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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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²[FM%JL·ÀHFOMFS TEST - 21 1. A 4. A DE 1BSL Oyun BMBO CBI¿FTJ BC 15° \"#$Ð¿HFOJOEF | AC | =+ 4 3 DNPMEVóVOB BG FC | |HËSF #$ LBÀDNEJS | | | |% m ( ABC ) = 15° DG =N GF =N A) 4 3 B) 6 C) 6 3 \"#$EJLÐ¿HFOTFMCËMHFTJõFLMJOEFLJCJSQBSTFMFCJS PLVMZBQMBDBLUS#VPLVM%&'(EJLËSUHFOJõFLMJO- D) 8 3 & EFPMBDBLõFLJMEFHËSTFMJZVLBSEBWFSJMNJõUJS[BC] LFOBSOBCJSEVWBSËSÐMFDFLUJS ²SÑMFOCVEVWBSLBÀNFUSFV[VOMVôVOEBPMNBMES \" # $ % & A 5. C ôFLJMEFLJ\"#$Ð¿- DN HFOJ \" OPLUBT FU- 2. A B SBGOEB QP[JUJG ZËOEF a B¿T LB- x EBS EËOEÐSÐMÐZPS WF#OPLUBT#h $ 1 8 C DN OPLUBT$hOPLUBT B PMVZPS \"#$Ð¿HFOJOEF m( % ) = 22, 5° | |[AC] a [$h#h] = {K} m(A%CB) = a AB =DN BAC m( % ) = 112, 5° | BC | =DNPMEVóVOBHËSF | | | |BC =DNPMEVôVOBHÌSF \", V[VOMVôVLBÀ ABC | |AC =YLBÀDNEJS CJSJNEJS A) 8 2 # $ 8 2 + 8 7 B) 2 5 C) 5 A) D) 4 2 13 2 E) D) 16 2 E) 16 2 + 16 2 6. .VSBU ±óSFUNFO BõBóEBLJ BENMBS J[MFZFSFL Ëó- SFODJMFSJOFCJSHFPNFUSJLõFLJM¿J[EJSFDFLUJS 3. A r m % = 90° PMBDBL õFLJMEF \"#$ Ð¿HFOJ ¿J[J- ( BAC ) OJ[ r [AC]Ð[FSJOEFCJS%OPLUBTBMO[ m ( A%BD ) = 50°WFm ( D%BC ) = 20°PMTVO 30° a C r [BC] LFOBSOO EõOEB CJS & OPLUBT TF¿JQ B \"#$Ð¿HFOJOEF m ( % ) = 30° m ( % ) = 105° m % = 20° PMBDBL õFLJMEF #&$ Ð¿HFOJ ¿J[J- ABC BAC ( CBE ) OJ[ | || AB | =DNPMEVóVOBHËSF #$ =BLBÀDNEJS | | | |\"# =DNWF EC =DNPMEVôVOBHÌSF A) 2 3 B) 2 3 + 1 C) 2 3 + 2 % m ( BCE ) = aLBÀEFSFDFEJS D) 2 3 + 3 E) 2 3 + 4 \" # $ % & 1. D 2. C 3. C 49 4. E 5. C 6. #

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr %m/*m ÷,÷;,&/\"3·¦(&/ ÖRNEK 2 A A \"#$Ð¿HFO a <#%>B¿PSUBZ D [ BD] m [ AE] m ( E%DC ) = 50° H 50° a BC B EC :VLBSEBLJWFSJMFSFHÌSF m ( A%ED ) kaç EFSFDFEJS öLJLFOBSV[VOMVóVFõJUPMBOÐ¿HFOFJLJ[LFOBS % | |\"#&ÑÀHFOJOEF #) EPôSVTVBÀPSUBZZÑLTFLMJLWFLF- | | | | | | | |OBSPSUBZES \"# = #& ve AH = HE PMVS üçgen EFOJS BAC UFQFB¿TES | | | |\"%&ÑÀHFOJOEF AH = HE ve [AE] m [DH]PMEVôVOEBO |AD| = | |DE PMVS A 2a = 50° j a = 25° %m/*m A |AB| = |AC| BHC FE [DF] // [CA] 5FQFOPLUBTOEBO¿J[JMFOZÐLTFLMJLB¿PSUBZWF [DE] // [BA] LFOBSPSUBZES BD C | |AH =Ia =Oa= vA |AB| = |AC| |DE| + |DF| = |AB| = |AC| |BH| = |HC| |AB| = |AC| A [ HP] m [AB] [HR] m [AC] ÖRNEK 1 PR A \"#$Ð¿HFO BH C 13 13 | AB | = | AC | =DN | | | |HP + HR =IC =ID | |BD =DN 12 5 | |DC =DN A |AB| = |AC| B 17H D 7 C F [HE] m [AE] [HF] m [AC] | |:VLBSEBLJWFSJMFSFHÌSF AD LBÀDNEJS [AH] m [#$]ÀJ[JMJSTF[#$]UBCBOOJLJFöQBSÀBZBBZSS H C B | | | |#) =DN HD =DNPMVr. | |\"#)EJLÑÀHFOJOEF AH 2 + 122 = 132 den E | | | |AH =DNCVMVOVS\")%EJLÑÀHFOJOEF AD 2 = 52+ 52 | |den AD = 5 2 CVMVOVS | | | |HF - HE =IC =ID 1. 5 2 50 2. 25°

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 3 ÖRNEK 5 A \"#$Ð¿HFO D E [ DE] m [ AB] H [ DF] m [ BC] A H4 bF D % b ( ABC m ) = 30° x5 30° | AB | = | BC | =DN aa B 8 FC B KE C | | | |:VLBSEBLJWFSJMFSFHÌSF DE + DF UPQMBNLBÀ \"#$JLJ[LFOBSÐ¿HFO [AK] m [BC] [DE] m [ BC ] DNEJS | AB | = | AC | | DE | |=DN AK | |=YDN FE | =DN |\"#| = |#$| =DN | |:VLBSEBLJWFSJMFSFHÌSF \", =YLBÀDNEJS |DE|+ |DF| = |CH| | |#)$ÑÀHFOJOEF HC =DNPMVS % = % = a PMTVO m ( ACB ) m ( ABC ) % = % = % = b m ( ADF ) m ( EFC ) m ( AFD ) %\"'JLJ[LFOBSÑÀHFOJOEF[AH]EJLNFTJÀFLJMJSTF | | | | | |DH = HF =DNPMVS \", =DN ÖRNEK 4 A \"#$Ð¿HFO %m/*m A | AB | = | AC |JTF E 45° [ DK] m [ AK] 7C =7D F OC =OD D H [ DF] m [ AC] IC =IDEJS B 5 |AB| = |AC| C K C | |DF =DN | |DK =DN B | |:VLBSEBLJWFSJMFSFHÌSF AC LBÀDNEJS |#)| = |DF| - |%,| A | AB | = | AC |JTF | |#) = 8 - 3=DN |BD| = |EC| | | | |\"#)ÑÀHFOJOEF AC = \"# = 5 2 DN |AE| = |AD| E D |EB| = |DC| F |BF| = |FC| | | | |B C FE = FD EJS 3. 4 4. 5 2 51 5. 7

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 6 \"%$ CJS JLJ[LFOBS ÖRNEK 8 \"#$Ð¿HFO Ð¿HFO [$%>B¿PSUBZ A A |AD| = |AC| [ CD] m [ AB] E' 7E 3 [ AH] m [ BC] 12 12 [ DE ] m [ AC ] D D | |AD =DN x 7 | |BC =DN 33 C | |EC =DN BH C B | |DE =DN 25 | |:VLBSEBLJWFSJMFSFHÌSF DH LBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF %# =YLBÀDNEJS \"#$ÑÀHFOJOEF[CD]IFNBÀPSUBZIFNEFZÑLTFLMJLPM- \"%$JLJ[LFOBSÑÀHFOJOEF[$&h] m [\"#]ÀJ[JMJSTF | |EVôVOEBO AC = |#$| |AD| = | |%# PMVS |DE|= |$&h| =DN | |\")#EJLÑÀHFOJOEF[DH]LFOBSPSUBZ DH =DNPMVS | |%&h =DNEJS #&h$EJLÑÀHFOJOEF (x +12)2 + 72 = 252 j x + 12 = 24 x =DN ÖRNEK 9 ÖRNEK 7 \"#$EJLÐ¿HFO A \"#$Ð¿HFO A [BE]LFOBSPSUBZ 7 D <#%>åB¿PSUBZ 4 B F F [AB] m [ BC ] [ BD] m [ DC] 3 x E [AD] m [BE] E |AE|å= |EC|å | |AB å=DN D7 |BD| = |AF| 15 | |C BC å=DN | |AF =DN BC | |EC =DN | |:VLBSEBLJWFSJMFSFHÌSF DE å=YLBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF AD =YLBÀDNEJS T \"WF%LÌöFMFSJOEFO 8 ÑÀHFO UBNBNMBOS- \"#$EJLÑÀHFOJOEF[#&]LFOBSPSUBZPMEVôVOEBO A TB JLJ[LFOBS ÑÀHFO elde edilir. |AE| = |EC| = | |#& PMVS | | | |\"#&JLJ[LFOBSÑÀHFOJOEF #' = AD [#'] m [AC]PMVS D |TD| = |DC| | | | |#' 2 = 4.(10) j #' = 2 10 F |#'| = |AD|= 2 10 DN | | | |7 x E 5# = #$ PMVS |AE| = |EC| ve B 15 C |TD| = |DC| den [DE][5#] YPSUBUBCBO Y=DN 6. 12 7. 2 10 52 8. 3 9. 4

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 10 ÖRNEK 12 \"#$Ð¿HFOJOEFm (WB) > 90° [ AC] Ð[FSJOEFTF¿JMFOCJS A | | | |%OPLUBT [ DB] m [ BC] AB = BC = 3 10 DN | | | |DB = 10 DNPMEVôVOBHÌSF AD V[VOMVôVkaç E KD 20° L DNEJS B #%$ EJL ÑÀHFOJOEF 40° 40° 20° ^ 3 10 h2 + ^ 10 h2 = DC 2 B C F 3 10 3 10 | |DC =DN 10 |#)| . |DC| = 10 . 3 10 | |#) =DN | | | | | | | |A#$JLJ[LFOBSÐ¿HFO AB = AC AE = AD A x D1H 9 C | | | | | |KD =DNWF % =DN BK =DN CF m ( EFB ) = 20° |#%|2 = |DH|2 + |#)|2 EJS | |10 = DH 2 + 9 j |DH| = 1 |AH| = |HC| j x =DN :VLBSEBLJWFSJMFSFHÌSF m ( % ) kBÀEFSFDFEJS DBC | |#% =DN ÖRNEK 11 |EC| = |#%| = |CF| | |j CF =DN &$'JLJ[LFOBSÑÀHFO m ( % ) = 40° ECB (FPNFUSJ EFSTJOEF ZBQMBO CJS FULJOMJL J¿JO BõBóEBLJ % = 40° BENMBSJ[MFONJõUJS m ( DBC ) | | | |r AB = AC =DNPMBDBLõFLJMEFCJS\"#$JLJ[- ÖRNEK 13 LFOBSÐ¿HFOJ¿J[JOJ[ ôFLJMEFWFSJMFO\"#$JLJ[LFOBSEJLÐ¿HFOCJ¿JNJOEFLJLº- r [ BC ]LFOBSOOPSUBOPLUBTOCFMJSMFZJQ%OPLUBT óU \"#LFOBS#$LFOBSÐ[FSJOFHFMFDFLCJ¿JNEF[BD] PMBSBLJTJNMFOEJSJO CPZVODBLBUMBOZPS A | |r [ AB ]EPóSVQBS¿BTÐ[FSJOEF BE =DNPMBDBL DD õFLJMEF&OPLUBTOCFMJSMFZJQ%OPLUBTJMFCJSMFõUJ- B CB A C SJQ[ ED ]EPóSVTVOV¿J[JOJ[ #VOBHÌSF BC PSBOLBÀUS r #&% Ð¿HFOJOJ [ ED ] EPóSVTV CPZVODB LBUMBZO[ ,BUMBNB ZBQMEóOEB # OPLUBTOO [ AB ] EPóSVTV DC Ð[FSJOEFLJ#hOPLUBTJMF¿BLõUóOHËSFDFLTJOJ[ #V BENMBS J[MFOFSFL ZBQMBO ÀJ[JNJO EPôSV PMNBT | |için #% V[VOMVôVLBÀDNPMNBMES A \"#$ JLJ[LFOBS ÑÀHFOJOEF A | |AD =LCSPMTVO 2 B' [AD] m [#$] kk+ k 2 ,BUMBOODB D 4 #%#h ÑÀHFOJ JLJ[LFOBS ÑÀ- m( % ) = % ) k 45° k 2 ABD m ( DBE E HFOPMVS[DE] m [\"#] 45° 4 |DE|2 = |#&| . |EA| B k+ k 2 E k C Bx D C BC k^ 2 + 2 h | |DE 2 = 4 . 6 j |DE|= 2 6 = = 2+1 | | | |#% 2 = 42 + ^ 2 6 h2 j #% = 2 10 DC k 2 10. 8 11. 2 10 53 12. 40 13. 2 + 1

TEST - 22 ÷LJ[LFOBS·ÀHFO 1. A \"#$Ð¿HFO 4. A [ AH ] m [ BC ] 22° 10 D |BH| = |HC| x E D |BC| = |CD| 2 % a m ( HAC ) = 22° BE C BHC B%AD % ) [ ] [ ] DAC % \"#$Ð¿HFO m ( ) = m ( AD m DC ACD :VLBSEBLJWFSJMFSFHÌSF m ( ) = a kaç dere- | | | |[ AB ] // [ DE ] DE =DN AB =DNEJS DFEJS \" # $ % & | |:VLBSEBLJWFSJMFSFHÌSF AC =YLBÀDNEJS \" # $ % & 2. A \"#$Ð¿HFO 5. A F |AB| = |AC| 8 E [ ED ] // [ AC ] Dx E [ AB ] // [ DF ] | |AB =DN B 14 C BD C A%BD % DBC \"#$Ð¿HFOJOEF m ( ) = m ( ) [ DE ] // [ BC ] :VLBSEBLJWFSJMFSFHÌSF ¦FWSF \"&%' LBÀDN | | | |[ AD ] m [ BD ] AB =DN BC =DNEJS EJS \" # $ % & | |: VLBSEBLJWFSJMFSFHÌSF DE =YLBÀDNEJS A) 2 B) 3 C) 4 D) 5 E) 6 6. A 3. A \"#$Ð¿HFO D (BóSMLNFSLF[J 20 20 G [ AH ] m [ BC ] B Dx E C | |AB =DN | |HC =DN B HC | | | |\"#$Ð¿HFOJOEF AB = AC =DN | |:VLBSEBLJWFSJMFSFHÌSF #% LBÀDNEJS | BC | | |=DN BE = | DC | = | AE | A) 3 14 B) 3 15 C) 3 17 | |:VLBSEBLJWFSJMFSFHÌSF DE =YLBÀDNEJS 54 D) 3 19 E) 3 21 A) 26 # $ 28 D) 29 & 3 33 1. # 2. C 3. C 4. C 5. # 6. C

÷LJ[LFOBS·ÀHFO TEST - 23 1. A 4. A \"#$Ð¿HFO 120° |AB| = |AC| D D 30° Ex C x [ BD ] m [ AC ] B 12 | |2 DC =DN % % | |BC =DN ABC BAC \"#$Ð¿HFOJOEF m ( ) = 30° m ( ) = 120° B3 C | | | | | |[ ED ] m [ AC ] AD = DC BE =DN | |:VLBSEBLJWFSJMFSFHÌSF \"# =YLBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF EC =YLBÀDNEJS A) 9 B) 11 C) 6 D) 13 & 4 2 2 A) 3 3 B) 4 3 C) 4 D) 6 3 E) 6 A 5. A \"#$Ð¿HFO 10° 2. [ AD ] m [ BD ] 130° x | AB | = | |AC DN x 6 20° 30° 8 C B2 D D |BC| = |BE| E m (\\DAC) = 10° \"#$Ð¿HFOJOEF m ( A%BC ) = 20° m ( A%DC ) = 30° BC | | | |% | | :VLBSEBLJWFSJMFSFHÌSF AD =YLBÀDNEJS m ( DAC ) = 130° BD = DN WF DC = DN A) 3 B) 6 C) 3 3 EJS D) 4 3 E) 6 3 | |:VLBSEBLJWFSJMFSFHÌSF \"# =YLBÀDNEJS A) 4 5 B) 3 6 C) 2 6 D) 3 7 E) 2 7 6. Ax D 3. A \"#$Ð¿HFO 15 20 |AB| = |AC| BC | BD | = | BC | =DN [ AB ] m [ AC ] [ AD ] m [ DC ] [ AD ] // [ BC ] D | | | |AB =DN AC =DN | |8 DC =DN | |:VLBSEBLJWFSJMFSFHÌSF AD =YLBÀDNEJS 4 \" # $ % & B 8C | |:VLBSEBLJWFSJMFSFHÌSF \"# LBÀDNEJS \" # $ % & 1. E 2. E 3. C 55 4. A 5. C 6. D

TEST - 24 ÷LJ[LFOBS·ÀHFO 1. A \"#$Ð¿HFO 4. A \"#$Ð¿HFO E I IBD =DN (BóSMLNFSLF[J 12 x I IBC =DN [BG] m [CG] 50° 40° C D IADI = IACI G |BG| = |GC| | |BC =DN I IEC =DN % m ( CDE ) = 50° 5 15 % = 40° B 10 C m ( DCB ) B | | :VLBSEBLJWFSJMFSFHÌSF AC =YLBÀDNEJS I I :VLBSEBLJWFSJMFSFHÌSF DE =YLBÀDNEJS A) 10 2 B) 5 10 $ A) 6 # $ % & D) 10 3 & 2. A \"#$Ð¿HFO 5. A A#$Ð¿HFO IBDI = IDAI 6 | |AD =DN D E IAEI = IECI D | |DB =DN | |DC =DN [ PD ] m [ AB ] 10 [ PE ] m [ AC ] 2 I IB C BC =DN30° 30° P B xC I I:VLBSEBLJWFSJMFSFHÌSF PA LBÀDNEJS | | | | :VLBSEBLJ WFSJMFSF HÌSF AC = #$ = x kaç A) 4 B) 4 3 C) 8 2 D) 8 3 E) 9 3 DNEJS A) 6 3 B) 4 7 $ % & 5 7 | | | |3. \"#$JLJ[LFOBSÐ¿HFOJOEF AC = BC [BD]EPó- | | | |6. \"#$JLJ[LFOBSÐ¿HFOJOEF AB = BC \"LËõFTJOF SVQBS¿BT [AC]OJOZÐLTFLMJóJ[AH]EPóSVQBS¿BT BJUB¿PSUBZO [BC]ZJLFTUJóJOPLUB%OPLUBTES [BC]OJOZÐLTFLMJóJPMNBLÐ[FSF | | | | | |E ` [AC]PMNBLÐ[FSF DE = AE = EC PMBDBL | | | |BH =DN DC =DN | | :VLBSEBLJWFSJMFSFHÌSF \"# LBÀDNEJS õFLJMEF[DE]EPóSVQBS¿BT¿J[JMJZPS A) 3 B) 4 C) 2 5 | | | |#% =DNPMNBLÑ[FSF DC LBÀDNEJS D) 5 E) 6 5 B) 5 C) 15 % & A) 22 1. C 2. # 3. C 56 4. # 5. # 6. #

÷LJ[LFOBS·ÀHFO TEST - 25 1. A A 3. A E DE DE F B DC BC A' ôFLJM A ôFLJM CB C E B ôFLJM ôFLJM F ôFLJM EFLJ \"#$ JLJ[LFOBS Ð¿HFOJ [DE] CPZVODB LBUMBOEóOEB\"OPLUBT\"hOPLUBTJMF¿BLõZPS BC | | | |AB = AC [ DE ] // [ BC ]WF ôFLJM % + % = 150°EJS | | | |,FOBSV[VOMVLMBS AB = AC = 6 13 DN m ( CEA' ) m ( BA'D ) | |BC = DN PMBO JLJ[LFOBS Ð¿HFO [AD] EPóSV- :VLBSEBLJWFSJMFSFHÌSF TVCPZVODBLBUMBOBSBLõFLJMFMEFFEJMJZPSôFLJM % - m ( D%A'E ) = x LBÀEFSFDFEJS EFLJÐ¿HFO[ EF ]CPZVODBLBUMBOEóOEB\"LËõFTJ m ( BA'C ) JMF#LËõFTJ¿BLõZPS \" # $ % & #VOBHÌSF öFLJMUFLJ&#$'EÌSUHFOJOJOBMBO LBÀDNEJS \" # $ % & A 4. E 2. A \"#$Ð¿HFO D F % = % m ( ABC ) m ( ACB ) x [ AB ] m [ EC ] BC 7 \"#$JLJ[LFOBSÐ¿HFO [CE] a [BD] = {F} E D [ DE ] // [ BC ] | |20 ED =DN [ BD ] m [ AC ] | AB | = | AC | | CE | = 2 | BD | | |B C m( % = 66° EC =DN ABD ) & :VLBSEBLJWFSJMFSFHÌSF A^ EBC hLBÀUS % :VLBSEBWFSJMFOMFSFHÌSF m ( ACE ) = x LBÀUS \" # $ % & \" # $ % & 1. C 2. C 57 3. A 4. #

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr &õ,&/\"3·¦(&/ %m/*m ÖRNEK 2 60° A ¶¿ LFOBS FõJU A \"#$FõLFOBSÐ¿HFO B V[VOMVLUB PMBO 30° 30° [ AD] m [ BC] 60° Ð¿HFOF FöLF- 3 nar üçgen EF- |AE| = |ED| OJS E | |DC =DN x 60° C 3 60° B 2 D 2C | |:VLBSEBLJWFSJMFSFHÌSF #& LBÀDNEJS A 2 = 2 + ^ 3 h2 & x = 7 30° 30° x 2 & 1JTBHPSUFPSFNJOEFO BDE a a3 a ÖRNEK 3 2 A 60° H 60° 2 3 30°60° 30° 2 3 22 Ba aC 2 2 |AB| = |AC| = |BC| 30° 60° 60° 120° 30° B2 D 2 E 2C m (WA) = m (WB) = m (XC) = 60° a3 |\"#$Ð¿HFOJOEF BD | = | AD | = | AE | = | EC | I=7=O= | |m(D%AE) = 60° DE =DNEJS 2 :VLBSEBLJWFSJMFSFHÌSF ¦FWSF \"#$ LBÀDNEJS Ia =IC =ID A&DE FöLFOBS A&BD ve A&EC mmÑÀHFOJ 7a =7C =7D Oa=OC =OD || || & Ia=7a =Oa=IC =7C=OC =ID =7D =OD \"# = 2 3 AC = 2 3 Ç^ ABC h = 4 3 + 6 & a2 3 h2 A^ ABC h = = 3 43 ÖRNEK 1 ÖRNEK 4 A \"#$FõLFOBSÐ¿HFO A \"#$FõLFOBSÐ¿HFO 30° | |AB =DN 5 60° [ DF]åm [ AB]å 10 | |DC =DN F | |AF å=DN 53 x B 30° | |CD å=DN 3 D2 C 53 E 60° D B5 43 30° 60° 30° C4 | |:VLBSEBLJWFSJMFSFHÌSF AD LBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF DF æLBÀDNEJS 2 = ^ 5 3 h2 + 2 = 2 21 1JTBHPSUFPSFNJOEFO | |A&FE mm FE = 5 3 x 3 | | | |& CED mm ED =4 3 DF =9 3 1. 2 21 58 2. 7 3. 6 + 4 3 4. 9 3

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 5 ÖRNEK 7 D \"#$FõLFOBSÐ¿HFO A \"#$WF\"%& a3 FõLFOBSÐ¿HFO % \" $EPóSVTBM 30° 15° A 30° [ DF] a [ AB] = {E} E |DF| = |FE| 30° |BF| = |FC| 2a | |6 3 E FC =DN 15° m ( B%EF ) = 45° 45° a3 63 F6 60° 30° 60° 60° 75° 60° B D 12 C BF aC | |:VLBSEBLJWFSJMFSFHÌSF #% =YLBÀDNEJS :VLBSEBLJWFSJMFSFHÌSF DA PSBOLBÀUS & DFC | | | | | |DF mmPMVS = FE JTF AF dikmedir. BA | |#% =DN & AFC 30–60–90 üçgen A&DF JLJ[LFOBSÑÀHFO ÖRNEK 8 DA a 3 3 A \"#$ FõLFOBS Ð¿- HFO == BA 2 a 2 [ KD] m [ BC] 2a 60° a [ KF] m [ AC] F [ FE] m [ BC] 30° K 2a 30° 43 3a 8 60° xE 60° | AC | = 4 | AF | B aD 3a . | |4 C FE = 4 3 ÖRNEK 6 | |:VLBSEBLJWFSJMFSFHÌSF DE =YLBÀDNEJS A #%$FõLFOBSÐ¿HFO 3a = x + 4 j 8 = x + 4 j x = 4 30–60–90 üçgenleri |AB| = |AC| AD = 3 cm x | |DC =DN ÖRNEK 9 3 D A \"#$Ð¿HFO 2 30° 2 3 60° 30° (BóSMLNFSLF[J B1 1C <$(>B¿PSUBZ | |:VLBSEBLJWFSJMFSFHÌSF \"# LBÀDNEJS 2a 3 2a <\")>åm [ BC] G 2a a 30° 2 = ^ 2 3 h2 + 2 jx= 13 30° x 1 1JTBHPSUFPSFNJOEFO B H a3 C :VLBSEBLJWFSJMFSFHÌSF AC PSBOOFEJS AG | | | |AH IFNLFOBSPSUBZIFNZÑLTFLMJL CG IFNLFOBSPSUBZ & AC 2a 3 ABC == IFNBÀPSUBZ FöLFOBSÑÀHFO 3 AG 2 a 3 6. 13 59 7. 12 8. 4 9. 3 5. 2

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 10 ÖRNEK 12 \"ZõF CJS LºóEB CJS LFOBSOO V[VOMVóV CJSJN PMBO A \"#$FõLFOBSÐ¿HFOJ¿J[FSFLBõBóEBLJBENMBSJ[MJZPS x D r [BC]LFOBSOBBJUZÐLTFLMJóJ¿J[FSFLEJLNFBZBóO- 9 EBLJOPLUBZ)PMBSBLCFMJSMJZPS 5 r )OPLUBTOO[AC]LFOBSOBHËSFTJNFUSJóJOJBMQCV 60° 60° B C OPLUBZB)hOPLUBTPMBSBLJTJNMFOEJSJZPS | |\"ZöFhOJOZBQUôÀJ[JNMFSTPOVDV #)h LBÀCJSJNCVM- NVöUVS % % ( ABC ) ( DCB ) | |[ AB]åm A A [ AD] m = m = 60° AB =DN 33 30° 6 33 | |DC =DN 30° | |:VLBSEBLJWFSJMFSFHÌSF AD =YLBÀDNEJS 30° 6 H' B 37 H' 33 / / C õFLMJFöLFOBSÑÀHFOJUBNBNMB- ZBOQBSÀBmmÑÀHFOJEJS B 3H 60° k | |#)h = 3 7 CJSJN 1JTBHPSUFPSFNJOEFO 2k 5 + 2k = 9 + k A k3 30° k=4 9 D x= 4 3 x 5 60° 60° B C ÖRNEK 11 A \"#$FõLFOBSÐ¿HFO ÖRNEK 13 k 60° |AD| = |DC| A \"#$FõLFOBSÐ¿HFO E 2k 2 [ EF] m [ BC] D | BE | = | ED | =DN k 30° [ DE] m [ AB] | |AD =DN 3 5+a D | |FC =DN 7 3k 30° a3 a 3k 3 2k 2 30° 60° 60° 8C B 7 E 2a C 3k B 2F | | | |:VLBSEBLJ WFSJMFSF HÌSF EF + ED UPQMBN LBÀ | |:VLBSEBLJWFSJMFSFHÌSF DC kBÀDNEJS DNEJS && 72 = (5 + a)2 + ^ a 3 h2 1JTBHPSUFPSFNJOEFO AED ve BFE 30–60–90 üçgeni 4a2 + 10a - 24 = 0 2a2 + 5a - 12 = 0 3k 5k 4k = 8 + =8 2a -3 2 2 a4 |EF| + |ED| = 5k 3 j8 3 2a = 3 a = -4 2 5 + 2a = |DC| j |DC| = 8 10. 3 7 11. 8 3 60 12. 4 3 13. 8

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 14 \"#$FõLFOBS Ð¿HFO E A \"#$FõLFOBS A 4 3 30° Ð¿HFO [ PL] m [ AC 2 ' # $EPóSVTBM BM [ PM] m [ BC] 4D KH L [ PK] m [ AB [ FD] m[ AC] 30° P C 23 |AE| = |EB| PMNBLÐ[FSF | |C AD =DN 30° 60° FB | |:VLBSEBLJWFSJMFSFHÌSF DF LBÀDNEJS [ PK] + [ PL] = [ PM] + [ AH]US AED 30–60–90 üçgeni |AE| | |= ED = 2 3 |#&| = 4 F&EB 30–30–120 üçgeni |DF| = 6 3 ÖRNEK 15 %m/*m A A \"#$ FõLFOBS Ð¿- HFO F a 1 Ð¿HFO J¿JOEF F 12 E IFSIBOHJ CJS OPL- 3K 5 E UB P 4 [PE] // [BC] B DH [PD] // [AB] 60° [PF] // [AC]PMNBL C BD C ) Ð¿HFO J¿JOEF IFSIBOHJ CJS Ð[FSF OPLUBJTF \"#$FõLFOBSÐ¿HFO [ KE] // [ BC] [ KD] // [ AB] |PD| + |PE| + |PF| = a | | | | | |[ KF] // [ AC] KE =DN KD =DN KF =DN A :VLBSEBLJ WFSJMFSF HÌSF \"#$ ÑÀHFOJOJO ZÑLTFLMJôJ LBÀDNEJS F E |AC| = |,&| + |',| + |,%| H a | |AC =DN | |AH = 6 3 DN 30–60–90 üçgeninden BD C | HD | + | HE | + | HF | =I= a3 EJS 2 14. 6 3 61 15. 6 3

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 16 ÖRNEK 18 \" # WF $ OPLUBMBSOEB CVMVOBO FWMFS BSBTOEBLJ ZPMMBS A CJSCJSMFSJOF FõJUUJS &WMFS BSBTOEBLJ ZPMMBSO PMVõUVSEVóV Ð¿HFOTFMõFLJMBõBóEBHËTUFSJMNJõUJS b+a 35° 25° A H b B 60° 2b a 35° Ea C x = K F | | | |\"#$FõLFOBSÐ¿HFO EC=BF m ( % ) = 25°EJS EAC BC :VLBSEBLJWFSJMFSFHÌSF m ( A%FE ) = x LBÀUS | |,OPLUBTOEBCVMVOBO,FNBM\"NDBhOO \"# ZPMVOB [EH] m [AF] | |FOLTBV[BLMôNFUSF AC ZPMVOBFOLTBV[BL- [EH] [AF]ZJJLJFöQBSÀBZBBZSS\"'&JLJ[LFOBSPMVS | |MôNFUSF #$ ZPMVOBFOLTBV[BLMôNFUSF x = 35° PMEVôVOB HÌSF \"#$ ÑÀHFOTFM CÌMHFTJOJO BMBO LBÀ m2EJS A 6[BLMLMBSO UPQMBN \"#$ ÑÀHFOJOJO ZÑL- TFLMJôJEJS 40 Aa & k = 80 3 .120 30 ABC 2 50 40 3 = 4800 3 60° B C ÖRNEK 19 80 3 %% ÖRNEK 17 \"#$FõLFOBSÐ¿HFO \"#$%EËSUHFOJOEF m ( BCA ) = m ( DCA ) = 60°EJS A | |DK å=DN $OPLUBTOO[\"&õOOBHËSFTJNFUSJóJ# [ AF õOOB | |DF =DN K 10 3 | |DE å=DN HËSFTJNFUSJóJ%OPLUBTES B 11 x E ; [ BC]Ð[FSJOEF F F ; [ CD]Ð[FSJOEFTF¿JMFOJLJOPLUB E 60° | EC | = | CF |WF| AC | =DN 5C | |:VLBSEBLJWFSJMFSFHÌSF #% V[VOMVôVLBÀDNEJS D3 F 3C 60° 60° 60° 3 D 6 E 3 | |:VLBSEBLJWFSJMFSFHÌSF #$ LBÀDNEJS 30° 30° A 30° 60° B x + 1= 5 + 11 6C x = 15 D 120° |#$| = 10 3 6 |%#| = 6 3 63 B 16. 4800 3 17. 10 3 62 18. 35° 19. 6 3

&öLFOBS·ÀHFO TEST - 26 1. A \"#$FõLFOBSÐ¿HFO 4. A \"#$FõLFOBSÐ¿HFO | |AD =DN [ ED ] m [ AC ] | |6 xD |AE| = |EF| DC =DN E3 |BF| = |FC| D | |ED DN x2 B FC BC | |:VLBSEBLJWFSJMFSFHÌSF \"# =YLBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF #% =YLBÀDNEJS A) 4 3 B) 6 C) 6 2 A) 2 11 B) 4 3 C) 2 13 D) 2 14 E) 2 15 D) 8 3 & 2. A 5. A \"#$FõLFOBSÐ¿HFO E [ DE ] m [ AC ] 1 D F B x [ EF ] m[ BC ] E F3 |AD| = |DB| | |FC DN 2 C 30° C DB | |\"#$FõLFOBSÐ¿HFO m ( F%DC ) = 30° AF =DN | |:VLBSEBLJWFSJMFSFHÌSF DE =YLBÀDNEJS | |BE =DNEJS A) 2 B) 3 C) 6 | |:VLBSEBLJWFSJMFSFHÌSF DC LBÀDNEJS D) 2 3 E) 3 3 \" # $ % & 3. A 6. \"#$ FõLFOBS Ð¿HFOJOJO J¿JOEFLJ IFSI BOHJ CJS , D OPLUBTOEBOLFOBSMBSBEJLNFMFS¿J[JMNJõUJS E | | | | | |KE DN KD DN KF DN A D E 3 B 18 CF K2 \"#$FõLFOBSÐ¿HFO # $ 'EPóSVTBM 4 | AD| = | EC| = | | | |CF BC DNEJS B FC | |:VLBSEBLJWFSJMFSFHÌSF DF LBÀDNEJS :VLBSEBLJWFSJMFSFHÌSF ¦ \"#$ LBÀDNEJS A) 6 3 B) 9 3 C) 12 3 A) 12 3 B) 15 3 C) 18 3 E) 24 3 D) 18 3 E) 24 3 D) 21 3 1. C 2. D 3. C 63 4. D 5. D 6. C

TEST - 27 &öLFOBS·ÀHFO 1. A \"#$FõLFOBSÐ¿HFO 4. \"#$FõLFOBSÐ¿HFOJOJO[BC]LFOBSÐ[FSJOEFCJS% D [ KE ] // [ BC ] B OPLUBTBMOZPS K [ KD ] // [ AC ] | | | | | |%# =DN DC =DNPMEVôVOBHÌSF AD F E [ KF ] // [ AB ] A (ABC) = 16 3 cm2 LBÀDNEJS C A) 3 7 # $ 4 7 D) 6 7 & | | | | | |:VLBSEBLJ WFSJMFSF HÌSF ,% + ,& + ,' 5. A UPQMBNLBÀDNEJS \" # $ % & E FK | | | |2. \"#$FõLFOBSÐ¿HFO BC =DN CF = 3 3 DN B DC EJS A D \"#$FõLFOBSÐ¿HFO [KD] m [BC] [KE] m [AC] xE | | | |[KF] // [BC] KE = 2 3 DN KF =DN | |KD = 3 3 DNEJS B CF :VLBSEBLJ WFSJMFSF HÌSF \"#$ ÑÀHFOJOJO BMBO LBÀDN2EJS % :VLBSEBLJWFSJMFSFHÌSF m ( AED ) = x kaç dere- DFEJS A) 72 3 B) 78 3 C) 81 3 \" # $ % & D) 90 3 E) 91 3 | |3. \"#$FõLFOBSÐ¿HFO [KD] m [BC] BD =DN 6. ' OPLUBT \"#$ Ð¿HFOJOJO IFN J¿UFóFU ¿FNCFSJOJO | | | |KA =DN AD =YDNEJS NFSLF[J IFNEFBóSMLNFSLF[JEJS K A 6 F A Ex BD E C B3 D C | | | | | | | |3 DE = #% AD = k. DE PMNBLÑ[FSF LLBÀ :VLBSEBLJWFSJMFSFHÌSF YLBÀDNEJS CJSJNEJS \" # $ 3 13 A) 2 7 B) 3 C) 6 % & 3 19 % & 3 7 1. # 2. C 3. C 64 4. A 5. C 6. D

&öLFOBS·ÀHFO TEST - 28 1. A \"#$FõLFOBSÐ¿HFO 4. A \"#$FõLFOBS Ð¿HFO DE õFLMJOEFLJLBSUPO E 6 [CE] m [ED] [DE] // [BC] PMBDBL õFLJMEF [DE] CPZVO- | |BE =DN | |BD =DN DBLFTJMJZPS | |DC =YDN BC B2 D x C \"%&Ð¿HFOJ\"OPLUBTFUSBGOEBOFHBUJGZËOEFa :VLBSEBLJWFSJMFSFHÌSF YLBÀDNEJS EËOEÐSÐMÐZPS % WF & OPLUBMBSOO ZFOJ LPOVNMBS \" # $ % & I ITSBTZMB,WF-PMVZPS CL =CS :VLBSEBLJ WFSJMFSF HÌSF , OPLUBTOO # OPLUB- TOBV[BLMôLBÀCSEJS A) 15 # $ % & 5. A 2 EH 2. A \"#$WF\"%' DB C FõLFOBSÐ¿HFO BD \"#$FõLFOBSÐ¿HFO [BH] m [AC] | |EC =DN |ED| = |EF| | | | |AE = EB =DN )OPLUBTPSUBOPLUB | |F | BH | = | DE | =YUJS E AB = x C :VLBSEBLJWFSJMFSFHÌSF YLBÀDNEJS :VLBSEBLJWFSJMFSFHÌSF YLBÀDNEJS A) 3 B) 3 C) 4 D) 3 3 E) 6 A) 4 B) 4 3 $ % & 6 3 3. A \"#$FõLFOBSÐ¿- 6. A \"#$FõLFOBS HFO Ð¿HFO | |AD [BC]LFOB- [EF] m [AD] FG E SOOLFOBSPSUBZ E |AE| = |ED| KH C F [KD] m [BE] % BD m ( BDA ) = 75° | |BH =DN | |KD =DN | |FB =DN | |AH =YDN B D xC | |DC =YDN :VLBSEBLJWFSJMFSFHÌSF YLBÀDNEJS :VLBSEBLJWFSJMFSFHÌSF YLBÀDNEJS \" # $ 8 2 A) 2 3 - 2 B) 4 - 2 3 C) 2 D) 8 3 & D) 2 3 E) 4 + 2 3 1. D 2. D 3. C 65 4. D 5. D 6. A

TEST - 29 &öLFOBS·ÀHFO 1. A \"#$WF$&%FõLF- 4. \"õBóEBLJõFLJMEFWFSJMFO\"#$WF%&'FõLFOBSÐ¿- OBSÐ¿HFOMFS x I I I IHFOWF EK = EN EJS E \" & ,WF%EPóSV- TBM A B K I IBD =DN E KD 4 C D BN C I I:VLBSEBLJWFSJMFSFHÌSF AE =YLBÀDNEJS \" # $ % & F #VOBHÌSF EB PSBOLBÀUS NC 2. A A) 1 # $ 3 D) 2 E) 5 2 2 2 BC \"#$FõLFOBSÐ¿HFOJJ¿JOF4IBSGJË[EFõFõLFOBS Ð¿HFOMFSLVMMBOMBSBLõFLJMEFLJHJCJZFSMFõUJSJMNJõUJS #VZFSMFöJNTPOVDVOEBPMVöBOCPZBMCÌMHFOJO 5. A A BMBOOOCPZBT[CÌMHFOJOBMBOOBPSBOLBÀUS 22 32 32 16 D) 55 & LK A) B) C) 81 49 25 81 M F 2D 2 E 3. A A#$FõLFOBSÐ¿HFO B C B2 2C 1 -PHPUBTBSNDMBSCJSõJSLFUJ¿JOMPHPUBTBSMBZBDBL- MBSESôJSLFUJOJTUFEJóJMPHPôFLJM*EFLJFõLFOBSÐ¿- E IAFI = IBFI HFOJôFLJM**EFLJHJCJLËõFMFSJOEFOJUJCBSFOCJSJN V[VOMVóVOEB LFTFO ZBS¿BQ CJSJN PMBO ¿FNCFS F I AE I = I DC I =CS õFLMJOEFEJS 5 I EC I = I BD I =CS G B 5 D1 C #VOBHÌSF FöLFOBSÑÀHFOJOCJSLFOBSV[VOMVôV LBÀCJSJNEJS I I:VLBSEBLJWFSJMFSFHÌSF FG V[VOMVôVLBÀCJ- A) 4 + 2 3 B) 6 C) 3 3 + 4 SJNEJS A) 3 B) 2 3 C) 13 3 D) 5 3 E) 3 3 % & 62 1. E 2. # 3. C 66 4. # 5. #

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, AÇIORTAY %m/*m ÖRNEK 3 A A |DE| = |DC| 6 m ( B%AD ) % BC = m ( DAC ) D E | |AE =DN \"¿PSUBZÐ[FSJOEFLJCJSOPLUBOOB¿OOLPMMBS- 10 4 | |BD =DN OBPMBOV[BLMLMBSFõJUUJS 25 |BD| = |DC| | |2 DE = 2 5 DN |AB| = |AC| B2 D | |C AB =YDN :VLBSEBLJWFSJMFSFHÌSF YLBÀDNEJS | |%OPLUBTOEBO AC ZFEJLJOEJSFMJN x =DN ÖRNEK 1 A \"#$CJSÐ¿HFO [AD]B¿PSUBZ % = 30° m ( ABC ) 42 42 % = 45° m ( ACB ) 30° 45° | |DC =DN B x D 8C | |BD =YDN :VLBSEBLJWFSJMFSFHÌSF YLBÀDNEJS ÖRNEK 4 | | | |%OPLUBTOEBO AC ve \"# ZFEJLNFMFSÀJ[FMJN A \"#$WF\"$%CJSÐ¿HFO %% x=8 2 4 m ( BAC ) = m ( CAD ) ÖRNEK 2 B 10 3 |CD| = |BC| A \"#$WF\"$%CJSÐ¿HFO 3 5x D | |AD =DN 7 .4 5 | |AB =DN m % ) = % | |BC =DN B ( BAC m ( CAD ) 5 | |AC =YDN C 12 [ CD ] m [ AD ] 13 x :VLBSEBLJWFSJMFSFHÌSF YLBÀDNEJS | |BC DN . D | |AB DN | | | |CD LFOBSOO AC LFOBSOBHÌSFTJNFUSJôJOJBMBMNWF$ 5 5 | |CD DN | |OPLUBTOEBO \"# V[BOUTOBEJLJOEJSFMJN C x2 = 42 + 72 x = 65 cm :VLBSEBLJWFSJMFSFHÌSF x kaç EFSFDFEJS | |x = \"# OJO V[BOUTOB $ OPLUBTOEBO EJLNF JOEJ- relim. 1. 8 2 2. 19 67 3. 10 4. 65

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr %m/*m ÷À\"ÀPSUBZ5FPSFNJ %m/*m A A DE [AN] J¿ B¿PSUBZ I c b PMNBLÐ[FSF c = b EJS xy B FC B xNyC ¶¿HFOJOJ¿B¿PSUBZMBSUFLCJSOPLUBEBLFTJõJS ÖRNEK 6 #VOPLUBÐ¿HFOJOJ¿UFóFU¿FNCFSJOJONFSLF[J- EJS A \"#$Ð¿HFO A |AD| = |AE| [ AD]B¿PSUBZ |BD| = |BF| |EC| = |FC| | |12 9 AB =DN DE | |AC =DN I | |BD =DN B4 Dx C B FC | |:VLBSEBLJWFSJMFSFHÌSF DC =YLBÀDNEJS |DI| = |EI| = |IF| =S 12 9 4 =x ÖRNEK 5 x =DN A 2 \"#$EJLÐ¿HFOJOEF 2 I OPLUBTO J¿UFóFU ¿FNCFSJOJO NFSLF- 2 I2 x [JPMNBLÐ[FSF ÖRNEK 7 \"#$Ð¿HFO 4 x | |IH =DN A [ CD]B¿PSUBZ 2 | |C BH =DN 2 D | |AD =DN B4H x+1 | |DB = ( x + DN | |AC = ( 4x - DN | | | |AB =DN HC =YDN B 3x + 3 4x – 2 | |BC = ( 3x + DN C :VLBSEBLJWFSJMFSFHÌSF YLBÀDNEJS :VLBSEBLJWFSJMFSFHÌSF YLBÀDNEJS | | | | | |I OPLUBTOEBO \"# ve AC ZF JOEJSJMFO EJLNFMFS IH a 3x + 3 4x - 2 FöJUUJS = \"#$ÑÀHFOJOEF1JTBHPSUFPSFNJOEFO x+1 2 (4 + x)2 = 62 + (2 + x)2 x =DN 3a x + 1 k 2^ 2x - 1 h = 2 x+1 x =DN 5. 6 68 6. 3 7. 2

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 8 ÖRNEK 11 &OPLUBT \"#$Ð¿HFOJOJ¿UFóFU¿FNCFSJOJONFSLF[JEJS A \"#$Ð¿HFO A | |\"% =DN 4 8 <$%>B¿PSUBZ 6 | |#$ =DN D 3 |%&| = |&$| | |\"$ =DN D k 5x | |#$ =DN 6 E :VLBSEBLJ | |\"% =DN WFSJMFSFHÌSF 3k Çevre ( ABC ) C LBÀDNEJS B 18 B 10 C | |:VLBSEBLJWFSJMFSFHÌSF CD = x LBÀDNEJS | |BD 18 ¦Ì[ÑN A = j BD = 6 cm a–2 k 3k 10–a 4 H' | |18 AC = j AC = 18 cm Dh 66 Ç(ABC) = 48 cm 5 x h ÖRNEK 9 B aH 10–a C A \"#$Ð¿HFO \"#$Ð¿HFOJOEFB¿PSUBZUFPSFNJOEFO 5 <$%>B¿PSUBZ | |8 = 10 j #% = 5 DNEJS 5k [\"#] m [#$] 4 BD D | |\"% =CS %OPLUBTOEBO [\"$> WF [#$] LFOBSMaSOBEJLNFMFSJOEJ- 3 SFMJN#%)WF\"%)hÐ¿HFOMFSJOEF1JTBHPSUFPSFNJVZ- B 3k | |%# =CS HVMBOSTB 25 – a2 = 16 – (a – 2)2 j a = 13 DNCVMVOVS C 4 :VLBSEBLJWFSJMFSFHÌSF \"#$ÑÀHFOJOJOÀFWSFTJLBÀ %)$Ð¿HFOJOEF1JTBHPSUFPSFNJVZHVMBOSTB CJSJNEJS h2 + (10 – a)2 = x2 AC BC | | | |AC =L BC =L . = 6 4447 4448 Ç(ABC) = 24 cm 2 2 53 25 - f 13 13 j x=2 15 cmEJS 1JTJBHPSUFPSFNJOEFO p + f 10 - p = x2 44 | |AB = 4k = 8 j k = 2 A #VTPSVOVO¿Ë[ÐNÐBõBóEB- ÖRNEK 10 c LJCBóOUkVMMBOMBSBLEBZBQ- nb MBCJMJS A ôFLJMEFLJ \"#$ Ð¿HF- n2 =CD-YZ OJOEF I OPLUBT J¿ UF- óFU ¿FNCFSJOJO NFS- B xNyC LF[JEJS 12 3m %ö\"ÀPSUBZ5FPSFNJ I 12 m | \"#| = | \"$| =DN %m/*m | |#$ =DN B4 H | |4 C \"I =YDN A :VLBSEBLJWFSJMFSFHÌSF YLBÀDNEJS [\"%] \"#$ Ð¿HFOJOJO | | | |AC HC c EõB¿PSUBZJTF = b x = b EJS j AI =N IH =N 4m)2 + 42 = 122 a x+a c AI IH x m = 2 2 j x = 6 2 cm BC D 8. 48 9. 24 10. 6 2 69 11. 2 15

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 12 ÖRNEK 15 A \"#$Ð¿HFOJOEF \"#$Ð¿HFO 10 [ AD ]EõB¿PSUBZ A 45° [AB] m [AC] 4 45° # $ %EPóSVTBM % = 45° m ( CAD ) | |AB =DN | |AC =DN 4 3 |BC| = |BD| | |D CD =DN Bx C | |2x D AC =DN BxC 6 | |:VLBSEBLJWFSJMFSFHÌSF #$ =YLBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF #$ =YLBÀDNEJS DC AC 2x 4 = &= 3x AB 64 DB AB = | |\"# =DN & 6 + x 10 ABC x =DN x2 = 62 + 42 ( ÑÀHFOJOEF1JTBHPSUFPSFNJOEFO x = 2 13 DN ÖRNEK 13 \"#$Ð¿HFOJOEF[ AN]\"B¿TOOJ¿B¿PSUBZ ÖRNEK 16 Bilgi: [AD] \"#$ÑÀHFOJOJOEõBÀPSUBZPMNBLÑ[FSF % (NAC) A | | | |m(B%AN) = m = 60° AB =DN AN =DN | |PMEVôVOBHÌSF AC V[VOMVôVLBÀ DNEJS A 60° NC 6 c = b 60° 60° 10 CB 10 ax 6 |NC| = 3k BC D |/#| = 2k | |AD 2 =Y Y+ a) -CD AC 10 B 2k N 3k = GPSNÑMÑJMFCVMVOBCJMJS 3k 2k | |C AC =DN ÖRNEK 14 \"#$Ð¿HFO A \"#$Ð¿HFO A [ AD ]EõB¿PSUBZ <\"%>J¿B¿PSUBZ # $ %EPóSVTBM <\"&>EõB¿PSUBZ x | |AB =DN [ AC] m [ BE] | |BC =DN 2k 86 6 B k D 3 C 12 E | |DC =DN B 4C 12 | |AC =DN | |CE =DN D | |:VLBSEBLJWFSJMFSFHÌSF \"# LBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF AD =YLBÀDNEJS % 2 | |CD 6 DAE = j DC =DN | | | |m CD + 4 8 ( ) = 90° AC = 3.12 j AC =DN ²LMJEUFPSFNJ x2 = 12.(16) - 6.8 j x =DN %öBÀPSUBZUFPSFNJ (2k)2 = 62 + (3 + k)2 jL 1JTBHPSUFPSFNJ | |\"# =DN 12. 9 13. 15 14. 10 70 15. 2 13 16. 12

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 17 ÖRNEK 20 A A \"%$Ð¿HFO k | |BC =DN 3k 4k Bb k | |BD =DNWF 2a 3k 4k 2 b D x B 3 E 4C aC 10 a | AB | = | AC |EJS \"#$Ð¿HFOJOEF [ AE]J¿B¿PSUBZ [ AD]EõB¿PSUBZ % % % m ( DBC ) = 2m ( BCD ) | | | |# & $EPóSVTBM BE =DN EC =DNPMEVôVOB | |HÌSF %# =YLBÀDNEJS D x 3k :VLBSEBLJWFSJMFSFHÌSF \"#$ÑÀHFOJOÀFWSFTJLBÀ = j x = 21DN DNEJS x + 7 4k | |10 2 = DC EöBÀPSUBZES ÖRNEK 18 10 + k k A \"%$Ð¿HFOJOEF 5 k= [ AB] EõB¿PSUBZ 2 ¦ \"#$ =DN 5 E [ DE]J¿B¿PSUBZ ÖRNEK 21 2 (FPNFUSJEFSTJOEFZBQMBOCJSFULJOMJLUFBõBóEBLJBEN- # % $EPóSVTBM MBSJ[MFOFSFLHFPNFUSJLCJS¿J[JNZBQMZPS B x D 3C | | | | | |AD =DN DC =DN EC =DNPMEVôVOBHÌ- | |SF #% = x LBÀDNEJS 53 10 = j AE = ÷ÀBÀPSUBZUFPSFNJ AE 2 3 r \"#$Ð¿HFOJ¿J[JOJ[ x5 j x =DN %öBÀPSUBZUFPSFNJ r \"LËõFTJOJOJ¿B¿PSUBZEPóSVTVOV¿J[JOJ[[BC]LF- = OBSOLFTUJóJOPLUBZ%OPLUBTPMBSBLCFMJSMFZJO x + 3 16 3 ÖRNEK 19 r $LËõFTJOJOJ¿B¿PSUBZEPóSVTVOV¿J[JOJ[[AB]LF- OBSOLFTUJóJOPLUBZ&OPLUBTPMBSBLCFMJSMFZJO &OPLUBT \"#$EJLÐ¿- r [CE] a [AD] = {F}PMTVO HFOJOJO Eõ UFóFU ¿FN- K CFSJOJONFSLF[JEJS | | | | | |r BC =DN AB =DN AC =DN 3k [ CA] m[ BK] :VLBSEBLJ BENMBS J[MFOFSFL ÀJ[JMFO ÑÀHFOEF AF 3|AB| = 2 |AK| A E | |AC =DN PSBOLBÀUS FD 2k A AB BD 6 = B 10 C AC DC | |:VLBSEBLJWFSJMFSFHÌSF \", LBÀDNEJS 8 2k 6 AC AF E = | |3k 6 = j #$ =DN F CD FD 5k BC \"#$ÑÀHFOJOEF1JTBHPSUFPSFNJOEFO k AF 43 =2 | |2k =DNj k =DN \", =DN BD C FD 17. 21 18. 45 19. 12 71 20. 7 21. 2

TEST - 30 \"ÀPSUBZ 1. A \"#$Ð¿HFOJOEF 4. A \"#$Ð¿HFOJOEF [ AB ] m [ AC ] 8 <\"/>J¿B¿PSUBZ 3 B 4N N <#/>J¿B¿PSUBZ | |x AB DN | |BN DN 6 | |AB DN | |NC DN | |C AN DN B 3C | |:VLBSEBLJWFSJMFSFHÌSF AC YLBÀDNEJS | | | | :VLBSEBLJWFSJMFSFHÌSF #$ + NC UPQMBN LBÀDNEJS A) 2 5 B) 2 6 $ % & \" # $ % & 2. #JMHJ [AN] \"#$ÑÀHFOJOJOJÀBÀPSUBZPMNBL 5. | |A BC =DN Ñ[FSF A O2 =CD-YZ c GPSNÑMÑ JMF IF- b TBQMBOBCJMJS B xNyC A \"#$Ð¿HFOJOEF B 20 C x <\"/>J¿B¿PSUBZ | |AB DN ôFLJMEF \"#$% Ð¿HFOTFM CËMHFTJ CJ¿JNJOEFLJ LºóU |AC| = | |BC DN WFSJMNJõUJS#VLºóU%` [BC]PMNBLÐ[FSF [AD]CP- BN C ZVODBLBUMBOEóOEBBõBóEBLJõFLJMFMEFFEJMJZPS | |PMEVôVOBHÌSF AN =YLBÀDNEJS A) 6 B) C) 2 2 D) 3 E) 10 A [DA] m [AC] 3. A \"#$Ð¿HFO | AB | = 4|&#h| 2 [ BD ] J¿ B¿PS- D UBZ | |AD DN BD Ex C 3 B' | |DC DN BC PMEVóVHËSÐMÐZPS :VLBSEBLJWFSJMFSFHÌSF YLBÀDNEJS | | :VLBSEBLJWFSJMFSFHÌSF \"# OJOFOCÑZÑLUBN TBZEFôFSJLBÀUS \" # $ % & \" # $ % & 1. D 2. E 3. # 72 4. D 5. E

\"ÀPSUBZ TEST - 31 1. A \"#$Ð¿HFO 4. A [ BA ] m [ CA ] 2 x D D N B E <#%>B¿PSUBZ 3 26 I IDE DN I IEC DN 24 B C KC I I I IEK =DNPMEVóVOBHËSF \"# =YLBÀDNEJS \"#$Ð¿HFOJOEF [ AD ]EõB¿PSUBZ [ BN ]J¿B¿PS- A) 2 3 B) 3 2 C) 2 6 D) 3 3 E) 4 2 | | | | | |UBZ AN =DN NC =DN DB =DN PMEVôVOBHÌSF ¦ \"%$ LBÀDNEJS A) 35 + 5 7 B) 35 + 8 7 C) 35 + 10 7 D) 35 + 12 7 E) 35 + 15 7 2. A \"#$Ð¿HFO [ AB ] m [ BC ] B 3N [ AN ]J¿B¿PSUBZ 5. E | |BN =DNWF A | AB | + | AC | =DN 6 C x4 & :VLBSEBLJWFSJMFSFHÌSF A^ ABC hLBÀDN2EJS B DC \" # $ % & \"#$Ð¿HFO m ( E%AB ) = m ( B%AD ) = % ) m ( DAC | | | |AC =DN AB =DN 3. #JMHJ [AD] \"#$ÑÀHFOJOJOEõBÀPSUBZ | | PMEVôVOBHÌSF AD =YLBÀDNEJS | |A AD 2 =Y Y+ a) -CD \" # $ % & c GPSNÑMÑ JMF IFTBQMBOBCJ- b MJS ax BC D 6. A %\"#$Ð¿HFOJOJ¿UF- óFU¿FNCFSNFSLF[J \"#$Ð¿HFO &\"#$Ð¿HFOJOJOEõ A D UFóFU¿FNCFS [ AN ]J¿B¿PSUBZ 2 NFSLF[JE JS 3 24 [ AD ]EõB¿PSUBZ | |B C DC = 2 3 DN | |AB =DN | |EC DNWF D3 | |B N C DB =DN 7 8 | |BE DN E | |AC =DN | | | |:VLBSEBLJWFSJMFSFHÌSF AN 2 + AD 2UPQMB- | |PMEVôVOBHÌSF #% LBÀDNEJS NLBÀDN2EJS A) 2 3 B) 3 3 C) 4 2 D) 4 2 E) 6 2 \" # $ % & 1. # 2. # 3. A 73 4. C 5. E 6. #

TEST - 32 \"ÀPSUBZ 1. \"#$CJSÐ¿HFO *J¿UFóFU¿FNCFSJONFSLF[JEJS 4. A \"#$Ð¿HFO <\"/>B¿PSUBZ A 2 [ CH ] m [ AB ] DE H K I 4 | |AH =DN | |HB =DN BC BN C | | | |[ DE ] // [ BC ] AB =DN AC =DN |KC| = 4 |HK| PMEVôVOBHÌSF ¦ \"%& LBÀDNEJS \" # $ % & | |:VLBSEBLJWFSJMFSFHÌSF #$ LBÀDNEJS A) 5 3 B) 2 19 C) 4 5 D) 3 15 E) 2 21 5. A \"#$Ð¿HFO 2. A [BA] m [CA] x [AH] m [BC] E BH C m (A%CB) = m (B%CD) D 6 I IHD =DN 18 9 2 I ID CD =DN BC \"#$CJSÐ¿HFO m ( D%CB ) = m ( D%CA ) = 2a I IPMEVôVOBHÌSF AH =YLBÀDNEJS | |% % A) 2 7 B) 4 2 C) 2 10 m ( DCE ) = m ( ECA ) = a BC =DN D) 4 3 E) 2 13 | | | |AB =DN AC =DN | |PMEVôVOBHÌSF ED LBÀDNEJS \" # $ % & 6. A \"#$Ð¿HFO 3. A \"#$CJSÐ¿HFO [ BE ]WF[ DE ] <$%>B¿PSUBZ 17 E B¿PSUBZ D | |D AD =DN 1 [ DH ] m [ BC ] Fx | |BD =DN | |C m % ) > 90° ( BAC BC =DN | |B H 13 C DH DN | |B FC =YDN | |AD = 17 cmWF HC DN | | :VLBSEBLJWFSJMFSFHÌSF FC =YLBÀDNEJS | |PMEVôVOBHÌSF AC LBÀDNEJS A) 1 B) 1 C) 2 % & 3 3 2 3 2 \" # $ % & 1. E 2. A 3. E 74 4. # 5. E 6. C

\"ÀPSUBZ 3. A TEST - 33 :FõJMBMBO 1. B :VLBSEB JLJ LFOBS EJL LFTJõFDFL õFLJM- A EFWFSJMFOCJSQBSLO ÐTUUFOHËTUFSJNJ¿J[- EF D HJMFSMFHËTUFSJMNJõUJS K BC C ôFLJM Ð¿ BSLBEBõ UBSBGOEBO ZBQMBO CJS TJTUFNJO | |,FOBSMBS ZÐSÐZÐõ ZPMV õFLMJOEF PMBO QBSLO \"# NPEFMMFONJõ IBMJEJS \"#$ EJL Ð¿HFOJOJO LFOBSMBS | | | |LFOBSNFUSF #$ LFOBSJTFNFUSF \"% FWMFSJCJSCJSJOFCBóMBZBOQBUJLBZPMMBSES | |WF %$ LFOBSMBS JTF CJSCJSMFSJOF FõJUUJS #V ZPMMBS [EF] // [#$] EõOEBZFOJCJSZÐSÐZÐõZPMVZBQNBLJTUFZFOQBSL ZËOFUJNJ # WF % OPLUBMBSO CJSMFõUJSFDFL õFLJMEF #VTJUFZF,NFSLF[MJWFQBUJLBZPMMBSBUFóFUPMBDBL EPóSVTBMCJSZPMZBQNBLJTUJZPSMBS õFLJMEFCJSZÐ[NFIBWV[VZBQMZPS :BQBDBLMBSCVZPMVOLBÀNFUSFPMNBTHFSFLJS | | | |#& =NFUSF '$ =NFUSF \" 90 2 # $ #VOBHÌSF #WF$OPLUBMBSOEBPUVSBOLPNöV- MBSBSBTLBÀNFUSFEJS % 110 2 & 130 2 \" # $ % & 2. Hasan 4. ôFLJMEF\"#$EJLÐ¿HFOTFMCËMHFTJCJ¿JNJOEFLJLºóU Ali Hüseyin WFSJMNJõUJS A A [\"#] m [\"$] [\"$] =DN BC BDC ôFLJMEFLJLºóU[\"#]LFOBS[#$]Ð[FSJOFHFMFDFLCJ- \"#$Ð¿HFOTFMCËMHFTJõFLMJOEFLJCJSQBSLUB\"OPL- | |¿JNEF \"$ LFOBSÐ[FSJOEFOBMOBOCJS%OPLUBT UBTOEBLJ\"MJ )BTBOWF)ÐTFZJOHËTUFSJMFOEPóSVM- JMF[#%]CPZVODBLBUMBOZPS UVMBSEB IBSFLFU FEJZPSMBS [\"%] Ð¿HFOTFM CËMHFOJO A | |\"h$ =DN B¿PSUBZ EPóSVTV PMNBL Ð[FSF CFMJSUJMFO EPóSVMUV- D | |%$ =YDN MBSEBLJ # % WF $ OPLUBMBSOB HFMEJLMFSJOEF EVSV- x ZPSMBS\"MJJMF)ÐTFZJOBSBTOEBNFUSF )BTBOJMF )ÐTFZJOBSBTOEBNFUSFNFTBGFPMEVóVWF)ÐTF- B A' C ZJOhJONFUSFZPMBMEóCJMJOJZPS | | :VLBSEBLJWFSJMFSFHÌSF %$ =YLBÀDNEJS #VOBHÌSF ÑÀHFOTFMCÌMHFOJOÀFWSFTJLBÀNFU- SFEJS \" # 15 $ % 17 & 4 4 \" # $ % & 1. A 2. D 75 3. D 4. D

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ,&/\"3035\": %m/*m ÖRNEK 2 \"#$ Ð¿HFOJOEF % WF & LFOBSPSUB OPL- #JSÐ¿HFOEFCJSLFOBSOPSUBOPLUBTOLBSõLË- A UBMBSES ZFõF CJSMFõUJSFO EPóSV QBS¿BTOB P LFOBSB BJU LFOBSPSUBZEFOJS 2(x+1) E | |AD = (x + 2 | GD | = x + | |A AD =7a 2x–1 | |BG = 2x - 2 C G 2x–1 x+1 BD BDC | |:VLBSEBLJ WFSJMFSF HÌSF GE OJO TBZTBM EFôFSJ a LBÀUS #JSÐ¿HFOEFLFOBSPSUBZMBSOLFTJõUJLMFSJOPLUB- ZBBôSMLNFSLF[JEFOJS(JMFHËTUFSJMJS (BôSMLNFSLF[JEJS A |AG|= 2.|GD| |#(| = 2.|GE| | |AD = 3(x + 1) = (x + 1)2 (x + 1) = 3 j x = 2 2x - 1 3 GE = = 22 Fk 2n E %m/*m 2m Gm 2k n BD C A [FE] // [BC] |AG| = 2 |GD| [FE] = 6BC@ |BG| = 2|GE| |CG| = 2|GF| 3x 2 F KE |FK| = |KE| x |AK| = |KD| ÖRNEK 1 G | AK | = 3x 2x | KG| = x A | |B D C GD = 2x 2x [FE]EPóSVQBS¿BTOB\"#$Ð¿HFOJOJOPSUBUBCB- E m Gk F OEFOJS 2k 2m x %JLÐ¿HFOEFIJQPUFOÐTFBJULFOBSPSUBZOV[VO- MVóVIJQPUFOÐTÐOV[VOMVóVOVOZBSTOBFõJUUJS BD C A \"#$Ð¿HFOJOEF (BóSMLNFSLF[JEJS cb Va | GD | + | GF | + | G E | =DN | | | | | |:VLBSEBLJWFSJMFSFHÌSF GA + (# + GC UPQla- B DC a NLBÀDNEJS | | | | | |AD = BD = DC .VIUFõFNÐ¿MÐ | | | |(BôSMLNFSLF[J GD =YJTF AG = 2x tir. Va = a x + k + m =DN 2 2(x + k + m) =DN 1. 20 76 3 2. 2

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 3 ÖRNEK 5 A \"#$ Ð¿HFOJOEF % & ' A \"#$EJLÐ¿HFOJOEF LFOBSPSUBOPLUBMBSES (BóSMLNFSLF[J 3x 4 EK | |KG =DN 8 Gx | |GD =DN | |AB =DN x F 2 G B 6D6 C 2x B DC | |:VLBSEBLJWFSJMFSFHÌSF AC =YLBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF AD LBÀDNEJS |GA| = 2.|GD| |AD |= |#%| = |DC| 6x = 12 x=2 1JTBHPSUFPSFNJOEFOY2 + 82 = 122 x = 4 5 DN ÖRNEK 6 \"#$EJLÐ¿HFOJOEF (LFOBSPSUBZMBSO A LFTJNOPLUBTES x | |AC =DN 12 D G x ÖRNEK 4 By E y C B A | | | |:VLBSEBLJWFSJMFSFHÌSF AG 2 + GC 2 UPQMBNLBÀ x DN2EJS 2 E3 8x 2 %#$1JTBHPSUFPSFNJ \"#&1JTBHPSUFPSFNJ G6 x | | | |DC 2 =Z2 + x2 AE 2 = 4x2 +Z2 4 2 x 2+ 2 5a 2 2 k DC AE = + x y DC | |AC 2 = 144 = 4x2 +Z2 j x2 +Z2 = 36 \"#$Ð¿HFOJOEF(LFOBSPSUBZMBSOLFTJNOPLUBTES \"#$1JTBHPSUFPSFNJOEFO | | | |[ AD] m [ CE] EG =DN GD =DNPMEVóVOBHË- |DC|2 + |AE|2 = 180 | |SF #( =YLBÀDNEJS 2|DC| = 3|GC| 2|AE| = 3|AG| | |#( OJOV[BOUT\"($ÑÀHFOJOEFONVIUFöFNÑÀMÑ DC 2 = 9 GC 2 x =DN 4 AE 2 = 9 AG 2 4 DC 2 + AE 2 = 9 a GC 2 + AG 2 k 4 180 = 9 a GC 2 + AG 2 k 4 |GC|2 + |AG|2 = 80 3. 2 4. 10 77 5. 4 5 6. 80

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER ÖRNEK 9 www.aydinyayinlari.com.tr ÖRNEK 7 A ABC üçgen (BóSMLNFSLF[J Bilgi:#JSEJLÑÀHFOEF EJLLÌõFEFOJOEJSJMFOLFOBS- 12 F G 32 E |AB| = |AC| PSUBZ JMF EJôFS LFOBSPSUBZMBS BSBTOEB BõBôEBLJ CB- 62 [ BE] m [ CG] ôOUWBSES 6 | AG | = 12 cm | |A BF = Vb | AE | = Va D F | CD | = Vc B 6 D 6C G 5V2b = Vc2 + V2a | |:VLBSEBLJWFSJMFSFHÌSF GE LBÀDN EJS BE C | | | | | | | |AB = AC EFO AG OJO V[BOUT GD NVIUFöFN ÑÀMÑ (%#ÑÀHFOJOEF1JTBHPSUFPSFNJOEFO | BG | | | | | | |BG = 6 2 GE = Buna göre, bir ABC üçgeninde m (WA ) = 90° ve 2 EFO GE = 3 2 cm Va2 + Vb2 + V2c = 294 olEVôVOBHÌSF 7BLBÀUS ÖRNEK 10 2 22 A 5V = V + V ABC üçgen a bc 7 | AB | = 7 cm 222 B3 | |5 AC å= 5 cm V + V + V = 294 | BD| = | DC | = 3 cm abc D3 C 22 6V = 294 j V = 49 = 7 aa | |:VLBSEBLJWFSJMFSFHÌSF AD kBÀDNEJS ¦Ì[ÑN A ÖRNEK 8 7 5 h A ABC üçgen 3–x [ AE] m [ CD] B 3 Hx D 3 3 C | AD | = | DB | = 3 cm D 2a | BE | = | EC | = 4 cm \")% \"#%WF\")$Ð¿HFOMFSJOEFPisagor teoremini uy- 3b x HVMBZBMN x/2 | |AD 2 = h2 + x2 * x a 2b 72 = h2 + -Y 2 ** 52= h2 + +Y 2 *** BEC | |:VLBSEBLJWFSJMFSFHÌSF AC LBÀDNEJS **WF***EFOLMFNMFSJOJUBSBGUBSBGBUPQMBZBMN 49 + 25 = 2h2 + 2x2 +PMVS#VEFOLMFNEF B2 + b2 =1JTBHPSUFPSFNJOEFO h2 + x2ZFSJOF*EFLJFõJUJOJZB[BMN 4b2 +B2 = 16 B2 + b2) = 25 74 = I2 + x2 + 18 | | | |56 = 2 AD 2 j AD = 2 7 DNEJS A #V TPSVOVO ¿Ë[ÐNÐ B2 + 4b2 = x2 j x2 = 20 j x = 2 5 BõBóEBLJCBóOULVMMB- 2 OMBSBLEBZBQMBCJMJS 2 9x c b a2 ¦LBSN V = Va 2 2Va2 = b2 + c2 - b4 2 + 2 = 9^ 2 + 2 h V V a b ac 2 22 7B m7DJTF 2 22 Ba D a C V = V + V V = V + V ) 22 b a c b a c 7. 7 8. 2 5 78 9. 3 2 10. 2 7

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 11 ÖRNEK 13 A Bilgi: ·ÀHFOJOCJSLÌõFTJOEFOJOEJSJMFOLFOBSPSUBZWF ZÑLTFLMJLBSBTOEBLJV[BLML A x 2 4 4 23 23 23 c ha b B D EC Va ABC üçgeninde, | BD | = | DE | = | EC | B H xD C | AD | = | AC | = 4 cm | |ve AE = 2 cm dir. a | |:VLBSEBLJWFSJMFSFHÌSF AB =YLBÀDNEJS | |2.a.x = b2 - c2 [AE] m [BC] x2 = 22 + ^ 4 3 h2 1JTBHPSUFPSFNJOEFO GPSNÑMÑJMFIFTBQMBOBCJMJS x = 2 13 A ABC üçgen |BD| = |DC| 10 12 [ AH ] m [ BC] | AB | = 10 cm x | BC | = 11 cm B HD C 11 . | AC | = 12 cm | |:VLBSEBLJWFSJMFSFHÌSF HD LBÀDNEJS | |2.x.11 = 122 - 102 x = 2 cm ÖRNEK 12 A ABC üçgen ÖRNEK 14 2k (BóSMLNFSLF[J (FPNFUSJEFSTJOEFZBQMBOCJSFULJOMJLUFBõBóEBLJBEN- MBSJ[MFOFSFLHFPNFUSJLCJS¿J[JNZBQMZPS G [ AB] m [ AC] 52 | | | |r AB = 8 cm, AC = 15 cm ve [ AB ] m [ AC ]PMBDBL |AB | = |AC| õFLJMEFCJS\"#$Ð¿HFOJ¿J[JOJ[ k | |C GC = 5 2 cm r \"#$Ð¿HFOJOJOBóSMLNFSLF[J(OPLUBTES B 3k x 3k r (OPLUBTOEBO[BC]ZFJOEJSJMFOEJLNFOJOBZBóO) | |:VLBSEBLJWFSJMFSFHÌSF BC å=YLBÀDNEJS | |PMTVO GH = x cm \"EBOJOEJSJMFOEJLNF(EFOHFÀFS | |:VLBSEBZBQMBOÀJ[JNFHÌSF GH YLBÀDNEJS 1JTBHPSUFPSFNJOEFO 9k2 + k2 = 50 A 5FNFM CFO[FSMJL UFPSFNJO- k= 5 EFO \" EBO JOEJSJMFO EJLNF |BC| = 6 5 cm YPMVS 8 2k Aa & k = 17.3x = 8.15 3x G ABC 15 22 xk 40 x = cm 17 B 17 C 11. 2 13 12. 6 5 79 13. 2 40 14. 17

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 15 ÖRNEK 17 ôFLJMEFWFSJMFOCJS\"#$Ð¿HFOJCJ¿JNJOEFLJLºóEO[BC] A LFOBS %&EPóSVTVOBQBSBMFMEJS(OPLUBT\"#$Ð¿HFOJ- M N OJOBóSMLNFSLF[JEJS D R A E P BC D E B G \"#$CJSEJLÐ¿HFO1OJO&ZFHËSFTJNFUSJóJ/ %ZF HËSFTJNFUSJóJ.EJS\"OO%ZFHËSFTJNFUSJóJ# &ZF C HËSFTJNFUSJóJ$EJS ôFLJMEFWFSJMFO\"%&Ð¿HFOJõFLMJOEFLJLºóU[DE]CPZVO- | | | |MN =DNPMEVôVOBHÌSF AP LBÀDNEJS DBLBUMBOEóOEBBõBóEBLJõFLJMFMEFFEJMJZPS 1OPLUBT\"#$ÑÀHFOJOJOBôSMLNFSLF[J[DE][MN] A | |KL =DN DE 1 9 2k == MN 2 18 | |DE =DN DE 1 9 == BC 2 18 |#$|= 3 |AP| | |j AP =DN D 6E kk G BK 3 C L k ÖRNEK 16 A' \"#$Ð¿HFOJOEF [ BD]LFOBSPSUBZ &`[AB]PMNBLÐ[F- | |:VLBSEBLJWFSJMFSFHÌSF #$ LBÀDNEJS SF [ BD] m [ CE] m ( % ) = 2m ( A%BD ) \"#$ÑÀHFOJOEFUFNFMCFO[FSMJLUFPSFNJ DBC I I[ BD] a [ EC] = {F} FD =CSPMEVóVOBHËSF 2k 6 | |#$ =DN = I I#$ LBÀCSEJS 3k BC K 12 A ,#$ JLJ[LFOBS ÑÀ- a HFOJPMVöUVSBMN E |,'| = |FC| 6D [FD][\",] 12 F PMEVôVOEBO aa 12 C m ( B%AK ) = a 2a |#$| = 12 B 15. 6 16. 12 80 17. 9

,FOBSPSUBZ TEST - 34 A 4. #JMHJ #JSÑÀHFOJOLFOBSMBSJMFCJSLFOBPSUBZ 1. BSBTOEBBõBôEBLJCBôOUWBSES DE A G c b 2V2a = b2 + c2 - a2 2 Va BF C \"#$ Ð¿HFOJOEF ( LFOBSPSUBZMBSO LFTJN OPLUBT- Ba D a C 22 | | | | | |ES GD + GE + GF DNPMEVóVOBHËSF | | | | | |AF + #& + CD UPQMBNLBÀDNEJS A \" # $ % & DE G 2. A BF C x+2 E \"#$Ð¿HFOJOEF (LFOBSPSUBZMBSOLFTJNOPLUBT G x+1 | | | | | |GE =DN DG =DN BF =DN 2y | |:VLBSEBLJWFSJMFSFHÌSF AF LBÀDNEJS y–1 BD C A) 6 3 B) 6 2 C) 10 \"#$Ð¿HFOJOEF (BóSMLNFSLF[J D) 2 10 E) 3 10 | |[ AD ] a [ BE ] = { G } AG = x +CS | | | | | |GE = x +CS BG =ZCS GD =Z-CS :VLBSEBLJWFSJMFSFHÌSF Y+ZUPQMBNLBÀCS 5. A \"#$Ð¿HFO EJS (BóSMLNFSLF[J \" # $ % & [ BD ] m [ CD ] 3. A \"#$Ð¿HFOJOEF G (BóSMLNFSLF[J BC K |AK| = |KD| | |4 G KG =DN D |BD| = |DC| = |AG| =DN BDC | | | |:VLBSEBLJWFSJMFSFHÌSF \"# = AC LBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF AD LBÀDNEJS A) 10 B) 2 10 C) \" # $ % & D) 2 11 E) 4 3 1. D 2. C 3. E 81 4. E 5. D

TEST - 35 ,FOBSPSUBZ 1. \"#$Ð¿HFOJOEFUBSBMCËMHFMFS[AD]WF[AK]CPZVO- 4. A 2 DB LBUMBOODB # WF $ OPLUBMBS ( OPLUBTOB HFM- NFLUFEJS 5 Va A B DC G | | | | | |\"#$Ð¿HFOJOEF BD = DC AB =DN BD KC | | | |AC = DN PMEVôVOB HÌSF AD = Va kaç GBSLMUBNTBZEFôFSJBMBCJMJS (OPLUBT\"%$ÑÀHFOJOJOBôSMLNFSLF[JPMEV- BD \" # $ % & ôVOBHÌSF PSBOLBÀUS KC A) 10 B) 5 C) 2 D) 5 E) 3 32 35 2. A 5. A E 42 B DC E D 2 \"#$Ð¿HFO [ AB ] m [ AC ] [ BE ] m [ AD ] F &BóSMLNFSLF[J BE = 4 2 cm Ba C | | :VLBSEBLJWFSJMFSFHÌSF AD LBÀDNEJS | | | |\"#$Ð¿HFOJOEF [ AB ] m [ AC ] AE = EB \" # $ % & | AD | = | DC | | BD | = 3 | B F | | EF | =DN | |:VLBSEBLJWFSJMFSFHÌSF #$ =BLBÀDNEJS 3. A \"#$Ð¿HFO \" # $ % & (BóSMLNFSLF[J B x [ CD ] m [ BE ] D | |CG =DN E | |GE =DN 6 G 5 C 6. )FSIBOHJCJSÑÀHFOJOJLJLFOBSPSUBZV[VOMVôV | |:VLBSEBLJWFSJMFSFHÌSF AG =YLBÀDNEJS DNWFDNPMEVôVOBHÌSF ÑÀÑODÑLFOBSPS- UBZV[VOMVôVOVOBMBCJMFDFôJFOCÑZÑL ve en kü- \" # $ % & çükUBNTBZEFôFSMFSJOJOUPQMBNLBÀDNEJS \" # $ % & 1. D 2. # 3. D 82 4. # 5. C 6. D

,FOBSPSUBZ A TEST - 36 1. 4. A 15° 12 16 N B DC \"#$Ð¿HFOJOEF [ AB ] m [ AD ] m ( % ) = 15° B DC DCA | | | |BD PMEVôVOBHÌSF m % = a =2 AC ( ACB ) kaç EFSFDFEJS \"#$Ð¿HFOJOEF [ AB ] m [ AC ] [ AD ]LFOBSPSUBZ \" # $ % & | | | |[ BN ]B¿PSUBZ AB =DN AC =DNPMEV- | |ôVOBHÌSF ND LBÀDNEJS 2. \"#$ CJS Ð¿HFO , WF . LFOBSPSUB OPLUBMBS ( 35 43 45 50 A) B) C) D) E) 5 BóSMLNFSLF[JEJS 8 10 11 11 A |KL| = |LM| K [ AG ] m [ BG ] A G | |AB =DN 5. L BM C x D | | | | :VLBSEBLJWFSJMFSFHÌSF GL + LM UPQMBN G 10 LBÀDNEJS B 16 \" # $ % & C \"#$Ð¿HFOJOEF (BóSMLNFSLF[J [ AG ]B¿PSUBZ 3. #JMHJ #JSÑÀHFOJOLFOBSMBSJMFCJSLFOBPSUBZ | AD | = | DC | | BG | | |=DN BC =DN | | :VLBSEBLJWFSJMFSFHÌSF AG =YLBÀDNEJS BSBTOEBBõBôEBLJCBôOUWBSES A 2V2a = b2 + c2 - a2 \" # $ % & 2 c b Va Ba D a C 6. A 22 A 7 G 9 G 8 B KD C BC \"#$CJSÐ¿HFO (BóSMLNFSLF[JEJS \"#$CJSÐ¿HFO (BóSMLNFSLF[JE JS | | | |m(B%GK) = m(K%GD) AG = 3 BG | | | | | |AG =DN GC =DNWF BG =DN | | | |BC =DNPMEVôVOBHÌSF ,% LBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF \"# LBÀDNEJS A) 3 B) 4 C) 3 2 % & \" # $ % & 1. C 2. A 3. E 83 4. D 5. D 6. A

TEST - 37 ,FOBSPSUBZ 1. (FPNFUSJEFSTJOEFZBQMBOCJSFULJOMJLUFBõBóEBLJ 4. (FPNFUSJEFSTJOEFFULJOMJLZBQBO.VSBU±óSFUNFO BENMBSJ[MFOFSFLHFPNFUSJLCJS¿J[JNZBQMZPS BõBóEBLJ BENMBS J[MFZFSFL CJS HFPNFUSJL ¿J[JN ZBQUSZPS r [AB] m [AC]PMBDBLõFLJMEFCJS\"#$Ð¿HFOJ¿J[J- r \"#$Ð¿HFOJOJ¿J[JOJ[ MJZPS r \"#$ Ð¿HFOJOJO ( BóSML NFSLF[JOEFO HF¿FO r \"#$Ð¿HFOJOJO[AB]LFOBSOBBJULFOBSPSUBZOO [AB]ZJLFTUJóJOPLUB%OPLUBTES EPóSV [AC] ZJ \" JMF $ BSBTOEB % OPLUBTOEB [AB]ZJ \"JMF#BSBTOEBLJ&OPLUBTOEBLFTJZPS r (OPLUBT\"%$Ð¿HFOJOJOBóSMLNFSLF[JPMNBL \"ôSML NFSLF[JOEFO HFÀFO EPôSVZB # OPLUB- Ð[FSF [CD] LFOBSOB \" LËõFTJOEFO ¿J[JMFO LF- TOEBO JOJMFO EJL V[VOMVL DN $ OPLUBTOEBO OBSPSUBZ[CD]ZJ&OPLUBTOEBLFTJZPS JOJMFO EJL DN PMEVôVOB HÌSF \" LÌöFTJOEFO JOJMFOEJLLBÀDNEJS I Ir [DG] m [AE]PMNBLÐ[FSF AG = 2 6 DNPMV- ZPS | | :BQMBOÀJ[JNMFSFHÌSF #$ LBÀDNEJS \" # $ % & A) 8 3 B) 9 3 C) 10 3 D) 12 3 E) 16 3 5. #JMHJ #JSÑÀHFOJOLFOBSMBSJMFCJSLFOBPSUBZ A BSBTOEBBõBôEBLJCBôOUWBSES A 2. c b a2 6 2 Va 2V2a = b2 + c2 - D G Ba D a C 22 CB A \"#$CJSEJLÐ¿HFO [ AB ]åm [ BC ]WF(BóSMLNFS- %% | | | |LF[J m(CGD) = m(DGA) 2 GC = 5 AG | | | |AD =DNPMEVôVOBHÌSF #( LBÀDNEJS \" # $ % & B CD Fabrika Fabrika Fabrika 3. A \"#$Ð¿HFO #JSLËZEFCVMVOBONFZWFBóB¿MBSOEBOZBQMBOIB- TBUMBS IBTBUZFSJOEFOCJSCJSJOFFõJUV[BLMLUBCVMV- DE |AC| = |BC| OBO GBCSJLBMBSB HËUÐSÐMFDFLUJS #V JõMFN ZBQMSLFO F UBõNBJõMFNJOJOZBQMBDBóWFGBCSJLBMBSBSBTOEB- <#&>WF<$%> LJZPMMBS\"#%Ð¿HFOJõFLMJOEFNPEFMMFONJõUJS LFOBSPSUBZMBS )BTBUZFSJOEFO#GBCSJLBTOBHJEFOZPMLN % GBCSJLBTOB HJEFO ZPM LN # WF % GBCSJLBMBS | |BE =DN BSBTLNPMEVôVOBHÌSF IBTBUZFSJJMF$GBCSJ- LBTBSBTLBÀLNEJS Bx | |C CD =DN | |:VLBSEBLJWFSJMFSFHÌSF #$ =YLBÀDNEJS A) 2 41 B) 4 10 C) 2 38 A) 3 2 B) 4 2 C) 34 D) 2 35 E) 2 31 D) 6 E) 6 2 1. D 2. C 3. A 84 4. D 5. C

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ·¦(&/%&#&/;&3-÷,* TANIM Kenar - Kenar - Kenar (K.K.K) Benzerliği \"#$ WF %&' Ð¿HFOMFSJOJO LËõFMFSJ BSBTOEBLJ TANIM CJSFCJS FõMFNFEF LBSõMLM B¿MBS Fõ LBSõMLM LFOBSMBSFõJUJTFCVJLJÑÀHFOFöJUUJSEFOJS öLJ Ð¿HFOJO LBSõMLM LFOBSMBS PSBOUM JTF Ð¿- HFOMFSCFO[FSEJS ABC b%&'õFLMJOEFHËTUFSJMJS Benzerlik Açı - Açı - Açı (A.A.A) Benzerliği TANIM \"#$ WF %&' Ð¿HFOMFSJOJO LËõFMFSJ BSBTOEB- TANIM LJCJSFCJSFõMFNFEFLBSõMLMB¿MBSFõLBSõML- MLFOBSMBSPSBOUMJTFCVJLJÑÀHFOCFO[FSEJS öLJõFSB¿MBSFõPMBOÐ¿HFOMFSCFO[FSEJS EFOJS A A&BC + D&EC ABC ~ DEF E õFLMJOEFHËTUFSJMJS BD C A #FO[FSJLJÐ¿HFOEFLBSõMLMLFOBSV[VOMVLMBS- OOPSBOOBCFO[FSMJLPSBOEFOJS DE AD 10 5 & + & 6 3 ABC ADE [DE] // [BC] B 8 CE 4 F A&BC + D&EF & 10 = 8 = 6 = 2 5 43 CFO[FSMJLPSBO BC ,FOBS\"À,FOBS ,\", #FO[FSMJôJ #FO[FSJLJÑÀHFOJO TANIM r ,BSõMLMZÐLTFLMJLMFSJOJOPSBO r ,BSõMLMLFOBSPSUBZMBSOOPSBO öLJ Ð¿HFOJO LBSõMLM LFOBSMBS PSBOUM WF CV LF- r ,BSõMLMB¿PSUBZMBSOOPSBO OBSMBSBSBTOEBLJB¿MBSFõJTFÐ¿HFOMFSCFO[FSEJS r ¥FWSFMFSJOJOPSBO r ö¿UFóFU¿FNCFSMFSJOJOZBS¿BQMBSPSBO AD r %õUFóFU¿FNCFSMFSJOJOZBS¿BQMBSPSBO r ¥FWSFM¿FNCFSMFSJOJOZBS¿BQMBSPSBO JLJ B CE F Ð¿HFOJOCFO[FSMJLPSBOOBFõJUUJS AB BC ve m ( A%BC ) = m ( D%EF )JTF #FO[FS JLJ Ð¿HFOJO BMBOMBS PSBO CFO[FSMJL = PSBOOOLBSFTJEJS DE EF & + D&EF õFLMJOEFHËTUFSJMJS ABC 85

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 1 ÖRNEK 4 A ABC üçgen A ABC üçgen 1 m ( A%BC ) = m ( E%DC ) m ( B%DF ) = m ( A%CB ) D 13 | |AD =DN | |AD =DN D E | |DB =DN | |3 8 C xF | |BC =DN EC =DN B 12 | |DC =DN B x E 2C | |:VLBSEBLJWFSJMFSFHÌSF #& =YLBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF #' LBÀDNEJS & + & & + F&BD ABC EDC ABC 4 x+2 12 21 j x =DN |#'| =DN = j x =DN = 23 8 12 + x ÖRNEK 2 ÖRNEK 5 A ABC üçgen %%% A ABC üçgen ca 4 m ( DCB ) = m ( FBA ) = m ( DAC ) % % m( BAD ) = m ( DCA ) x | |DF =DN | AB | = 4 DN a Da+b 6 F | |EF =DN b a+c a+b B | BD | = 2 DN E9 | |b a BC =DN B 2D x C 18 C | |:VLBSEBLJWFSJMFSFHÌSF DC = x LBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF \"# LBÀDNEJS A&BD + C&BA A&BC + E&FD 4 x+2 18 x = j x =DN = j x =DN 24 69 ÖRNEK 3 ÖRNEK 6 A 6 m ( % ) = m ( % ) A ABC üçgen D BAC EAD 16 8 | | | |a AC = BC =DN 6 | |AB =DN | |AE =DN x D E4 | |EC =DN 10 b | | | |15 BD = DC =DN | |AD =DN Bx C a 15 10 b B | |ED =DN a | |:VLBSEBLJWFSJMFSFHÌSF #$ LBÀDNEJS C | |:VLBSEBLJWFSJMFSFHÌSF \"% =YLBÀDNEJS & + A&ED ,\",CFO[FSMJôJOEFO && ABC ABC + BCD 15 10 + x 16 12 x j x = DN = = = 2 j x =DN = 10 15 8 66 1. 4 2. 6 3. 12 86 4. 14 5. 27 6. 12,5

www.aydinyayinlar2i..cMomO.DtrÜL ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 7 ÖRNEK 9 B B A ABC üçgen 15 E <\"$>m<#$> x 59 2k F * ** B' D <&'>m<\"#> D' k ( A%BD ) % D m ( DBC ) A7 D7 C A ôFLJM** 4 m = ôFLJM* B 12 C |BF| = 2 |FD| ôFLJM*EFLJ\"#$Ð¿HFOJCJ¿JNJOEFLJLBSUPO#%CPZVODB | | | | | |AB DN BC = 12 cN PMEVôVOBHÌSe, &' LBÀ LFTJMJQ*WF**OPMVQBS¿BMBSFMEFFEJMJZPS*QBS¿BTBCJUUV- UVMVQ**QBS¿B$OPLUBTJMF#OPLUBT¿BLõBDBLõFLJMEF DNEJS #%LFOBSCPZVODBZBQõUSMQôFLJM**FMEFFEJMJQ%WF#h OPLUBMBSCJSMFõUJSJMJZPSæ \"ÀPSUBZEBO A&BC EFQJTBHPSEBO|\"$| = 9 | | | | | |\"% = DC =DNWF %#h =DNPMEVôVOBHÌ AB AD | |SF #% LBÀDNEJS æ = BC DC 15 AD = 12 DC B & B&DE & ` & ABC BEF BCD ba b 2k x 8 7 = j x = cm D' 7+x b x2 + +Y 2 = 172 3k 4 3 x 1JTBHPSUFPSFNJOEFO 17 a j x =DN ÖRNEK 10 A7 D |#%| =DN A ôFLJMEF CJS QBSLO \" # $ % 1 OPLUBMBSOEBLJ PZVO BMBOMBS ÖRNEK 8 C BSBTOEBLJZPMMBSHËTUFSJMNJõUJS B # PZVO BMBOOEBO TSBTZMB \" \"#$ EJL Ð¿HFOJOEF <\"#> m <#$> & <\"#> Ð[FSJOEF D; 2 $ % PZVO BMBOMBSOB HJEFO <\"$>Ð[FSJOEFTF¿JMFOOPLUBMBSWF<&%>m<\"$>EJS D ZPMMBS N N N $ PZVOBMBOOEBOTSBTZMB\"WF | | | || | & %PZVOBMBOMBSOBHJEFOZPMMBS NWFNEJS AE = BC AD =DNPMEVôVOBHÌSF A^ ABD h LBÀDNEJS :PMMBSBSBTOEBCVMVOBOWFOVNBSBMCËMHFMFSBóB¿- MBOESMBDBLUS A A&ED , B&CF a 10 #VOVOJÀJOBOMBöMBOCJSQFZ[BKGJSNBTN2CBöOBTB CJUÑDSFUBMNBLÑ[FSFCÌMHFJÀJO5-ÑDSFUCF MJSMFEJôJOFHÌSF CÌMHFJÀJOLBÀ5-GJZBUCFMJSMFNJö UJS |\"%| = |#'| = 10 D A^ ABD h = 10.10 = 50 2 A % % ABC BCD 2 cm 180 + B b F 120 180 120 90 E 90 = = =2 10 60 90 60 45 C #FO[FSMJL PSBOMBS 45 a b D CÌMHFMFSJO BMBOMBS PSB B C O UÑS OPMV CÌMHF JÀJO 5- GJZBU CFMJS MFOJS 7. 15 8. 50 87 8 9. 10. 600 3

TEST - 38 ·ÀHFOEF#FO[FSMJL* 1. D6 C \"#$%EËSUHFO 4. (FPNFUSJEFSTJOEFFULJOMJLZBQBO.VSBU)PDBBõB- m ( A%DB ) = % óEBLJ BENMBS UBLJQ FEFSFL CJS HFPNFUSJL ¿J[JN ( BCD ) ZBQUSZPS 23 | |AD DN r % = 60°PMBOCJS\"#$Ð¿HFOJ¿J[JOJ[ m ( ABC ) 4 | |BD DN r D ` [BC]BMQ[AD] = [BD]¿J[JOJ[ Ax B | |BC DN r E ` [AC]BMQ[DE]ZJ¿J[JOJ[ | |DC DN r % = 120°EJS m ( AED ) | | :VLBSEBLJWFSJMFSFHÌSF \"# =YLBÀDNEJS | | | | | |\"& =DN EC =DNPMEVôVOBHÌSF \"% \" # 3 $ % 5 & LBÀDNEJS 2 2 \" # $ % & 2. A [ AB ] m [ BD ] A x <&%>m<#%> 5. E <\"$>m<$&> 5 3 5 C 2D | |ED =DN B6 | |CD =DN Bx D 6C | BC | = 6 cN | | :VLBSEBLJWFSJMFSFHÌSF \"& =YLBÀDNEJS | | | |ABC üçgen [ AB ] m [ AC ] AD = AC =DN | | | |DC =DNPMEVôVOBHÌSF #% =YLBÀDN \" 2 15 # 62 $ 3 7 % & 65 EJS \" # 7 $ 8 % & 10 33 3 3. A 6. D ABC üçgen x 2 m % = % D A ( DFC ) m ( BAC ) 6 E 6 | |DA =DN B4 E 8 C | |AC =DN % % ACB BDE | |\"#$Ð¿HFO m( ) = m ( ) BE =DN | |BF =DN | | | |BD =DN EC =DNPMEVôVOBHÌSF B2 F x C | |\"% =YLBÀDNEJS | | :VLBSEBLJWFSJMFSFHÌSF '$ YLBÀDNEJS \" # 3 $ % 5 & \" # $ % & 2 2 1. # 2. E 3. C 88 4. D 5. # 6. \"

·ÀHFOEF#FO[FSMJL* TEST - 39 1. A 4. A x x 6 4 E x B 4D 5 C B 4D 6C | | | | | |\"#$Ð¿HFO AD = BD =DN DC =DN ABC üçgen m (A%DB) = % *BD * =DN m (CEB), | | | |PMEVôVOBHÌSF \"# = \"$ =YLBÀDNEJS * * * *DC =DN EA =DNPMEVóVOBHËSF \" # 13 $ % 15 & * *&# =YLBÀDNEJS 2 2 \" # $ % & 2. A 5. D C \"#$%EËSUHFO 68 [AC]B¿PSUBZ B 9D x E4C m % = m % (ABC) (ACD) \"#$Ð¿HFOJOEF \"%&FõLFOBSÐ¿HFO * *AD =DN | | | |% A xB m ( BAC ) = 120° BD =DN EC =DN * AC *=DN | |PMEVôVOBHÌSF DE =YLBÀDNEJS * *:VLBSEBLJWFSJMFSFHÌSF \"# =YLBÀDNEJS \" # $ % & \" # $ 22 % 28 & 32 3 33 3. A 66 AD 6. 6 4 C E 8 3 B xD C B | | | |\"#$Ð¿HFO AD = DC * * * * * *ôFLJMEF AC =DN CB =DN CD =DN | | | |AB= =DN A^ & h =DN2 & =DN2 AC ADC * *CE =DNWF A^ CDE h | |:VLBSEBLJWFSJMFSFHÌSF #% YLBÀDNEJS PMEVôVOBHÌSF A^ & hLBÀDN2EJS ACB \" 7 # 8 $ 9 % & 11 \" # $ % & 5 55 5 1. \" 2. # 3. E 89 4. C 5. E 6. E

TEST - 40 ·ÀHFOEF#FO[FSMJL* 1. E 4. A ABC ve DFC birer A D 4 Ð¿HFO 5 12 m ( % ) = m ( % ) F DBA DFC E B8 D x C | |EB = 3 br 3 x B | EA | = 5 br \"#$Ð¿HFO $ \"WF&OPLUBMBSEPóSVTBMES C * * * *maB%AEk = maA%DCk, BD = 8 br ve AB = 12 br * * PMEVôVOBHÌSF DC =YLBÀCJSJNEJS | AF | = 4 br | |PMEVôVOBHÌSF $' =YLBÀCJSJNEJS \" # $ % & \" # $ % & A ABC üçgen 2. 4 m % = m % ) ( AED ) ( ABC 3 D | |E AD =DN | |x AE =DN 5 | |DB =DN B C | |:VLBSEBLJWFSJMFSFHÌSF EC =YLBÀDNEJS 5. A D \" # $ 5 % & 7 2 2 BB EE C 3. A K B DCE üçgen ve \"#$%LBSFEJS x <%,><%&> ôFLJM CJS ZFMLFOMJ HFNJOJO ZBOEBO HËSÐOÐõÐEÐS C m ( K%EB ) = 24° [AB] ZFMLFO EJSFóJEJS WF HFNJZF EJLUJS \" $ OPLUB- DF UBMBS BSBTOB EPóSVTBM HFSHJO CJS IBMBU ¿FLJMNJõUJS 24° :FMLFOJ EBIB I[M UPQMBZBCJMNFL J¿JO CV IBMBUB % OPLUBTOEBO#WF&OPLUBMBSOBFLIBMBUMBSCBóMBO- NõUS | | | | | |#%IBMBUOOV[VOMVôVNFUSF \"$ = 3 #&, E % m ( BDE ) = 30°PMEVôVOBHÌSF EJSFôJO#OPLUB :VLBSEBLJWFSJMFSFHÌSF m ( A%DK ) = x LBÀEFSF DFEJS TJMFHFNJOJOCVSOVOVO$OPLUBTBSBTV[BLM ôLBÀNFUSFEJS \" # $ % & \" # $ % & 1. D 2. # 3. # 90 4. # 5. C

·ÀHFOEF#FO[FSMJL* TEST - 41 1. A 4. F A 10 80° E 20° B5 D E 9C B C xD \"#$Ð¿HFO $ \" 'EPóSVTBM, maD%AEk = 20° % % | | | | | | | |maB%AFk = 80° AD = AE BD =CS EC = 9 br AED ACD * * * * ôFLJMEFm ( ) = m ( ) EB = BC * *AE = 10 br PMEVôVOBHÌSF YLBÀCJSJNEJS | | :VLBSEBLJWFSJMFSFHÌSF \"% =YLBÀCJSJNEJS \" # $ 3 5 % 4 5 & \" # $ % & 2. A ôFLJMEF 5. A \"#$EJLÐ¿HFO x+7 E B \" & % $EPóSVTBM 6 | AD | = 6 br D | BD | = 14 br 3x–5 *AB* = *BC* 14 x | BC | = 16 br *AE* = *DC* * *BE Y E <\"$><#$> *BD * = 3x - 5 B 16 C <&%><\"#> D C | | :VLBSEBLJWFSJMFSFHÌSF ED =YLBÀCJSJNEJS :VLBSEBLJWFSJMFSFHÌSF YLBÀUS \" # $ % & \" # $ % & 6. A A T' 3. (FPNFUSJEFSTJOEFFULJOMJLZBQBO.VTB±óSFUNFO T BõBóEBLJBENMBSJ[MFZFSFLËóSFODJMFSJOFCJSHFP- T NFUSJL¿J[JNZBQUSZPS r [CE ve [$,õOMBSO¿J[JOJ[ r [$&õOÐ[FSJOEFCJS\"OPLUBT [$,õOÐ[F- B CB C SJOEF%` [CB]PMBDBLõFLJMEF%WF#OPLUBMBS ôFLJM* ôFLJM** CFMJSMFZJOJ[ ôFLJM*EFLJ\"#$FõLFOBSÐ¿HFOJCJ¿JNJOEFLJLBSUPO * * * * * *r AB =DN AD =YDN BD =DN [AT] ve [TC]EPóSVMBSCPZVODBLFTJMJQ\"5$Ð¿HFOJ *AC * =DN \"OPLUBTFUSBGOEBTBBUZËOÐOEF[AB] ve [AC]¿B- % LõBOBLBEBSEËOEÐSÐMÐZPSWFôFLJM**FMEFFEJMJZPS m ( ADC ) r = m( % m( % = 100° PMEVóVOB HËSF m ( B%T'T ) BÀT BAE ) ATC ) * *PMEVôVOBHÌSF \"% =YLBÀCJSJNEJS LBÀEFSFDFEJS \" # $ % & \" # $ % & 1. E 2. C 3. D 91 4. C 5. # 6. #

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ·¦(&/%&#&/;&3-÷,** 5IBMFT5FPSFNJ ÖRNEK 1 ABC üçgen TANIM A A D ôFLJMEF 6 8 [ DE] // [ BC] B E AD // BE // CF C F PMNBLÐ[FSF D E | |AD =DN 3 x | |DB =DN | |AE =DN B C AB DE AB DE | |:VLBSEBLJWFSJMFSFHÌSF EC =YLBÀDNEJS = = 5FNFMPSBOU5FPSFNJ BC EF AC DF 68 j x =DN 3=x 5FNFM0SBOU5FPSFNJ ÖRNEK 2 TANIM D1 C \"#$%EËSUHFO #JSÐ¿HFOJOCJSLFOBSOB¿J[JMFOQBSBMFMCJSEPó- 3 3k 3n <%$><&'><\"#> SVÐ¿HFOJOJEJóFSJLJLFOBSOLFTFSTFCVLFOBS- MBSEBPSBOUMQBS¿BMBSBZSS E1 x–1 F | |DC =DN A DE // BC | |DE =DN x | |EA =DN | |AB =DN 4 4k 4n B 1 14 A 15 DE | |:VLBSEBLJWFSJMFSFHÌSF &' =YLBÀDNEJS 5IBMFT 5FNFM0SBOU5FPSFNJ BC DE CF CF x - 1 3 j x =DN AD AE DE = ,== == AB AC BC EH FB CB 14 7 AD AE = ÖRNEK 3 DB EC D A F d1 E1E2E3 A 3k 3n AB = 3 B4 K BC 2 E 9 E d2 2k 2n | |BK å=DN C D d3 | |KE å=DN BF C [ AB]å[ CD] // [ EF] | | | |PMEVôVOBHÌSF \"' æ CD æUPQMBNLBÀDNEJS 1=1+1 CB BK 24 j |\"'| =DN EF AB CD = = j |CD| =DN AB BF BE CA AF 5 AF |\"'| + |CD| = 25 == 39 FE KE DC FC ED = = 5 CD FD CD 92 1. 4 2. 7 3. 25

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 4 ÖRNEK 7 x D ABC ve ACD D ABC ve DBC üçgen A birer üçgen <\"#><&'><%$> 3 3n F K [ EF] // [ BC] A E E 12 3 x | |AB =DN 4 [ FK] // [ AD] 4n 6 | |AE =DN | |DC =DN BC | |EB =DN BF C | |FK =DN | |:VLBSEBLJWFSJMFSFHÌSF &' =YLBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF \"% =YLBÀDNEJS 1 11 j x =DN x=3+6 4n 12 & = & x = 21cm ACD EF505 7n x ÖRNEK 8 ÖRNEK 5 A ABC üçgen A ABC üçgen [ KL>å< AB> 5k L |KE|å= |EL|å | |DE å=DN 8 <%&><#$> 3k | |C BD å=DN D 4n E | |AD DN B 5 D 3E x 4 | |DF DN | |FC DN 3k xF 5 K B 5n C | |:VLBSEBLJWFSJMFSFHÌSF EC æ=YLBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF %# LBÀDNEJS EK 3 EL CE 3k =, = = AB 5 AB CB 5k 8 4n j x =DN & EF505 = ABC 8 + x 5n x3 = j x =DN x+8 5 ÖRNEK 6 ÖRNEK 9 A \"#$Ð¿HFOJOEF &WF' A ABC üçgen PSUBOPLUBMBSES 3k <\"#>m<\"$> EF <#'>a<&,>\\%^ E 3F <\"%>WF<$&> D FD = 3 LFOBSPSUBZ DB 4 k G [ EF] // [ BC] 2k B6 | |D 6 C EF =DN | |B 12 K C BK DN | |:VLBSEBLJWFSJMFSFHÌSF '( LBÀDNEJS | |:VLBSEBLJWFSJMFSFHÌSF KC LBÀDNEJS AE EF 1 = = EF = 3 |&'| // |#$| AB BD 2 4k 12 j |&'| =DN = EF FG 3 == 3k EF DC GD 6 AE 9 1 FG = k GD = 2k AF = 3k = = j x =DN Ek = 6 & k = 1 AB 12 + x 2 4. 21 5. 2 6. 6 93 7. 2 8. 12 9. 1

·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÜÇGENLER www.aydinyayinlari.com.tr ÖRNEK 10 ÖRNEK 12 A ABC üçgen A \"#$Ð¿HFO <#'>WF<$'>B¿PSUBZ 6 <%&><#$> <$%>B¿PSUBZ D 2 F1 E | |AD =DN D 2n [ EF] // [ CD] 6 2k 4 |EF| = 3 |KC| | |AC =DN | |2 1 DB =DN E K | |FC =DN | |B x C EC =DN 3k n 4k Bx F 3C | |:VLBSEBLJWFSJMFSFHÌSF #$ =YLBÀDNEJS % % | |:VLBSEBLJWFSJMFSFHÌSF #' LBÀDNEJS DFB DBF ÷ÀUFSTBÀMBS m^ h = m^ h ma % k = ma % k \"ÀPSUBZEBO 505 505 FEC ECF AC AK AK DK BF EF = JLJ[LFOBSÑÀHFOMFS|%#| = |%'| = 2 =, =, BC DC |'&| = |EC| =1 FC KF AF EF 63 x3 8 = x j x =DN = j x =DN x+3 6 ÖRNEK 11 ABC üçgen ÖRNEK 13 4m A ABC üçgen <(&><#'> F 4k 4 <#$><%&> A D 5k |DF| |= DE| 5m E [ DC] // [ FE] D 4m |4 AC | |= AE | 5 k | |BC =DN | |AE =DN | |EC =DN G 8E 3m k BC B 14 C x F :VLBSEBLJWFSJMFSFHÌSF AF PSBOLBÀUS BD FA 4 FA = 4k T.O.T =& AD 9 DF = 5k | |:VLBSEBLJWFSJMFSFHÌSF $' LBÀDNEJS AD 4 AD = 4m T.O.T =& AB 9 BD = 5m AE GE 4 GE , |GE| =DN = = , BC 7 14 AC 4k AF = DE GE 1 8 , |#'| = 16 j x =DN = ,= 5m BD DF BF 2 BF 9k = 4m k4 505 = m5 4 4 16 .= 5 9 45 10. 4 11. 2 94 16 12. 3 13. 45

www.aydinyayinlari.com.tr ÜÇGENLER 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 14 \"#$%QBSBMFMLFOBS ÖRNEK 16 # $ &EPóSVTBM E OPLUBMBS (FPNFUSJEFSTJOEF4FSEBS±óSFUNFOBõBóEBLJBENMB- SJ[MFZFSFLËóSFODJMFSJOEFOHFPNFUSJL¿J[JNJZBQNBMBS- x | |AK =DN OJTUJZPS D 2k F | |FK =DN r [AB] m [AC]PMBDBLõFLJMEFCJSEJLÐ¿HFO¿J[JOJ[ 2 2k C K r \"LËõFTJOEFO[BC]LFOBSOBEJL¿J[JOJ[[BC]ZJLFT- 4 UJóJOPLUBZ)PMBSBLJTJNMFOEJSJO A 4k B | | | |r [\")] // [$% [)%] a [AC] = {E} ve DE = DC | |:VLBSEBLJWFSJMFSFHÌSF '& æ=YLBÀDNEJS PMBDBLõFLJMEF%WF&OPLUBMBSOCFMJSMFZJOJ[ FK DF 2 DF = 2k == AB = 4k | | | | | |r AE =DN EC =DN AB =YDN FC = 2K AK AB 4 :VLBSEBLJBENMBSJ[MFOFSFLÀJ[JMFOÑÀHFOJÀJO x 2k | |\"# =YLBÀDNEJS = j x =DN x + 6 4k A D 2 x F B 2 E bb ÖRNEK 15 6 b x DB a HC A \"#$EJLÐ¿HFO [)'] m [\"$], |)'|2 = 2.8 |DB| = |BC| |)'| =DN 3 AB =DN | |4 CF HF 84 | |AC =DN = j 10 = x CA AB C 505j x =DN | |:VLBSEBLJWFSJMFSFHÌSF \"% æ=YLBÀDNEJS E 8 3 x A 43 DB C [\"#] // [DE] j505j |DE| = 8 1JTBHPSUFPSFNJOEFO x2 = 82 + 32 j x = 73 DN 14. 6 15. 73 95 16. 5

TEST - 42 ·ÀHFOEF#FO[FSMJL** 1. A \"#$Ð¿HFOJOEF 4. A \"#$Ð¿HFOJOEF % = ( % \" , 'EPóSVTBM m ( ACH ) HCB ) H D 2 F <$)>m<\"#> |DE| = |EF| E |BE| = |ED| D <%'><\"$> Bx C 2 6 C | |EK DN BxE K | |KC DN | FC | | )'| | | | |)& =DNPMEVôVOBHÌSF #$ =YLBÀDN F EJS \" # $ % & | |PMEVôVOBHÌSF #& =YLBÀDNEJS \" # $ % & 2. A 5. A DK E xD G BC 6 \"#$Ð¿HFOJOEF [ BK ] ve [ CK ]B¿PSUBZ BE C | | | |[ DE ] // [ BC ] DE =DN BC =DN \"#$ Ð¿HFOJOEF [BD] LFOBSPSUBZ ( BóSML NFS PMEVóVOBHËSF ¦FWSF \"%& LBÀDNEJS | |LF[J [ AB ] // [ GE ] GE =DNPMEVôVOBHÌSF | |\"# =YLBÀDNEJS \" # $ % & \" # $ % & 3. A 6. A D x 12 9 B EC BD C | | | |\"#$Ð¿HFOJOEF [ AB ] // [ DE ] AD = 3 DC | | | |\"#$Ð¿HFOJOEF [ AD ] m [ AC ] BD = DC ¥ \"#$ =DNPMEVôVOBHÌSF ¦ %&$ LBÀ | | | |AD =DN AC =DNPMEVôVOBHÌSF DNEJS | |\"# =YLBÀDNEJS \" # $ % & \" 3 13 # 6 13 $ 3 15 % 6 15 & 3 17 1. C 2. C 3. \" 96 4. D 5. E 6. #

·ÀHFOEF#FO[FSMJL** TEST - 43 1. A ABC üçgen 4. A 5 N B 6 | EB | =DN F M E | ED | =DN BK | BD | =DN 3 63 x C x L E | DC | =DN 8 y C D | EA | =DN 4D 14 :VLBSEBLJWFSJMFSFHÌSF |\"$| =YLBÀDNEJS ôFLJMEF[FK] // [BC] [AN] // [KL] // [CD] ve \" # $ % & * * * *[-.] // [DE]EJS2 FB = *AF * AN =CS * * * * * * * *CD =CS -. = CS KL =YCS DE =ZCS :VLBSEBLJWFSJMFSFHÌSF Y+ZUPQMBNLBÀUS \" # $ % & 2. A ABC üçgen D <\"#>m<#$> x <#%>m<&%> 3 * *DE =DN B EC 5. %PóSVTBM CJS ZPM Ð[FSJOEF BSBMBSOEBLJ V[BLML * * * * * *AB = AD = BE PMEVôVOBHÌSF *#%*=YLBÀ NFUSF PMBO WF NFUSF ZÐLTFLMJóJOEFLJ JLJ MBN- CBEJSFóJWFCVEJSFLMFSJOBSBTOEBCVMVOBONFUSF DNEJS ZÐLTFLMJóJOEFLJCJS¿VCVLõFLJMEFHËTUFSJMNJõUJS \" # 11 $ % 9 & 2 2 8 3. A ABC ve 6 2 20 D DBC üçgen 10 B E x <&'><#$> %JSFLMFSÐ[FSJOEFLJMBNCBMBSO¿VCVóVOIFSJLJUBSB- C F <\"#><%$> GOEB PMVõUVSEVóV HËMHFMFSJO CPZMBS CJSCJSJOF FõJU- UJS * DC * = 15 *DF * = x #VOB HÌSF MBNCBMBSEBO CJSJOJO PMVöUVSEVôV HÌMHFOJOCPZVLBÀNFUSFEJS :VLBSEBLJWFSJMFSFHÌSF YLBÀDNEJS \" 15 # 30 $ 45 % 60 & 75 \" # $ % & 7 7 777 1. \" 2. \" 3. C 97 4. E 5. D

TEST - 44 ·ÀHFOEF#FO[FSMJL** 1. öTB\"NDBCBI¿FTJOEFCVMVOBOBóB¿MBSZVLBSEBLJ 3. A \"#$ \"$% WF HJCJJTJNMFOEJSJQBóB¿MBSBSBTOB¿JUMFS¿FLFSFLIBZ- F E ADE birer WBOMBSOCVCËMNFMFSFZFSMFõUJSFDFLUJS B 2 üçgen A L M [FK] // [BC] F 6K D <,-><$%> <-.><\"&> 8C | FK | = 6 br B EC | | | | | |BC =CS -. = 2 br PMEVôVOBHÌSF \"&LBÀ CJSJNEJS \" # $ % & D #VOVOJ¿JOZVLBSEBLJÐ¿HFOJNPEFMMFNJõUJS#VNP- 4. (FPNFUSJEFSTJOEFCJSFULJOMJLZBQBO.FINFU±ó- EFMMFNFMFSEF\" $WF%OPLUBMBSWF# & $OPLUB- MBSEPóSVTBMES SFUNFOBõBóEBLJBENMBSJ[MFZFSFLCJSHFPNFUSJL ¿J[JNZBQUSZPS ¥JUMFSJZBQULUBOTPOSBLBQZBQNBEóOGBSLFEJQ' OPLUBTOBCJSLBQZBQZPS r #JS\"#%Ð¿HFOJ¿J[JOJ[$` [ BD ]PMBDBLõFLJM- EF$BMQ[ AC ]ZJ¿J[JOJ[ | | | | .PEFMMFOFOCËMHFJ¿JO AF =N AD =O r E ` [ AC ]PMBDBLõFLJMEF[ BE ]ZJ¿J[JOJ[ | | | | | | | |EC m ( B%AE ) % = CD BF = BE = m ( EAC ) r |AB| = |AC| |BC| = 2| CD| ve | | PMEVôVOBHÌSF \"& =YJONWFOUÑSÑOEFOJGB %% m ( EBC ) = m ( CDA )ES EFTJBöBôEBLJMFSEFOIBOHJTJEJS | |r AD = 48 br \" m.n # N+O $ N- n | | PMEVôVOBHÌSF #& LBÀCJSJNEJS % m & m + n \" # $ % & n n 2. D C 5. (FPNFUSJEFSTJOEFCJSFULJOMJLZBQBO:VOVT±óSFU- E NFOBõBóEBLJBENMBSJ[MFZFSFLCJSHFPNFUSJL¿J- [JNZBQUSZPS T K F r [ AB ] // [ CD ]PMBDBLõFLJMEF\"#$%ZBNVóVOV 3 ¿J[JOJ[ A 12 B r %# WF \"$ LËõFHFOMFSJOJO LFTJõJN OPLUBTO ( PMBSBLJTJNMFOEJSJOJ[ \"#$%EËSUHFO #$,Ð¿HFOEJS[ DC ] // [ TF ] // [ AB ] r \"LËõFTJOEFO&` [DC]PMBDBLõFLJMEFCJS[ AE ] [FE] // |[BK] CF | = 3 | FE | | BK | = | DC | EPóSVTV¿J[JOJ[ * *% r [AE] a [ DG ] = { F} m (CBE) = m (E%BK) FB =DN | AB | =DN r | DF | |=DN GB | |=DN DE | = | EC | | | PMEVôVOBHÌSF '( =YLBÀDNEJS PMEVôVOBHÌSF | 5'|LBÀDNEJS \" # $ % & \" # $ % & 1. \" 2. C 98 3. C 4. C 5. C

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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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