[ # Y>[>Z $ Z> x >[ % Z>[>Y & [> x >Z :VLBSEBLJWFSJMFSFHÌSF \"#$ÑÀHFOJOJOÀFWSF- TJOJOFOCÑZÑLUBNTBZEFôFSJLBÀUS \" # $ % & 3. A 6. A 5 13 B z y D 12 y x–5 x+4 50° 65° C B D xC \"#$Ð¿HFOJOEF m ( % ) = 50° m ( % ) = 65° | |\"#$%EËSUHFO YUBNTBZ AB =DN ABC ACB | | | | | |AD =DN AC =DN DC = ( x + DN | |CB = ( x - DN | | | | | | | |AD = AC =ZDN AB =[DN DC =YDN :VLBSEBLJ WFSJMFSF HÌSF \"#$% EÌSUHFOJOJO :VLBSEBLJ WFSJMFSF HÌSF Y Z [ BSBTOEBLJ T ÀFWSFTJFOÀPLLBÀDNEJS SBMBNBBöBôEBLJMFSEFOIBOH JTJEJS \" # $ % & A) x <Z<[ # Y<[<Z $ Z< x <[ % [< x <Z & [<Z< x 1. D 2. C 3. A 26 4. C 5. D 6. #

\"À,FOBS#BôOUMBS TEST - 10 1. #JS\"#$Ð¿HFOJOEF m ( % ) > m( % ) 4. ,FOBS V[VOMVLMBS WF Y DN PMBO CJS BAC ABC EÌSUHFOEFYJOBMBCJMFDFôJFOCÑZÑL ve en kü- | | | |AB =DN AC = ( 4x + DNWF çükUBNTBZEFôFSMFSJUPQMBNLBÀUS | |BC = ( 5x - DNEJS \" # $ % & :VLBSEBLJ WFSJMFSF HÌSF Y JO BMBCJMFDFôJ LBÀ UBNTBZEFôFSJWBSES \" # $ % & 5. A 2. A \"#$Ð¿HFO x 7 [AN]B¿PSUBZ | |AN =DN B3 D C 8 % % ABC DAC | |NC =DN | |\"#$Ð¿HFO m ( = ( ) =DN ) m AD | |B N 5 C AC =YDN | | | |BD =DN AB =YDN :VLBSEBLJ WFSJMFSF HÌSF Y JO BMBCJMFDFôJ UBN TBZEFôFSMFSJUPQMBNLBÀUS :VLBSEBLJWFSJMFSFHÌSF YJOEFôFSJBöBôEBLJ- MFSEFOIBOHJTJPMBCJMJS \" # $ % & \" # $ % & 3. A 4 6. \"õBóEBLJBENMBSJ[MFOFSFLCJSÐ¿HFO¿J[JNJZBQM- 6 ZPS D5 r ,ºóEOÐ[FSJOEFCJS\"OPLUBTJõBSFUMFOJZPS B aC r \"OPLUBTJMFBSBTOEBLJV[BLMóDNPMBOCJS % \"#$ Ð¿HFOJ J¿JOEF IFSIBOHJ CJS OPLUB PMNBL #OPLUBTJõBSFUMFOJZPS | | | | | |Ð[FSF AB = 6 DN AD =DN DC =DNEJS | |:VLBSEBLJ WFSJMFSF HÌSF #$ = B OO BMBCJ r m % = 92°PMBDBLõFLJMEF$OPLUBTCFMJSMF- ( BAC ) MFDFôJFOLÑÀÑLUBNTBZEFô FSJLBÀDNEJS A) 2 B) 3 C) 4 D) 5 E) 6 | |OJZPS AC =DN \" #WF$OPLUBMBSJMFÑÀHFOPMVöUVSVMBCJMEJôJ- | |OFHÌSF #$ V[VOMVôVOVOBMBCJMFDFôJLBÀEF- ôFSWBSES \" # $ % & 1. # 2. # 3. C 27 4. # 5. D 6. A

TEST - 11 \"À,FOBS#BôOUMBS 1. \"öBôEBLJTFÀFOFLMFSEFOIBOHJTJZBEBIBOHJ 4. MFSJOEFLJÌMÀÑMFSWFSJMEJôJOEFCJS\"#$ÑÀHFOJÀJ- A [JMFCJMJS x * a =DN C=DN D=DN D 6 3 ** a =DN C=DN Ia =DN *** a =DN m^ XC h= 30° B 11 C *7 C=DN D=DN m^ WB h = 45° c = 4 2 cm | |\"#$Ð¿HFOJOEF m ( B%AC ) > 90° AC =DN | | | |BC =DN BD =DN \" :BMO[* # :BMO[*7 $ *WF** | |:VLBSEBLJWFSJMFSFHÌSF AD = YJOBMBCJMFDFôJ % **WF*** & *WF*7 LBÀGBSLMUBNTBZEFô FSJWBSES \" # $ % & 2. A 5. Ahmet A i B6 C Ceren Eren | | | |\"#$Ð¿HFOJOEF BC =DN AB = 3 2 DNWF m % = i ES BC (ACB) 0LVM CBI¿FTJOF ¿J[JMNJõ EBS B¿M \"#$ Ð¿HFOJOEF \"#$ÑÀHFOJOJOÀJ[JNJOJZBQBOCJSÌôSFODJ\"$# \"INFU \" LËõFTJOEF $FSFO $ LËõFTJOEF &SFO # BÀTOOÌMÀÑTÑOÑFOGB[MBLBÀEFSFDFÀJ[FCJMJS LËõFTJOEFEVSNBLUBES\"INFU $FSFOWF&SFOFO LTBZPMEBOLBSõMBSOEBEVSBOLFOBSBEPóSVLPõB- \" # $ % & DBLMBSES&õJUI[MB\"INFUEL $FSFOELEBBMB- DBóNFTBGFZJLPõNBLUBES 3. A #VOB HÌSF &SFOhJO LPöNBT HFSFLFO NFTBGFZJ 8 BMEôTÑSFOJOLBÀGBSLMUBNTBZEFôFSJWBSES \" # $ % & B HND C 6. A \"#$Ð¿HFO \"#$CJS¿FõJULFOBSÐ¿HFO [ AH ] m[ BC ] 60° < m (WA) < 90° WF % % 55 BAN NAC ) | | | | | |BD= m ( ) = m( =DN | AB | = | AC | =DN DC AN EJS | | | |AH = ( x + DNWF AD = ( 3x - DNEJS Ba C :VLBSEBLJ WFSJMFSF HÌSF Y JO BMBCJMFDFôJ UBN | |:VLBSEBLJ WFSJMFSF HÌSF #$ = B OO BMBCJMF TBZEFôFSMFSJUPQMBNLBÀUS DFôJGBSLMUBNTBZEFôFSMFS JOJOUPQMBNLBÀUS \" # $ % & \" # $ % & 1. # 2. C 3. C 28 4. # 5. C 6. #

\"À,FOBS#BôOUMBS TEST - 12 1. A \"#$CJSÐ¿HFO 4. A | AE | å| EC | 8 10 duba 12 E % x m ( ABC ) > 120° \"ZõF Cem B C D | |AD =CS 2 16 | |DB =CS | |C B BC =CS | |:VLBSEBLJWFSJMFSFHÌSF DE = x JOBMBCJMFDF- 0UFMJO EBJSFTFM CJ¿JNEFLJ IBWV[VO \" OPLUBTOEB CVMVOBOJ¿FDFLTUBOEOB#OPLUBTOEBLJ\"ZõFhOJO ôJUBNTBZEFôFSMFSJOJOUPQMBNLBÀCSEJS | |V[BLMó AB =N $OPLUBTOEBCVMVOBO$FNhJO \" # $ % & | |V[BLMó AC = N JMF HËTUFSJMNJõUJS )BWV[VO NFSLF[JOEFJTFCJSEVCBCVMVONBLUBES \" # WF $ OPLUBMBS CJSMFöUJSJMNFTJZMF CJS ÑÀHFO PMVöUVSVMEVôVOBHÌSF \"ZöFJMF$FNBSBTOEBLJ V[BLMLLBÀGBSLMUBNTBZEFôFSJBMBCJMJS 2. \"#$WF\"$%CJSFSÐ¿HFO[ AD ]WF[ CD ]EõB¿PS- \" # $ % & K | | | | | |UBZ AC =DN CD =DNWF AD =YDNEJS 5. A C x A D #BOLB 7 4 \"$ZPMVÐ[FSJOEFCVMVOBO#BOLBCVZPMJMFB¿ BC ZBQBO [\", ZPMV Ð[FSJOEF CBOLBZB FõJU V[BLMLUB :VLBSEBLJ WFSJMFSF HÌSF Y JO BMBCJMFDFôJ UBN TBZEFôFSMFSJOJOUPQMBNLBÀUS PMBO WF CBOLBZMB V[BLMó UBN TBZ PMBDBL õFLJMEF \" # $ % & JLJUBOFBUNLVSNBLJ¿JOBSBõUSNBZBQZPS 3. A | |AC =NFUSFPMEVôVOBHÌSF CBOLBOOZBQ- 20 20 UôBSBöUSNBEBCBOLBZBFöJUV[BLMLUBPMBOCV JLJOPLUBZLBÀGBSLMöFLJMEFTFÀFCJMJS \" # $ % & 6. A \"#$Ð¿HFO BP C | |AB = 5 2 DN 24 \"#$ JLJ[LFOBS Ð¿HFO # JMF $ BSBTOEB EFóJõLFO 52 | |x BC =DN CJS1OPLUBTBMOZPS B % < 45° m ( ABC ) | | | | | |AB = AC =DN BC =DN 13 C | |:VLBSEBLJ WFSJMFSF HÌSF AP OJO BMBCJMFDFôJ | | :VLBSEBWFSJMFOMFSFHÌSF AC =YLBÀDNPMB- UBNTBZEFôFSMFSJOJOUPQMBNLBÀDNEJS CJMJS \" # $ % & \" # $ % & 1. D 2. D 3. A 29 4. # 5. C 6. A

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr %÷,·¦(&/* 1JTBHPS#BôOUT ÖRNEK 3 %m/*m A \"#$Ð¿HFO #JS EJL Ð¿HFOEF IJQPUFOÐT OJO LBSõTO- x a [AB] m [AC] EBLJLFOBS V[VOMVóVOVOLBSFTJ EJLLFOBSMBSO 63 V[VOMVLMBSOOLBSFMFSJOJOUPQMBNOBFõJUUJS(Pi- D |AD| = |DC| TBHPSUFPSFNJ a A a2 =C2 +D2 BD = 6 3 DN EJS | |B 18 C BC =DN c | |:VLBSEBLJWFSJMFSFHÌSF \"# =YLBÀDNEJS b B aC \"#%ÑÀHFOJOEF 2 = ^ 6 3 h2 - a2 x \"#$ÑÀHFOJOEFY2 = 182 - (2a)2 182 - (2a)2 = ^ 6 3 h2 - a2 ÖRNEK 1 a = 6 2 cm Y=DNEJS A \"#$%&CFõHFO 2 [ ED]åm [ CD] B 2 [ EC] m [ BC]å x C [ EB] m [ AB]å 2 | AB | = | BC | = | CD | =DN | |E 4 D DE =DN | |:VLBSEBLJWFSJMFSFHÌSF AE å=YLBÀDNEJS | | | | | |EC 2 = ED 2 + DC 2 = 16 + 4 = 20 ÖRNEK 4 | | | | | |&# 2 = EC 2 + #$ 2 = 20 + 4 = 24 | | | | | |AE 2 = &# 2 + AD 2 = 24 + 4 = 28 D 14 \"#$%EËSUHFO x | |AE = 2 7 DN [AD] m [ DC ] ÖRNEK 2 [AB] m [ BC ] A A 16 C \"#$Ð¿HFO | |AB =DN | |2 [ AD] m [ BC] BC =DN | |B DC =DN | |AD =YDN | |5 | |:VLBSEBLJWFSJMFSFHÌSF \"# =YLBÀDNEJS h 35 AB =DN mæY AC = 3 5 cm | | | | | |AC 2 = \"# 2 + #$ 2= 162+ 22 = 260 | | | | | |AC 2 = DC 2 + AD 2 = 142 + x2 | |B D x C BC =DN 9 x2+ 142 = 260 | |:VLBSEBLJWFSJMFSFHÌSF DC =YLBÀDNEJS x2 = Y=DNEJS I2= 52- (9 - x)2 jI2 = ^ 3 5 h2 - 2 x 52 - (9 - x)2 = ^ 3 5 h2 - x2 j 101 x = cm 18 1. 2 7 101 30 3. 6 4. 8 2. 18

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 5 ÖRNEK 7 A \"#$%EËSUHFO A \"#$Ð¿HFO 7 x [AC] m [BD] a #%$Ð¿HFO a 13 D [AE] m [ BC ] Bb d | |D AB =DN 2b 10 2 | |BC =DN 5 x | |AB =DN c 24 | |CD =DN Bc E | |BD = 5 2 DN 15 | |AD =YDN d | |C AC = 10 2 DN | |DC =YDN C | |:VLBSEBLJWFSJMFSFHÌSF AD =YLBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF DC =YLBÀDNEJS a2 + b2 = 72 (a + b)2 +D2 = 169 b2 +D2 = 152 b2 +D2 = 50 D2 + d2 = 242 (a + b)2 + d2 = 200 a2+ d2 = x2 b2+ d2 = x2 x2 + 152 = 72 + 242 j x =DNEJS 169 + x2 = 200 + 50 x2 = 81 j x =DN ÖRNEK 6 ÖRNEK 8 D \"#$%EËSUHFO A \" $ &OPLUBMBS [AB] m [BC] EPóSVTBMES [AD] m [DC] A6 20 [ AB ] m [ BD] a |AE| = |DC| E | DE | = | EC | =DN D [ DE ] m [ BD ] a6 BC | |AB =DN 4 DE =DN | |4 Bx C K 18 | |E BD =DN | |:VLBSEBLJWFSJMFSFHÌSF #$ =YLBÀDNEJS | |:VLBSEBWFSJMFOMFSFHÌSF AE =YLBÀDNEJS | |ADE üçgeninde AD 2 = a2- 36 |AE|2= |\",|2 + |,&|2 | | | | | |ADC üçgeninde AC 2 = AD 2 + DC 2 = a2 - 36 + 122 | |AE 2 = 242+ 182 | |\"#$ÑÀHFOJOEF AC 2 = a2+ x2 | |AE =DNEJS a2 + x2 = a2 - 36 + 122 j x = 6 3 DNEJS 5. 20 6. 6 3 31 7. 9 8. 30

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 9 # $ %EPóSVTBM ÖRNEK 11 A [ AB ] m [ BD ] :VTVG ±óSFUNFO ËóSFODJMFSJOEFO BõBóEBLJ BENMBS J[- MFZFSFL EFGUFSMFSJOF HFPNFUSJL ¿J[JN ZBQQ TPSVZV DF- 6 E WBQNBMBSOJTUJZPS BC [ ED ] m [ BD ] r [BA] m [AC]PMBDBLõFLJMEF\"#$EJLÐ¿HFOJOJO¿J[J- 3 K 40 . | |3 AB =DN OJ[ | |D ED =DN r [AB]Ð[FSJOEF\"WF#EFOGBSLMCJS,OPLUBT[AC] 3 Ð[FSJOEF\"WF$EFOGBSLMCJS-OPLUBTJõBSFUMFZJ- | |BD =DN OJ[ E' r [KC] [BL]WF[KL]ZJ¿J[JOJ[ | | | |:VLBSEBWFSJMFOMFSFHÌSF AC + CE UPQMBNFOB[ :BQMBO¿J[JNEF LBÀDNEJS | | | | | |KC =DN BL =DN BC =DN | |PMEVôVOBHÌSF ,- LBÀDNEJS &OPLUBTOO 0OPLUBTOBHÌSFTJNFUSJôJ&hPMTVO a A |\"&h| = |AC| + |CE| K b |\"&h|2 = |\",|2 + |,&h|2 L | |\"&h 2= 92+ 402 | |\"&h =DNEJS 12 10 B 15 C ÖRNEK 10 | |a2 + AC 2 = 102 | |+ b2 + \"# 2 = 122 D' 2 B+BbB2C + AC 2 + AB 2 = 244 A B B B2B2B5 B BB C aAB A 8 D a2 + b2 = 19 x K C' 4 ,-= 19 DNPMVS B' C B \"#$%EJLEËSUHFO \"OPLUBTTBCJULBMNBLõBSUJMFQP[J- UJG ZËOEF a EFSFDF EËOEÐSÐMFSFL \" #h $h %h EJLEËSUHFOJ | | | | | |FMEFFEJMNJõUJS AD =DN AB =DN DK =DN | |:VLBSEBLJWFSJMFSFHÌSF #h, LBÀDNEJS | |\", 2 = 82 + 12 | |\", 2 = 42 + x2 65 = 16 + x2 j x =DNEJS 9. 41 10. 7 32 11. 19

1JTBHPS#BôOUT TEST - 13 1. A 4. A \"#$%EËSUHFO x+8 32 m (WA) = m (XC) = 90° x–9 B I BC I = 4 3 cm 43 6 I IAB = 3 2 DN B x+9 C I IAD =DN I I\"#$CJSEJLÐ¿HFO AB = ( x - CS CD I I I IAC = ( x + CS BC = ( x + CSEJS I I:VLBSEBLJWFSJMFSFHÌSF \"# kaç biSJNEJS I I :VLBSEBLJWFSJMFSFHÌSF CD LBÀDNEJS A) 6 B) 2 3 C) 4 D) 3 3 E) 6 \" # $ % & 2. A \"#$Ð¿HFO 5. A \"#$Ð¿HFO H [ BH ] m [ AC ] 13 15 | |AB =DN | |AC =DN 10 | |AB =DN | |BC =DN 8 | |BC =DN | |BH =DN C B 14 C B 17 | | :VLBSEBLJWFSJMFSFHÌSF AC LBÀDNEJS :VLBSEBLJ WFSJMFSF HÌSF \" OPLUBTOO [#$] ZF \" # $ % & V[BLMôLBÀDNEJS \" # $ % & 3. A \"#$Ð¿HFO 6. A \"#$Ð¿HFO 13 [ AH ] m[ BC ] [AD] m [BC] I IAC =DN x 7 I IAC =DN I IHC =DN 5 I IEC =DN I IBH =DN E 2 C BD I IC BE =DN B4 H 12 I I:VLBSEBLJWFSJMFSFHÌSF \"# =YLBÀDNEJS I I:VLBSEBLJWFSJMFSFHÌSF \"# LBÀDNEJS A) 2 6 B) 5 C) 2 7 A) 3 B) 2 5 C) 6 D) 4 2 E) 6 D) 41 E) 4 15 1. D 2. # 3. D 33 4. A 5. E 6. C

TEST - 14 1JTBHPS#BôOUT 1. A \"#$Ð¿HFO 4. A \"#$EJLÐ¿HFO D |AB| = |AC| D IADI = ICDI x 5 I IBC =DN [ BD ] m [ AC ] I IBD =DN 2 | |DC =DN | |BC =DN B3 C B 12 C | | :VLBSEBLJWFSJMFSFHÌSF \"# =YLBÀDNEJS I I :VLBSEBLJWFSJMFSFHÌSF AC LBÀDNEJS 9 B) 11 C) 6 D) 13 & \" # 2 13 C) 6 13 A) 2 2 4 D) 13 6 E) 12 6 2. A \"#$Ð¿HFO 5. A \"#$%EËSUHFO [AC] m [BC] 4 [AC] m [BD] B 24 x | |12 AB =DN | |AB =DN | |D | |AC =DN H | |C BC = 5 DN B 83 D BD = 8 3 DN 5 5 | |CD =DN C | |AD =YDN I I:VLBSEBLJWFSJMFSFHÌSF DC LBÀDNEJS A) 2 3 B) 3 3 C) 6 D) 4 3 & | | :VLBSEBLJWFSJMFSFHÌSF AC =YLBÀDNEJS A) 3 3 B) 6 C) 3 5 D) 4 2 E) 4 5 3. A \"#$EJLÐ¿HFO 6. A BH [AB] m [AC] 4 [AH] m [BC] D x AB = 1 C AC 2 4 4 B E 2C BH | |\"#$Ð¿HFO [ ED ] m [ AB ] EC =DN | AD| = | DB | = | DE | =DNEJS :VLBSEBLJWFSJMFSFHÌSF PSBOLBÀUS | | :VLBSEBLJWFSJMFSFHÌSF AC =YLBÀDNEJS HC A) 1 B) 1 C) 1 D) 1 E) 1 \" # $ % & 5 2 2 3 4 1. A 2. D 3. E 34 4. C 5. # 6. #

1JTBHPS#BôOUT TEST - 15 1. A 6B 4. D \"#$%EËSUHFO 46 1 x+1 D A [AB] m [BC] C [AD] m [DC] 5 E |AD| = |AE| I I[AB] m [BC] [BC] m [CD] [CD] m [DE] AB =CS B2 E x C | |DC = 4 6 DN I I I I I IBC =CS CD = (x + CS DE =CS | |BE =DN \" JMF & OPLUBMBS BSBTOEBLJ V[BLML CS PMEV- | |:VLBSEBLJWFSJMFSFHÌSF EC =YLBÀDNEJS ôVOBHÌSF YLBÀUS A) 3 6 B) 4 3 C) 4 6 \" # $ % & % & 6 2 2. A \"#$ %&' WF ,-/ CJSFS EJL Ð¿- 5. A [ AC ] m d HFO D9 E [ BD ] m d 24 [BC] // [DE] B 6 I IAB =DN | |AC =DN 12 I IDC =DN I IKF =DN 3 B CK | |2 BD =DN 2F | |d 12 C E D CD =DN IL 5 N I DE =DN 5 | | | |E `{ d }PMNBLÐ[FSF AE + &# UPQMBNOO I I I I I IEF = KL =DN WF LN =DNPMEVóVOBHË- en küçükEFôFSJLBÀDNEJS I ISF NA kaç DNEJS A) 2 3 B) 3 2 C) 5 \" # $ % & D) 5 2 E) 5 3 3. B G 6. A Duvar [ AB ] m [ BC ] D 5 [ DC ] m [ BC ] AF C | AB | =N | |BC =DN ôFLJMEFLJ ( OPLUBT BóSML NFSLF[J PMBO \"7. OJO D | |DC =DN [FNJOLBUOOÐTUUFOHËSÐOÐNÐWFSJMNJõUJS\"7.OJO E J¿JOFZBQMBDBLPZVOBMBOJ¿JO[AB]EVWBSOBQBSB- 5 MFM[GF]WF[AC]EVWBSOBQBSBMFM[DG]CBSJZFSMFSJJMF B 7 C zemin///////////////////////////////////////////// LBQBMCJSCËMHFPMVõUVSVMVZPS :VLBSEBLJ WFSJMFSF HÌSF [FNJOF EJL EVSVNEB | | | |GF =NFUSF GD =NFUSFPMEVôVOBHÌSF PMBO CJS EVWBSO \" LÌöFTJOEFLJ LBSODB EVWBS | |#C = x kaÀNFUSFEJS WF[FNJOÑ[FSJOEFJMFSMFZFSFL%OPLUBTOBFOB[ LBÀNFUSFZÑSÑZFSFLVMBöS \" # $ % & \" # $ % & 1. A 2. A 3. # 35 4. D 5. D 6. #

TEST - 16 1JTBHPS#BôOUT 1. #JS\"#$Ð¿HFOJOEF #WF$B¿MBSOBBJUJ¿B¿PSUBZ- 4. #JSEVWBSBZFSEFOZÐLTFLMJLMFSJFõJUPMBDBLõFLJMEF MBSO LFTJNOPLUBTI EõB¿PSUBZMBSOLFTJNOPL- DN BSBZMB Ð¿ ¿JWJ ZFSMFõUJSJMNJõUJS \"S[V CJS UBC- UBT.EJS MPZVV[VOLFOBSDNPMBOWFV[VOLFOBSOOV¿ OPLUBMBSO CJSMFõUJSFO CJS JQMF JLJ GBSLM õFLJMEF BTB- | | | | | |#I =DN CI =DN #. =DNPMEVôVOB SBLUBCMPOVOOBTMEVSBDBóOBCBLZPS | |HÌSF CM V[VOMVôVLBÀDNEJS DN A) 2 17 B) 2 11 C) 3 2 D) 3 5 E) 5 7 DN DN 2. \"WF#OPLUBMBSOEBEVWBSBNPOUFFEJMNJõEJLEËSU- DN HFOõFLMJOEFLJSFTJN¿FS¿FWFTJ #OPLUBTOEBLJ¿JWJ #VEVSVNEBUBCMPOVOZFSEFOZÐLTFLMJLMFSJOJWF ZFSJOEFO ¿LBSBL $ LËõFTJ [FNJOF EFóFDFL õFLJM- DNPMBSBLËM¿ÐZPS | | | |EFEVSNVõUVS \"#h =N CB = N #VOB HÌSF UBCMPOVO JQJOJO V[VOMVôV LBÀ DN | |#h& = N EJS A B \" # $ % & A 2 5. B' 1,6 A D K Dx D EC C zemin BE N C | | :VLBSEBLJ WFSJMFSF HÌSF DE = x kaç metre- ôFLJM* EJS \" # $ % & A 3. D [AB] m [BC] K 4 [BC] m [CD] D 9 B 15 A 3 E [DE] m [DC] E TN [AF] m [FK] ôFLJM** 10 C [FK] m [KL] [ KL ] m [ LE ] ôFLJM\"#$EJLÐ¿HFOJõFLMJOEFLBUMBOBCJMJSCJSNB- K 45 TBOO ÐTUUFO HËSÐOÐNÐEÐS [DE] WF [KN] EPóSVMB- FL SCPZVODBNFOUFõFMFSZFSMFõUJSJMNJõUJS#%&Ð¿HF- OJ LBUMBOEóOEB # OPLUBT 5 OPLUBT JMF ¿BLõZPS | | | | | |AB =DN BC =DN DC =DN ,/$ Ð¿HFOJ LBUMBOEóOEB $ OPLUBT 5 JMF ¿BLõB- SBLõFLJM**PMVõVZPS | | | | | | | |DE =DN AF =DN FK =DN KL =DN | | | | | |AD = AK =CS BC =CSPMEVôVOBHÌSF | |:VLBSEBLJWFSJMFSFHÌSF EL =YLBÀDNEJS NBTBOOÀFWSFTJLBÀCJSJNEJS \" # $ % & \" # $ % & 1. # 2. E 3. # 36 4. A 5. #

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, %÷,·¦(&/** ²LMJU#BôOUMBS ÖRNEK 2 %m/*m A \"#$Ð¿HFO 2 H [ AB] m [ BC] \"#$EJLÐ¿HFOJOEFm (WA) = 90° a [ BH] m [ AC] 45 [AH] m [BC] x | |AH =DN B | |C BC = 4 5 cm A | AB | =D cb | AC | =C | |:VLBSEBLJWFSJMFSFHÌSF #) = x kaÀDNEJS h | BH | =Q |HC| = q | |#$ 2 = a. (a + 2) (Öklit teoremi) B p HqC 80 = a (a + 2) j a =DN x2= 2.a (Öklit teoremi) | |AH =IPMNBLÐ[FSF x2 = 16 j x =DNEJS i) CD=I Q+ q ) ii) I2 =QR iii) D2 =Q Q+ q ) C2 =R Q+ q ) iv) 1 = 1 + 1 EJS h2 b2 c2 #VFõJUMJLMFSFÌLMJECBôOUMBSEFOJS ÖRNEK 3 ÖRNEK 1 \"#$Ð¿HFO A \"#$EJLÐ¿HFO A [BA] m [AC] [BA] m [AC] [AH] m [BC] 45 h 4 [AB] m [BD] |BC| = 5 |BH| [AD] m [BC] | |q C AB = 4 5 DN Bp H B pH q | |C AH =DN 1 | |HD =DN D | | | |:VLBSEBLJ WFSJMFSF HÌSF #$ + AH UPQMBN LBÀ | |:VLBSEBWFSJMFOMFSFHÌSF AC LBÀDNEJS DNEJS q =Q B&AD EFÌLMJEUFPSFNJ Q2 = 1.4 jQ= 2 | |\"# 2 =Q Q+ q) =QQ= 16.5 | |Q= R= #$ =Q+ q =DNEJS | |AH 2 =QR= 2.q = 16 j q = 8 | |AC 2 = 42 + 82 I2 =QR= 4.16 = 64 jI=DNEJS | |AC = 4 5 DN | | | |#$ + AH = 8 + 20 =DNEJS 1. 28 37 2. 4 3. 4 5

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 4 ÖRNEK 6 D 23 E 83 C \"#$%EJLEËSUHFO A \"#$WF%&$EJL 63 Ð¿HFO x [FE] m [DC] x F [AF] m [FB] D [ BA ] m [ AC ] [ DE ] m [ DC ] y | |DE = 2 3 DN 10 [ AH ] m [ BC ] A 23 83 B | EC | = 8 3 DN B a+b E a H b C | |EF =YDN | BE | = | EC | | DC | |=DN AC | =YDN | |:VLBSEBLJWFSJMFSFHÌSF EF =YLBÀDNEJS | |:VLBSEBWFSJMFOMFSFHÌSF AC =YLBÀDNEJS Z2 = 2 3 .8 3 = 48 j y = 4 3 | | | | | |EH =BDN HC =CDN #& = a +CDN x +Z= 6 3 x = 2 3 cm dir. DEC üçgeninde 102 = b (b + a) Öklid teoremi \"#$ÑÀHFOJOEFY2 = b (2a + 2b) (Öklid teoremi) x2 = 200 j x = 10 2 DNEJS ÖRNEK 5 ÖRNEK 7 #JSLºóEB[BA] m [AC]PMBDBLõFLJMEFCJSEJLÐ¿HFO¿J[J- A [BA] m [AC] MJZPS%` [BC]PMBDBLõFLJMEFCJS%OPLUBTCFMJSMFOJZPS \"#%Ð¿HFOJ [AD]CPZVODBLBUMBOEóOEB#OPLUBT [BD] m [DC] #h` [#$PMBDBLõFLJMEF#hJMF¿BLõZPS [AH] m [BC] | | | | | |#% = DN $#h = DN PMEVôVOB HÌSF \"# B9 H 11 T 5 C [DT] m [BC] V[VOMVôVLBÀDNEJS | |BH =DN A | |TC =DN 20 12 | |D TH =DN B 16 D 9 C 7 B' | | | |:VLBSEBLJWFSJMFSFHÌSF \"# + TD UPQMBNLBÀDN 16 EJS # OPLUBT [AD] CPZVODB LBUMBOEôOEB [AD] m [##h] |\"#|2 = |#)| . |#$|= 9.25 = 225 | |PMVS \"# 2 = |#%|.|#$| |\"#| = 15 | | | |\"# 2 = 16 . 25 j \"# =DN |TD|2 = |5#| . |TC| = 20.5 = 100 |TD| = 10 |\"#| + |TD| = 25 4. 2 3 5. 25 38 6. 10 2 7. 20

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 8 ÖRNEK 10 \"#$EJLÐ¿HFOJOEF[ AB] m [ AC]WF[ BC]OJOZÐLTFLMJóJ A \"#$Ð¿HFO [ AE] #JMF&OPLUBMBSBSBTOEBTF¿JMFO%OPLUBTPMNBL 8 15 [ AB] m [ AC] | |Ð[FSFm ( B%AD) = m ( D%AE) AC =DNWF B DC | | | |DE =DNPMEVóVOBHËSF #%LBÀDNEJS |BD| = |DC| | |AB =DN A m ( A%DC ) = m ( D%AC ) | |AC =DN = 90°- a | |:VLBSEBLJWFSJMFSFHÌSF AD LBÀDNEJS a 90°–2a 17 \"%$JLJ[LFOBS a |AC| = |DC| |EC| =DN 8 | | | | | |\"#$EJLÑÀHFOJOEF AD = #% = DC 90°–a \"&$EJLÑÀHFO | |#$ 2 = 82 + 152 = 172 Bx D 2 E 15 | |C AE =DN |DC| = 17 j |AD| = 17 2 2 |AE|2 = |#&| . |EC] (Öklid) 34 64 = (x + 2) . 15 j x = DN 15 ÖRNEK 11 UYARI A \"#$Ð¿HFO \"#$ EJL Ð¿HFOJOEF IJQPUFOÐTF BJU LFOBSPSUBZ a [ AC] m [ AD] V[VOMVóV IJQPUFOÐTÐO V[VOMVóVOVO ZBSTOB FõJUUJS a 15° a |DC| = 2|AB| A 2a 2a % = 15° BD aN m ( BAD ) a aC :VLBSEBLJWFSJMFSFHÌSF m % = a LBÀEFSFDFEJS ( ACB ) | |\"#$ÑÀHFOJOEF AN LFOBSPSUBZÀJ[JMJSTF % % BD C | | | | | |AN= = m NAC ) = m ( NCA ) = a DN NC ( | AD | = | BD | = | DC |EJS % = % = 2a m ( AND ) m ( ABC ) 2a + 90° + 15 + a = 180° 3a = 75° j a= 25° dir. ÖRNEK 9 A \"#$Ð¿HFO ÖRNEK 12 5 [ AC] m [ BC] A D 4 | DE | = | BE | = | EC | =DN 36° D | |x BD =DN 20 3 20 72° x C 36° K 20 72° 20 18° 18° B B 3 E3 C \"#$Ð¿HFO [DB] m [ BC ] m ( % ) = 2 m ( % ) = 36° BAC BCA | |:VLBSEBLJWFSJMFSFHÌSF AC =YLBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF DC =YLBÀDNEJS |#$|2 = |#%| . | |DA = 4.|#\"| [#,]LFOBSPSUBZOÀJ[FMJN | | | |9 = #\" j AD =DNEJS | |AC 2 = x2= 5.9 j x = 3 5 DNEJS |#,| = |%,| = |,$| =DN | | | |x = %, + ,$ =DNEJS 34 39 17 8. 9. 3 5 10. 11. 25 12. 40 2 15

TEST - 17 ²LMJE#BôOUMBS 1. 6óVS±óSFUNFOHFPNFUSJEFSTJOEFBõBóEBLJBEN- 4. A \"#$Ð¿HFO MBSJ[MFZFSFLHFPNFUSJLCJS¿J[JNZBQUSZPS [BA] m [AC] r % = 90°PMBOCJSEJLÐ¿HFO¿J[JOJ[ m ( BAC ) r ¶¿HFO J¿JOEF CJS % OPLUBT BMQ % = a F [EF] m [FC] m ( ABD ) 8 [AH] m [BC] PMBDBLõFLJMEFCJS\"#%Ð¿HFOJOJ¿J[JOJ[ B E H C |BE| = 2 |EH| | |FH =DN r %BIB TPOSB [AC] Ð[FSJOEFO CJS 5 OPLUBT BMQ | |:VLBSEBLJWFSJMFSFHÌSF AF =YLBÀDNEJS [AD]JMFLFTJõNFZFOm ( % ) = a PMBDBLõFLJM- TBC EF[BT]ZJ¿J[JOJ[ r m ( A%DB ) + m ( A%TB ) = 180° r [AD]ZJV[BUQ[BC]JMFLFTJõUJóJOPLUBZB)EJZF- \" # 8^ 3 - 1 h C) 4 MJN D) 8^ 2 - 1 h E) 4^ 3 - 1 h | | | |#) =CJSJN HC =CJSJNPMEVôVOBHÌSF | |AC LBÀCJSJNEJS A) 4 B) 6 C) 4 3 D) 2 13 & 5. B 2. A %JLÐ¿HFO õFLMJOEFLJ CJS * ** CBI¿FOJO FUSB- GOEB ZÐSÐZÐõ ZBQBDBL PMBO 5BNFS WF :V- A x D4 C TVG FõJU I[MBS- \"#$Ð¿HFOJOEF[AB] m [AC] [ AH ] m [ BC ] B E x C MB \" OPLUBTO- EBO * WF ** OVNBSBM ZPMMBSMB ZÐSÐNFZF CBõMZPSMBS WF&OPLUBTOEBELTPOSBLBSõMBõZPSMBS | | | |HC =DN AB = 4 6 DNEJS | |:VLBSEBLJWFSJMFSFHÌSF #) =YLBÀDNEJS | | 5BNFS BC ZPMVOVELEBZÐSÐZFCJMJZPS | | | | | |AC > \"#PMEVôVOBHÌSF 5BNFS EC ZPMV- A) 6 B) 4 3 C) 3 6 OVLBÀELEBZÑSÑZFCJMJS % & \" # $ % & 3. A \"#$Ð¿HFO 6. A x D \"#$WF\"%$Ð¿HFO [BA] m [AC] [BA] m [AC] [AD] m [DC] [AD] m [BC] 15 20 B8 | |BD =DN [AD] // [BC] | |D 2 C | |B C HC =DN AB =DN | | | |:VLBSEBLJ WFSJMFSF HÌSF \"# + AC UPQMBN | |AC =DN | |:VLBSEBLJWFSJMFSFHÌSF AD =YLBÀDNEJS LBÀUS A) 6 3 B) 6 5 C) 8 2 D) 8 3 E) 8 5 \" # $ % & 1. # 2. C 3. # 40 4. # 5. D 6. D

²LMJE#BôOUMBS TEST - 18 1. A 4. A \"#$Ð¿HFO E B |AE| = |EB| | |AC =DN x E 13 | |AD =DN 12 | |DC =DN | |BD =DN x B DC 16 D 5 C | |\"#$Ð¿HFO [BA] m [AC] AB = 20 3 DN | | :VLBSEBLJWFSJMFSFHÌSF ED =YLBÀDNEJS |BD| = 3 |DC| |AE| = |EC| = |DE| | | :VLBSEBLJWFSJMFSFHÌSF DE =YLBÀDNEJS \" # $ % & \" # $ % & 2. A \"#$Ð¿HFO 5. A B [ AB ] m [ BC ] E8 D [ BD ] m [ AC ] x E |AE| = |EB| 40° 6 |BF| = |FC| DC BF | |C DF =DN \"#$WF#%$CJSFSÐ¿HFO [AB] // [DC] I I I I[AB] m [BD] AE WFm % = 40°EJS =2 BC ( ACB ) | | | |DE =DNPMEVóVOBHËSF AC LBÀDNEJS :VLBSEBLJWFSJMFSFHÌSF m ( A%EB ) = x kaç de- \" # $ % & SFDFEJS \" # $ % & 3. A 17 E 6. A \"#$Ð¿HFO 5 [ AB ] m [ AC ] E 11 | |CE =DN 35 DE = 3 5 cm Bx D6 C | | | |\"#$Ð¿HFO AB =DN DC =DN B 10 D 10 C | AE | = | EC | = | ED | =DN | | | | | | | |BD = DC =DNPMEVóVOBHËSF \"# + AE | |:VLBSEBLJWFSJMFSFHÌSF #% =YLBÀDNEJS UPQMBNLBÀDNEJS \" # $ % & \" # $ % & 1. D 2. D 3. E 41 4. D 5. E 6. C

TEST - 19 ²LMJE#BôOUMBS 1. D C \"#$%EJLEËSUHFO 4. A \"#$Ð¿HFO [DE] m [EC] 4 [AH] m [BC] xD [HD] m [AC] [EH] m [AB] xE 15 B 129 H | |AC =DN A5 H | |AD = 8 3 DN | |C AD =DN B | |BH = 129 DN | |AH =DN | |HB =DN | |:VLBSEBLJWFSJMFSFHÌSF EH =YLBÀDNEJS | |:VLBSEBWFSJMFOMFSFHÌSF \"# =YLBÀDNEJS A) 3 B) 2 3 C) 3 3 \" # $ % & D) 4 3 E) 5 3 5. A \"#$WF\"#% Ð¿HFO 2. A \"#$Ð¿HFO [BA] m [AC] [BA] m [AC] x | |BD =DN [AB] m [BD] 43 | |DC =DN C [ AD ] m [BC] | |C B H 9 x 3 | |HC =DN B6 D 8 AD = 4 3 DN | HD | = 3 DN D | |:VLBSEBLJWFSJMFSFHÌSF AC =YLBÀDNEJS | | :VLBSEBLJWFSJMFSFHÌSF #% =YLBÀDNEJS A) 4 5 B) 4 6 C) 4 7 D) 8 2 E) 8 3 A) 3 B) 2 3 C) 3 3 D) 3 6 E) 4 3 3. F 6. A A x B EC D 6 B xH C \"#%Ð¿HFO [AC] m [BD] m ( % ) = m ( % ) BAE EAC 3 D | |m(C%AD) = m (F%AD ) EC = 3 2 DN \"#$WF\"%$Ð¿HFO [BA] m [AC] [AD] m [BC] | |CD = 6 2 DN | | | |% m ( ABC ) = m ( % ) HC =2 HD =DN BCD | |:VLBSEBLJWFSJMFSFHÌSF AE =YLBÀDNEJS | | :VLBSEBWFSJMFOMFSFHÌSF #) =YLBÀDNEJS A) 3 6 B) 4 6 C) 6 A) 24 B) 18 3 $ D) 6 2 E) 6 3 D) 12 3 & 1. C 2. C 3. A 42 4. # 5. # 6. A

²LMJE#BôOUMBS TEST - 20 1. A \"#$WF#%$ 4. A BA x B H K [BA] m [AC] EF E 4 [BD] m [DC] C [AH] m [BC] 6 [DK] m [BC] C D ôFLJM* B FC ôFLJM** 5 | BH | = 4 | HK | | KC | |=DN DK | =DN ôFLJM*EFLJCJOBZB#&'SFLMBNCSBOEBTBTMNõUS | |:VLBSEBWFSJMFOMFSFHÌSF AH =YLBÀDNEJS #VCSBOEBOO&OPLUBT[AC]LËõFHFOJÐ[FSJOEFEJS A) 4 B) 6 C) 4 2 ôFLJM**EFCSBOEBOOEÐ[MFNTFMõFLMJ\"#$EJLÐ¿- % & 8 2 HFOJCJ¿JNJOEFNPEFMMFONJõUJS 2. E | | | | | | | |[BE] m [EF] EF = FC AE =CS EC =CS A | |PMEVôVOB HÌSF CJOBOO \"# V[VOMVôV LBÀ CJ- SJNEJS 6 A) 3 2 B) 2 5 C) 2 6 D) 4 2 E) 4 3 BH C 4D \"#$WF&#%Ð¿HFO [BA] m [AC] [BE] m [ED] | | | |[AH] m [BD] [EC] m [BD] HC = BH | | | |CD =DN EC =DN 5. A [AB] m [BC] [BE] m [ED] | | :VLBSEBWFSJMFOMFSFHÌSF AC LBÀDNEJS E A) 8 3 B) 8 2 C) 4 6 D) 6 3 E) 6 2 3. A \"#$ WF #%& Ð¿- B DC HFO xD \" % )EPóSVTBM \"INFU%BZEJLÐ¿HFOTFMCËMHFõFLMJOEFLJQBODBS 16 UBSMBTOTVMBNBLJ¿JO#WF%OPLUBMBSOEBO&OPL- [BA] m [AC] UBTOEBLJ¿FõNFZFTVMBNBCPSVMBSZFSMFõUJSNJõUJS B HE C [BD] m [DE] ¥FõNF \" WF $ LËõFMFSJOF FõJU V[BLMLUB CVMVO- NBLUBES4VMBNBOOZFUFSTJ[PMEVóVOVHËSFO\"I- | | | | | |[AH] m [BC] BE = EC BD =DN NFU %BZ % OPLUBTOEBO $ OPLUBTOB NFUSFMJL | |AB =YDN #OPLUBTOEBO\"OPLUBTOBEBNFUSFMJLZFOJTV CPSVMBS¿FLFSFLUBSMBZTVMVZPS | |:VLBSEBLJ WFSJMFOMFSF HÌSF \"# = Y LBÀ DN \"INFU %BZhOO # WF % OPLUBMBS BSBTOB EB TV CPSVTVÀFLNFLJTUFSTFLBÀNFUSFEBIBTVCPSV- EJS TVOBJIUJZBDWBSES A) 16 2 # $ \" # 20 5 $ D) 20 2 E) 32 D) 20 13 E) 30 13 1. # 2. E 3. A 43 4. C 5. D

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr %÷,·¦(&/*** Açılarına Göre Özel Dik Üçgenler ÖRNEK 3 %m/*m A \"#$Ð¿HFO 30° - 60° - 90° Üçgeni 4x [ BA] m [ AC] -- Ð¿HFOJOEF MJL B¿OO LBSõ- D 2 3x [DH] m [BC] TOEBLJ LFOBS V[VOMVóV IJQPUFOÐTÐO V[VOMV- óVOVOZBSTOB MJLB¿OOLBSõTOEBLJLF- 2x 60° % = 60° OBSV[VOMVóVJTFMJLB¿OOLBSõTOEBLJLF- C m ( ACB ) OBSOV[VOMVóVOVO 3 LBUOBFõJUUJS 30° A B x3 H 63 2 | AB | = 3 | DA | | HC | = 6 3 DN | |:VLBSEBLJWFSJMFSFHÌSF \"# =YLBÀDNEJS a a3 & EFOJOLBSöT 2 3 x JTFOJOLBSöT4 3x ABC 60° 30° B 2a C 4 3x = x 3+6 3 3 3x = 6 3 | |x = \"# = 12 ÖRNEK 1 ÖRNEK 4 A \"#$Ð¿HFO A \"#$Ð¿HFO 30° [BA] m [AC] [ BA] m [ AC] 3 [AH] m [BC] x [AH] m [ BC ] 23 D % m ( ABC 30° 60° 1 [HD] m [AC] ) = 60° B 30° 60° 6 H2C 60° 30° B | |DC =DN H | | | |3x C HC - BH =DN % 2 m ( ABC ) = 30° | |:VLBSEBLJWFSJMFSFHÌSF \"# =YLBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF #$ LBÀDNEJS & ^ ABH hÑÀHFOJOEFOJOLBSöTYJTFOJOLBSöT % = 60° , m ( % = 30° x 3x x m ( ACB ) DHC ) dir. - = 8 jYDN | | | |DC =JTF HC = 2 2 22 m ( D%AH ) = 30°, m ( A%DH ) = 60° & AHC | | | |a k de HC = 2 JTF AC =4 ÖRNEK 5 |AC| = 4 iTF|#$| = 8 ÖRNEK 2 A \"#$Ð¿HFO A \"#$Ð¿HFO 6 60° 5 [ BE] m [ AC] DE [CD] m [ AB ] x [ AB] m [ AC] x 30° 7 | |AD =DN 30° | |AE =DN 30° 1 m (WB ) 1 60° | |EC =DN | |BC =DN BC B 12 C | |:VLBSEBLJWFSJMFSFHÌSF #% =YLBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF \"# = x in alabileDFôJLBÀ GBSLMUBNTBZEFôFSJWBSES | | | |\"#$ÑÀHFOJOEF AC = 2 AD PMEVôVOEBO | |30°< m(XB) < < \"# < 6 3 % = 60° m ( % ) = 30° dir. | |\"# = x ` { } YJOBMBCJMFDFôJUBNTBZEF- m ( BAC ) DCA ôFSJWBSES 0IBMEF m ( A%BE ) = 30°EJS\"#&ÑÀHFOJOEFY+ 6 = 2.5 x =DNEJS 1. 8 2. 4 44 3. 12 4. 8 5. 4

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 6 ÖRNEK 8 A A \"#$Ð¿HFO 60° 60° 45° % = 30° 2 m ( ABC ) . 22 4 6 x % 3 32 m ( ACB ) = 45° 30° 45° | |AB =DN 30° B 33 H 3 C H2 B x C | |:VLBSEBLJWFSJMFSFHÌSF AC =YLBÀDNEJS %% | | |\"#)ÑÀHFOJOEF \"# =JTF[AH = 3 \"#$Ð¿HFO m ( ACB ) = 30° m ( ABC ) 2 90° | | |AHC üçgeninde [AH = 3 ve AC = 3 2 | |AC =DNWF AB = 2 2 cmEJS | |:VLBSEBLJWFSJMFSFHÌSF #$ =YLBÀDNEJS | | | |AHC üçgeninde HC = 3 AH ÖRNEK 9 x+2= 2 3 % ABC x = 2 3 - 2 DNEJS | |#JS\"#$Ð¿HFOJOEFm =DN = 135° ( ) AB | |BC = 8 2 DNEJS ÖRNEK 7 :VLBSEBLJWFSJMFSFHÌSF \"#$ÑÀHFOJOEF\"$LFOBS- OOV[VOMVôVLBÀDNEJS \"#$EJLÐ¿HFOJOEF[ AB] m [ BC]WFÐ¿HFOJ¿JOEFCJS% A OPLUBTTF¿JMJZPS 45° | | | |m(B%AD) = 30° AD =DN DC =DNWF | | | |BC =DNPMEVôVOBHÌSF #% kaç DNEJS 82 16 D A | |#% 2 = 42 + 82 = 80 45° 135° 82 C | |#% = 4 5 DNEJS 82 B 8 K4 D30° C | |AC 2 = ^ 8 2 h2 + ^ 16 2 h2 | |AC = 8 10 DNEJS 8 17 B 4 H 15 ÖRNEK 10 A \"#$Ð¿HFO %m/*m 4 [BA] m [AC] 45° - 90° - 45° Üçgeni 22 % = 45° --Ð¿HFOJOEF IJQPUFOÐTÐOV[VOMV- 2 xH m ( ADC ) óV EJLLFOBSV[VOMVóVOVO 2 LBUES 45° B | |C AD =DN A D2 | BD | = 2 DN | |:VLBSEBLJWFSJMFSFHÌSF #$ =YLBÀDNEJS a a | | | |\"#$ÑÀHFOJOEF [AH] m [DC] [AH]2 = #) . HC (Ök- 45° a2 45° lit) B C 8 = 2 . | HC | | | | |4 2 = HC #$ = 5 2 DNEJS 6. 2 3 - 2 7. 4 5 45 8. 3 2 9. 8 10 10. 5 2

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 11 %m/*m .FSU ËM¿ÐTÐPMBOCJS\"#$B¿T¿J[JZPS%BIBTPOSB 15° - 75° - 90° Üçgeni \"OPLUBTOEBO[#$õOOBCJSEJLNFJOEJSJZPSWF)OPL- A (2 + A UBTPMBSBLJTJNMFOEJSJZPS4POPMBSBL)OPLUBTOEBO[ BA a 3)a h õOOBCJSEJLNFJOEJSJZPSWFEJLNFOJOBZBóO%OPLUBT 75° 15° 75° 15° C | | | |PMBSBLJTJNMFOEJSJZPS HD =DNPMEVóVOBHËSF AC OJOBMBCJMFDFôJFOLÑÀÑLUBNTBZEFôFSJOFPMBCJMJS B ( 2+ 6)a C 4h B A |AC| > |AH| - - 90° Üçgeni |AC| > 5 2 5 | |AC OJOFOLÑÀÑLDNDJO- A A 45° a TJOEFOUBNTBZEFôFSJ D 8 dir. 52 C (1 + 5 45° 2)a 45° 45° BH 67,5° 22,5° h 22,5° 67,5° B 4+2 2a C B 2 2h C %m/*m 30° - 120° - 30° Üçgeni --Ð¿HFOJOEF MJLB¿OOLBS- õTOEBLJLFOBSV[VOMVóVFõJULFOBSV[VOMVLMB- SOO 3 LBUES A 120° a a 30° 30° ÖRNEK 13 \"#$Ð¿HFO B C a3 A % = 30° 135° m ( ABC ) x % m ( BAC ) = 135° 30° 10 | |C BC =DN B ÖRNEK 12 | |:VLBSEBLJWFSJMFSFHÌSF AC =YLBÀDNEJS A \"#$Ð¿HFO 10x [BA] m [AC] | |$OPLUBTOEBO \"# OBEöBSEBOEJLJOEJSJMJSTF1JTBHPS D teoreminden 63 m( % = 120° EDC ) 60° B 43 8 120° 8 | |AB = 6 3 DN 5 |AC| = 5 2 30° 30° E 83 C | |BE = 4 3 DN 5 | |:VLBSEBLJWFSJMFSFHÌSF AD =YLBÀDNEJS A 45° 135° 5 2 | | | |\"#$ÑÀHFOJOEF \"# = 6 3 JTF #$ = 12 3 30° 45° |EC| = 8 3 B 15° | | | | | |DEC üçgeninde DC = AC = AD =EVS 10 C 11. 8 12. 10 46 13. 3 2

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 14 ÖRNEK 17 A \"#$Ð¿HFO A \"#$Ð¿HFO 30° 6 [ BH ] m [ AC] m ( B%AC ) = 60° x+6 H % = 75° 60° 24 % = 15° x m ( ACB ) m ( ACB ) 23 75° |AB|å= |AC| 12 | |AB =DN 60° 30° K | |AH å=DN 12 3 12 3 BC 15° 15° B C | |:VLBSEBLJWFSJMFSFHÌSF HC =YLBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF AC LBÀDNEJS |\"#| = |AC| = 6 + x | |% #, \"#)ÑÀHFOJOEFY+ 6 = 2 . 2 3 m ( ABK ) = 90° PMBDBLöFLJMEF çekelim. x = 4 3 - 6 DN | | | |mm \"#, ÑÀHFOJOEFO \", = #, = 12 3 |#,|= |,$|= 12 | |3 AC = 24 + 12 3 ÖRNEK 15 ÖRNEK 18 A \"#$Ð¿HFO \"#$ \"%$Ð¿HFO x % = A 60° 2 m ( ABC ) H2 + 2 3 75° [AD] m [AC] x x3 m ( A%CB ) = 45° 308° 83 % x3 2 60° 30° xK m ( ABC ) = 45° 30° 44 15° 16 754°5° 2 16 B 45° AC = 2 + 2 3 cm 45° 15° % = 15° m ( ACB ) C B 42 D C | BD| = 4 2 | |:VLBSEBLJWFSJMFSFHÌSF \"# =YLBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF AC =YLBÀDNEJS || || x D den \"#)ÑÀHFOJOEF \"# =Y AH = | | | |genleri 2 \"el#de ZeFd EeJlLim J.OEAJSDJQ= m mm( K%DWCF)=m15°m PMBDÑBÀL- | | | |x 3 x 3 #) = HC = Y=DN | |öFLJMEF %, ÀJ[FMJN\"%,mmveriliZPS 22 | | | | | | | | | |AD = \", = 8 3 %, = ,$ = AC = 8 3 + 16 x x3 = 2 + 2 3 jYDN AC = + 22 ÖRNEK 16 ÖRNEK 19 A \"#$Ð¿HFO A \"#$Ð¿HFO 4 m ( % ) = 67, 5° ABC 2k | AB | = | AD | 4 45° Hx m ( % ) = 22, 5° k |BD| = |AC| 42 42 ACB 45° 45° a [AB] m [AD] 627,25,°5° | |AB =DN kD C B Bk H 22,5° % C :VLBSEBLJWFSJMFSFHÌSF m ( ACB ) = aLBÀEFSFDFEJS | | | |\"# = AD m( A%DB ) = 45°PMEVôVOEBO | |:VLBSEBLJWFSJMFSFHÌSF AC å=YLBÀDNEJS |AH| = |HD|= |#)| = k |#%|= |AC| = 2k | |& | | | |AH =L AC =LPMEVôVOEBOa = 30° AC = 4 + 4 2 ^ CBH h = PMBDBLöFLJMEF #) | | | |ÀJ[FMJN\"#)mm \"# = AH = |#)| = |HC| = 4 2 14. 4 3 - 6 15. 4 16. 30 47 17. 24 + 12 3 18. 8 3 + 16 19. 4 + 4 2

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 20 ÖRNEK 22 A \"#$JLJ[LFOBSEJLÐ¿HFO 4FSIBU LFOEJTJOF /FXUPO EFOHF UPQVOV ËSOFL BMBSBL ZFOJCJSEFOHFUPQVZBQNBLJTUJZPS 45° |AB| = |BC| &õJUV[VOMVLUBLJJQMFSVDVOBFõUPQMBSTBCJUMFZFSFLJQMFSJ 12 K ,OPLUBTOBTBCJUMJZPSôFLJM*EFLJEÐ[FOFóJPMVõUVSVZPS [AB] m [BC] 62 [BH] m [DC] K DH x 30° % B 15° m ( DCA ) = 30° C | |AD =DN | |:VLBSEBLJWFSJMFSFHÌSF #) =YLBÀDNEJS A BC | | | |[%,] m [AC] %, = 6 2 DC = 12 2 ôFLJM* %#$ÑÀHFOJOEF ÑÀHFOJ | |&óFS\"UPQVOVm ( A%'KB ) = 30°WF \"h# =DNPMBDBL |DC| = 4 |#)| õFLJMEF ¿FLJQ CSBLSTB $ UPQV m ( A%'KC' ) = 90° PMBDBL | |#) = 3 2 DNEJS õFLJMEF IBSFLFU FUNFLUF \" UPQVOVO ¿FLJMEJóJ LPOVN \"h $UPQVOVOTPOLPOVNV$h ôFLJM**EFLJHJCJPMNBLUBES ÖRNEK 21 K ôFLJMEFWFSJMFOCJSCJOBOOIFSLBUBSBMóFõJUNFTBGFEF WFFSNFUSFEJSLBU¿J[HJTJ[FNJOEFONFUSFZVLBS- A' C' EBES#JOBEB¿LBOCJSZBOHOTPOVDVHFMFOJUGBJZFBSB- B CBTOONFSEJWFOJOJOCBõMBOH¿OPLUBTNZVLBSEBWF \"OPLUBTOEBEVSBSBLLBUUBLJLJõJMFSJLVSUBSNõUS ôFLJM** 9 | |#VOB HÌSF 4FSIBUhO ZBQUô EFOHF UPQVOEBLJ \", 8 7 LBÀDNEJS öQMFSHFSHJOEVSVNEBIBSFLFUFEFDFLUJS 6 5 K 4 5 6 30° 3 2 52 5 2+5 6 1 52 45° N 60° C' 45° 45° N A' 30° 10 75° A BC 10 75° N B | | | |AC =N BC =N \"ZONFSEJWFOV[VOMVôVZMBJUGBJZFBSBDOONFSEJWF- OJOJO CBöMBOHÀ OPLUBT # OPLUBTOB HFMEJôJOEF LB- ÀODLBUUBLJMFSJLVSUBSBCJMJS 3 3 25 m 15 m 3 25 24 1.kat 7 20 m 6 1m 1m 1m 1m 20 m )FSLBUBSBTNFUSFPMEVôVOEBOZFSEFOJUJCBSFOLBU NFUSFNFTBGFEFEJS 20. 3 2 21. 25 48 22. 5 6 + 5 2

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TYT AYT Geometri Ders İşleyiş Modülleri 2. Modül Üçgenler

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TYT AYT Geometri Ders İşleyiş Modülleri 2. Modül Üçgenler

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