#VLJUBCOIFSIBLLTBLMESWF\":%*/:\":*/-\"3*OBBJUUJSTBZMZBTBOOIÐLÐNMFSJOF HËSFLJUBCOEÐ[FOJ NFUOJ TPSVWFõFLJMMFSJLTNFOEFPMTBIJ¿CJSõFLJMEFBMOQZBZNMBOB- NB[ GPUPLPQJZBEBCBõLBCJSUFLOJLMF¿PóBMUMBNB[ :BZO4PSVNMVTV $BO5&,÷/&- :BZO&EJUÌSÑ &TSB:·,4&-)BLBO\"ó$\" %J[HJ–(SBGJL5BTBSN \"ZEO:BZOMBS%J[HJ#JSJNJ *4#//P :BZOD4FSUJGJLB/P #BTN:FSJ &SUFN#BTN:BZO-UEõUJr ÷MFUJöJN \":%*/:\":*/-\"3* JOGP!BZEJOZBZJOMBSJDPNUS 5FMr 'BLT 0533 051 86 17 aydinyayinlari aydinyayinlari * www.aydinyayinlaricom.tr %¸O¾P.DSDáñ11.SINIF Çember ve Daire KARMA TEST-1 Karma Testler 11. SINIF 5. MODÜL 1. B 0 NFSLF[MJ ¿FZSFL 4. \"#$% EJLEËSUHFOJOF 5 OPLUBTOEB UFóFU ZBSN ¿FNCFSWFSJMNJõUJS ¿FNCFSWFSJMNJõUJS BC m DC D TC Alt bölümlerin C |OD| = |DC| F Modülün sonunda EDĜOñNODUñQñL©HULU xE tüm alt bölümleri ÇEMBER ve DAİRE x L©HUHQNDUPDWHVWOHU O DA AB \\HUDOñU :VLBSEBLJWFSJMFSFHÌSF m ( A%DC ) = x kaç de- recedir? | | | |[DB]LËõFHFO &' = &#PMEVóVOBHËSF \" # $ % & m ( A%ED ) = x kaç derecedir? \" # $ % & ³ Çemberin Temel Elemanları t 2 2. B 5)m OC 5. A ³ Çemberde Açılar t 13 T B Dx H | |0) = 4 br x | |\"$ = 8 br C ³ Çemberde Teğet ve Uzunluk - I t 35 O4 H A8 C #\" WF #$ ¿FNCFSF TSBTZMB \" WF $ OPLUBMBSOEB ³ Çemberde Teğet ve Uzunluk - II t 45 UFóFU %)m\"$ m % = m ( & ( % ) = 80° (AD) DC) m ABC 0NFSLF[MJ¿FZSFL¿FNCFSEF5UFóFUEFóNFOPLUB- PMEVóVOBHËSF % = x kaç derecedir? <D]ñOñ6RUXODUñ m ( ADH ) | |TPMEVóVOBHËSF OB = x kaç birimdir? 2NXO\\D]ñOñVñQDYODUñQGD ³ Dairenin Çevresi ve Alanı t 53 6ñQñIð©LðĜOH\\LĜ \" # $ % & ©ñNDELOHFHNVRUXODUñL©HULU %XE¸O¾PGHNL¸UQHN % & YAZILI SORULARI\" # $ Çember ve Daire ³ Ka1r1m. SIaNIFTest5l.eMrODÜtL 65¦&.#&37&%\"÷3& www.aydinyayinlari.com.tr 5. C 6. A 7. #JSJNLBSFMFSFBZSMNõYBZSUMBSOEBLJLBSF- OJOJ¿JOF\"0#$NFÐS¿LHFF[OMJEBJSF¿J[JMNJõUJS 3. C ³ Yazılı Soruları t 69 DA %&#$ ¦&.#&3÷/5&.&-&-&.\"/-\"3* 45° x |\"#| = |\"$| ÷MJöLJMJ,B[BONMBS DNE | |4 3 ³ Yeni Nesil Sorular t 7111.5.1.1 : ¥FNCFSEFUFóFU LJSJõ ¿BQ ZBZWFLFTFOLBWSBNMBSOB¿LMBS O BD %& = 6 br 11.5.1.2 : ¥FNCFSEFLJSJõJOË[FMMJLMFSJOJHËTUFSFSFL JõMFNMFSZBQBS AH 12 B | |K M BC = 12 br O O | |% 0NFSLF[MJJLJ¿FNCFSZBZWFSJMNJõUJS :BSÀBQ ÖRNEK 2 %)m\"# m ( BDC ) = 45° %) = 4 3 br % TANIM %Ð[MFNEFLJ TBCJU CJS OPLUBEBO FõJU V[BLMLUB E 0 NFSLF[MJ ¿FZSFL ¿FN- VRUXODUñQ©¸]¾POHULQH | |)# = 12 br | | | | | | OB = 3 OD \"# + AB =CSPMEVóVOBHË- C CVMVOBO OPLUBMBSO LÐNFTJOF ÀFNCFS EFOJS ber DNñOOñWDKWDX\\JXODPDVñQGDQ #V TBCJU OPLUBZB ¿FNCFSJO NFSLF[J NFSLF[JO XODĜDELOLUVLQL] & BL ¿FNCFS Ð[FSJOEFLJ IFSIBOHJ CJS OPLUBZB PMBO | | | |[AB]ÀBQMÀFNCFSEFWFSJMFSFO MFCSFDHÌ+SFC DBCUP=QMxBNLBç birimdir? V[BLMóOB¿FNCFSJOZBSÀBQEFOJS 0 NFSLF[MJ ÀFNCFSEF , -# V .OB H/Ì USFFô FUBUSEBMFôBNMBFOMBSOUPQMBNLBÀCJSJNLB- y 0\"#$EJLEËSUHFO kaç birimdir? A r 1O OPLUBMBSPMEVôVOBHÌSF \"r#ed$irÑ?ÀBHFuOluJOnJuOzÀ. FWSF- AB & | |r ôFLJMEFLJ¿FNCFSJONFSLF[J0 0\" =SJTF CD &AB$ =4 C 12 | |#$ = 12 br \" 8 2 # = CD 33 si kaç birimdir? ¿FNCFSJOZBS¿BQES 5 \" # B 5BSBM BMBOMBS UBöOSTB UPQMBNMBS ÀFZSFL EBJSFZF FöJU $ olur. % & | |5 r 5 \"# = 5 br % 4 2 & 18 3 25π = 4 x & 5 O 12 A D CD + CD 2. C & 65 4. C 5. E 6. B | |1. D C3D. A+ CD = | | | |:VLBSEBLJWFSJMFSFHÌSF CE + \"% LBÀCJSJNEJS | OB | =SZBSÀBQ r= 22 jS= 13 5 + 12 y = 13 - 5 = Y= 13 - 12 = 1 8. D 6 L C ôFLJMEF\"#$%LBSF- | CE | + | \"%| = 8 + 1 =CS 6. A TJOJOJ¿UFóFU¿FNCF- <HQL1HVLO6RUXODU %Ð[MFNEF CJS ¿FNCFSJO ¿J[JMFCJMNFTJ J¿JO NFS- S SJJMF%NFSLF[MJ¿FZ- 0RG¾O¾QJHQHOLQGH\\RUXP LF[WFZBS¿BQCJMHJMFSJOJOCJMJONFTJZFUFSMJEJS \\DSPDDQDOL]HWPHYE ÖRNEK 3 $OW%¸O¾P7HVWOHUL S SFLEBJSF¿J[JMNJõUJS EHFHULOHUL¸O©HQNXUJXOX K Çember ve Daire VRUXODUD\\HUYHULOPLĜWLU Her alt bölümün <(1m1(6m/6258/$E 5 $\\UñFDPRG¾OVRQXQGD VRQXQGDRE¸O¾POHLOJLOL WDPDPñ\\HQLQHVLOVRUXODUGDQ WHVWOHU\\HUDOñU S ROXĜDQWHVWOHUEXOXQXU ÖRNEK 1 ¦FNCFSJO5FNFM&MFNBOMBS B 0NFSLF[MJ¿FZSFL¿FN- TEST - 4 1. -VOBQBSLBHJEFO.FMJT¿FNCFSIBMLBBUNBPZVOV S3. A 6 A ôFLJMEFLJ IBNTUFS ¿BSL CFSWF\"0%$EJLEËSUHF- PZOBZBDBLUS .FMJT ZBS¿BQ CS PMBO ¿AFNCFSJ BU- F 6 BL B TÐTMFOFSFL Fõ BSBMLM \" 0NFSLF[MJ¿FNCFS 2 OJWFSJMNJõUJS UóOEB TUBOEEBLJ EJLEËSUHFOMFSEFO CJSJ ¿FNCFSJO # $ % & ' , -OPLUB- xE 6 A | |1B. 0\" = ( 3x - 8 ) br C |BD | = 2 br J¿JOEFLBMSTBPZVOVLB[BOBDBLUS I IDL = 6 cm PMEVôVOBHÌKSF UBSBMCÌMHFOJOCBMBOMB SOBCJSFSBNQVMZFSMFõ- 3x–8 | |x–2 0# = ( x - 2 ) br A D | |0% = 8 br #JSJNLBSFMFSFBZSMNöEÑ[MFNEFWFSJMFOÀFN- kaç7cm2 dir? UJSJMNJõUJS )BNTUFS ¿BSL r=10 4. 8 D EBLJLBEB UVS I[ZMB O A 8 CFSZBZMBSZMBPMVöUVSVMNVöCÌMHFOJOÀ5FWSFTJOJ 4 89 7 O bulunuz. F PL ZËOÐOEF EËOEÐSFCJM- OA r=10 O 5 8 6.6 E NFLUFEJS :BSÀBQCSPMBOJLJÀFZSFL 9 6 6A + S = 2 = 18 :VLBSEBLJWFSJMFSFHËSF 2A +4= 36 cm2 | |B 4 a) CE =YLBÀCJSJNEJS ZBSÀBQCSPMBOJLJÀFZSFL #VOBHÌSF TOIJÀEVSNBEBOZÑSÑZFOIBNT- B D C ZBSÀBQCSPMBOJLJÀFZSFL UFSEVSEVôVBOEBÀBSLOTPOHÌSÑOUÑTÑBöBô- EBLJMFSEFOIBOHJTJPMVS :VLBSEBLJ WFSJMFSF HÌSF ÀFNCFSJO ZBSÀBQ LBÀ CTJ- 8 C b) \"0%$EJLEÌSUHFOJOJOBMBOLBÀCS2EJS SJNEJS ZBSÀBQCSPMBOCJSZBSNÀFNCFSMFSJOÀFWSFMFSJUPQ- ôFLJMEF[$5 0NFSLF[MJ¿FNCFSF5OPLUBTOEBUF- 0NFSLF[MJ¿FNCFSEF \"#$пHFO [\"#] m [\"$] MBN 4π 6π 8π 4UBOEEBLJ EJLEÌSUHFOMFSJO BZSU V[VOMVLMBS öF- A) B B) K C) F 10π A C F L E = B8 cmS= 10 2 + 2 + 2 + 2 = 14πLJMEFLJ HJCJ PMEVôVOB HÌSF .FMJThJO PZVOV LB- K &0%EJLÑÀHFOJOEFO]%&B]=D=CS | | | | | | | | | | | |óFU \"$m$5 #$ $5 ]0\"]= |OB|=SZBSÀBQ =DN %$ 0% =DN \"% =DN [BONBLJÀJOIFEFGBMBCJMFDFôJEJLEÌSUHFOTBZT 3x - 8 = x - 2 L D E AD L x=3 :VLBSEBLJWFSJMFSFHÌSF ÀFNCFSJOZBSÀ0B\"Q$%LEBJÀLEÌSUHFO + x:=V1L0BSjExBL=J4WFSJMFSFHÌSF ÀFNCFSJOÀBQLBÀDN BöBôEBLJMFSEFOIBOHJTJEJS S=CJSJN DNEJS C \" \"0$% = 10 . 8 =CES2JS \" # $ % & KE DB CA F C B \" # 4 5 $ 4 3 D) 5 E) 4 2 \" # 10 5 $ D) E) E 5. 30 6. Ö 25π D DF 70 7. 8. 36 CE D) 10 10 E) 15 4 B FC K 1. 1 2 2. 9 3. a) 4 b) 80 BL A AK L 2. C ôFLJMEFLJ 0 NFSLF[MJ 5. C B A 2 ¿FNCFSEF D E 4. 5FMEFOZBQMNõ¿FWSFTJÕDNPMBO\"#$FõLFOBS B [\"#] m [$%] K2 | | | |,$ = KB =CJSJN пHFOJOF õFLJM WFSJMFSFL ËODF CJS LBSFZF BSEOEBO | |KD =CJSJN O6 2. EBCJS¿FNCFSFEËOÐõUÐSÐMÐZPS A A1 A2 D AF O )HQ/LVHOHULQH<¸QHOLN C1 :VLBSEBLJWFSJMFSFHÌSF ÀFNCFSJOZBSÀBQLBÀ )HQ/LVHVLP¾IUHGDWñQGD olup Anadolu Lisesi müfre- CJSJNEJS GDWñQGDROPD\\DQL©HULNYH O B C B1 B2 C2 \" 5 VRUXODUSHPEH]HPLQOH 0NFSLF[MJ¿FZSFL¿FNCFS \"0#$LBSF YHULOPLĜWLU | | | |11. SINIBF) 2 55. MODÜL $ ¦&.#&37&%\"÷3& www.aydinyayinlari.com.tr %&0'EJLEËSUHFO #$ =DN DF =DN ¶¿HFOJOLËõFMFSJ\" # $OPLUBMBSLBSFOJOÐ[FSJOEF \"1 #1 $1 EBJSFOJOÐ[FSJOEFJTF\"2 #2 $2OPLUB- | |D) 3 5 )(1/m6(/&( 5m1(<q1(/m. :VLBSEBLJWFSJMFSFÖHRÌNSFE K \"2'1LBÀDNEJS MBSOBEËOÐõNFLUFEJS. TANIM \" # A$ % & \"$%'EËSUHFOJ¿FN- ,BSF õFLMJOEFLJ CJS CBI¿FOJO BóSML NFSLF[JOF EFOL HFMFO OPLUBEB CJS TVMBNB TJTUFNJ WBSES #V #ÐUÐOLËõFMFSJCJS¿FNCFSJOÐ[FSJOEFCVMV- x B CFSMFSJ#WF&OPL- TJTUFN FO GB[MB NFUSF V[BLMóB LBEBS TVMBZBCJM- #VOBHÌSF LBSFOJOJÀJOEFPMVöBO\"1B1C1ÑÀHF- NFLUFEJS#VCBI¿FOJOEËSULËõFTJOFJQV[VOMVLMBS 3. OôBFOLEJMËESFULHJF O0FLNJSFJöSLMFFS[MEJÌSUHFOJEFOJS 70° C UBMBSOEB LFTNFLUF- BZOPMBOEËSULPZVOCBóMBONõUS OJOJOBMBO41, çemberin içinde oluöBn A2B2C2 ¿FNCFSEF EJSm ( % ) = 70° S1 PSBOBöB- ,JSJõMFSEËSUHFOJOJOLBSõMLMB¿MBSOOUPQMB- ACD S2 N[\"0][E#JS$ ] AO | |#$ =DDN F D ÑÀHFOJOJOBMBO42 olmakÑ[FSe, | |0$ =DN E 17 \"#6$.%LI:JBSBJOõSHM¿FJBSÐQ¿ÐEDPNóSPVMBTOBM#¿PFVMNNOBCBFZHSBÌOJMSFFB BMUZmOG(BCSE%LAÐM[FMOF)PN=LEUBxF BLIMBFOÀS--EFSFDFEJS #BIÀFOJOBMBON2PMEVôVOBHÌSF LPZVOMB- ôEBLJMFSEFOIBOHJTJEJS EËSUHFOZJPE SJS #V O PL UBMBDSNOE¿JSFN[CBFES]JO PNSUBFLSLLFJ[SJJöOJFÀJV[[JMBJSLTFM LM\"B'S& # WF #&%$ LJSJöMFS SOTMBONBEBOPUMBZBCJMNFMFSJJÀJOLVMMBOMBDBL 30 C UPQMBN JQ V[VOMVôV FO GB[MB LBÀ NFUSF PMNBM- 27 3 93 $ 4π2 B ES \" # 27 3 AC EÌSUHFOJ 4 2 23 & | | :VLBSEBLJWFSJMFSFHÌSF \"# LBÀDNEJS #VOB HÌSF CV OPLUBMmBS(B%ELDÌ)ö=F1L8B0°C-V7M0F°E=F1O10Ñ° À- \" # $ % & 4 3π2 HFOMFSEFO LBÀ ÀFNCFmSJ(OB%EJÀF)C=Ì7MH0°FTJOEF ZFS BM- % 3π2 % % 3 BEF FAB \" # 4 17 $ NB[ m ( ) + m ( ) = 180° B \" $ % 70+ x =&1 80° & x = 110° m ( BE%A) D2) % # 1. D 2. D 72 3. B 4. C BCD D) 3 17 r +17m ( ) = 180° rm %% = ÖRNEK 22 3. E ( ADC ) + m ( ABC ) 11810° 4. B 5. C 6. D E 1. \" 2. B \"#$%LBSF [ DE ] m [ EB ] ÖRNEK 19 D C m ( E%BC ) = 25° C ôFLJMEFLJ¿FNCFSEF #VOBHÌSF B m ( D%AE ) = x LBÀEFSFDF- % = 55° x 25° 55° m ( ACF ) EJS AB A 180–x° x Dx % = 15° m ( BEA ) ,BSF CJS LJSJöMFS EÌSUHFOJEJS [ DB] ÀBQ PMBDBôOEBO F ÀFNCFS&OPLUBTOEBOHFÀFS 15° #VOBHÌSF m ( B%DF ) = x LBÀEF- %% SFDFEJS m ( EC ) = 50°, m ( DE ) = 2x° E 2x + 50 =j x = - x ++= x x = ÖRNEK 23 ÖRNEK 20 A \"#$%EËSUHFO AE C ôFLJMEFLJ¿FNCFSEF 70° 65° % OD [ ED ] m [#$] m ( BAC ) = 70° B [\"#] m [\"$] m % ) = 65° ( DAC |\"#| = |\"&| By x D % #VOBHÌSF m ( ACB ) = 10° m ( A%DE ) LBÀEFSF- DFEJS m % ) = 35° ( ACD 10° 35° m % = x° ( ADB ) C % m ( CBD ) = y° #VOBHÌSF x +ZLBÀEFSFDFEJS \"#%&LJSJöMFSEÌSUHFOJEJS[ EB ]ÀBQUS m ( B%AD ) + m ( % ) = 180° &% BCD AE = AB & m ( AB ) = m ( AE ) = 90° PMEVôVOEBO\"#$%LJSJöMFSEÌSUHFOJ & m ( A%DE ) = 45° x = Z= Y+ y = 19. 125 20. 45 26 21. 22. 23.
www.aydinyayinlaricom.tr 11. SINIF 11. SINIF 5. MODÜL ÇEMBER ve DAİRE ³ Çemberin Temel Elemanları t 2 ³ Çemberde Açılar – I t 13 ³ Çemberde Açılar – II t 22 ³ Çemberde Açılar – III t 31 ³ Çemberde Teğet ve Uzunluk - I t 35 ³ Çemberde Teğet ve Uzunluk - II t 45 ³ Dairenin Çevresi ve Alanı t 53 ³ Karma Testler t 65 ³ Yazılı Soruları t 69 ³ Yeni Nesil Sorular t 71 1
11. SINIF 5. MODÜL ¦&.#&37&%\"÷3& www.aydinyayinlari.com.tr ¦&.#&3÷/5&.&-&-&.\"/-\"3* ÷MJöLJMJ,B[BONMBS 11.5.1.1 : ¥FNCFSEFUFóFU LJSJõ ¿BQ ZBZWFLFTFOLBWSBNMBSOB¿LMBS 11.5.1.2 : ¥FNCFSEFLJSJõJOË[FMMJLMFSJOJHËTUFSFSFL JõMFNMFSZBQBS :BSÀBQ ÖRNEK 2 TANIM %Ð[MFNEFLJ TBCJU CJS OPLUBEBO FõJU V[BLMLUB E 0 NFSLF[MJ ¿FZSFL ¿FN- CVMVOBO OPLUBMBSO LÐNFTJOF ÀFNCFS EFOJS ber #V TBCJU OPLUBZB ¿FNCFSJO NFSLF[J NFSLF[JO ¿FNCFS Ð[FSJOEFLJ IFSIBOHJ CJS OPLUBZB PMBO y 0\"#$EJLEËSUHFO V[BLMóOB¿FNCFSJOZBSÀBQEFOJS C 12 | |#$ = 12 br A rO B | |5 r 5 \"# = 5 br x O 12 A D | | | |:VLBSEBLJWFSJMFSFHÌSF CE + \"% LBÀCJSJNEJS | |r ôFLJMEFLJ¿FNCFSJONFSLF[J0 0\" =SJTF | OB | =SZBSÀBQ ¿FNCFSJOZBS¿BQES 22 %Ð[MFNEF CJS ¿FNCFSJO ¿J[JMFCJMNFTJ J¿JO NFS- r = 5 + 12 jS= 13 LF[WFZBS¿BQCJMHJMFSJOJOCJMJONFTJZFUFSMJEJS y = 13 - 5 = Y= 13 - 12 = 1 | CE | + | \"%| = 8 + 1 =CS ÖRNEK 3 ÖRNEK 1 xE 6 B 0NFSLF[MJ¿FZSFL¿FN- C r=10 2 CFSWF\"0%$EJLEËSUHF- B 0NFSLF[MJ¿FNCFS OJWFSJMNJõUJS x–2 | |0\" = ( 3x - 8 ) br D | |0# = ( x - 2 ) br |BD | = 2 br | |8 0% = 8 br A A r=10 O 3x–8 O :VLBSEBLJWFSJMFSFHËSF | |a) CE =YLBÀCJSJNEJS b) \"0%$EJLEÌSUHFOJOJOBMBOLBÀCS2EJS :VLBSEBLJ WFSJMFSF HÌSF ÀFNCFSJO ZBSÀBQ LBÀ CJ- B S= 10 SJNEJS &0%EJLÑÀHFOJOEFO]%&]=CS ]0\"]= |OB|=SZBSÀBQ 0\"$%EJLEÌSUHFO + x = 10 j x = 4 3x - 8 = x - 2 C \" \"0%$ = 10 . 8 =CS2 x=3 S=CJSJN 1. 1 2 2. 9 3. a) 4 b) 80
www.aydinyayinlaricom.tr ¦&.#&37&%\"÷3& 5. MODÜL 11. SINIF ,JSJöWF¦BQ ÖRNEK 5 0NFSLF[MJ¿FNCFS 7$1,0%m/*m ¥FNCFSJO JLJ GBSLM OPLUBTO CJSMFõUJSFO EPóSV B % = 30° QBS¿BTOBLJSJöEFOJS 12 30°r m ( OBA ) ¥FNCFSJONFSLF[JOEFOHF¿FOLJSJõF¿FNCFSJO A rO ÀBQEFOJS | |\"# = 12 br ¥FNCFSJOFOV[VOLJSJõJ¿BQUS ¥BQ¿FNCFSJJLJFõQBS¿BZBBZSS #VOB HÌSF ÀFNCFSJO ¥BQV[VOMVóVZBS¿BQV[VOMVóVOVOJLJLBUES ÀBQLBÀCJSJNEJS D & r= 12 =4 3 j 2r = 8 3 OCB den C AB 3 O ÖRNEK 6 E .NFSLF[MJCJS¿FNCFSÐ[FSJOEFLJ\" - WF# F OPLUBMBS.OPLUBTOBHËSFTJNFUSJLUJS 0NFSLF[MJ SZBS¿BQM¿FNCFSEF #VOBHÌSF BOBMJUJLEÑ[MFNEFCVÀFNCFSJJLJFöQBS- ÀBZB BZSBO WF FôJNJ PMBO EPôSVOVO EFOLMFNJOJ r [$%]WF[EF]CJSFSLJSJõ CVMVOV[ r [\"#]LJSJõJ¿BQ \"WF#OPLUBMBS.ZFHÌ- | | r \"# = 2r B(3, 1) SFTJNFUSJLJTF. CV- A(–3, 5) M MVOVS &ôJNJ PMBO WF . UFO HFÀFO EPôSV- OVO EFOLMFNJ Z = 2x + 3 PMVS ÖRNEK 4 ,FTFOWF:BZ C [\"#] ¿BQM 0 NFSLF[MJ TANIM ¿FNCFSJO ZBS¿BQ CJ- ¥FNCFSEF JLJ GBSLM OPLUB WF CV OPLUBMBS BSB- TOEBLJ ¿FNCFSJO OPLUBMBSOEBO PMVõBO LÐNF- 2x–5 SJNEJS ZFÀFNCFSJOZBZEFOJS | |\"$ = ( 2x - 5 ) br ¥FNCFSJJLJGBSLMOPLUBEBLFTFOEPóSVZBÀFN- CFSJO LFTFOJEFOJS AB C 9O 9 B A \" # $ CJSCJSJOEFO GBSLM OPLUBMBS PMEVôVOB HÌSF Y E JOBMBDBôFOCÑZÑLUBNTBZEFôFSJLBÀUS F \" # $GBSLMOPLUBMBSPMEVôVOEBO|\"$| < |\"#| &'¥FNCFSJOLFTFOJ 2x - 5 < 18 ) 23 ACB \"$#ZBZ x< ) 2 m (ACB)\"$#ZBZOOËM¿ÐTÐ ) YJOFOCÑZÑLUBNTBZEFôFSJEJS ACB \"$#ZBZOOV[VOMVóV 4. 11 3 5. 8 3 6. y = 2x + 3
11. SINIF 5. MODÜL ¦&.#&37&%\"÷3& www.aydinyayinlari.com.tr 5FôFU ÖRNEK 8 7$1,0%m/*m ¥FNCFS ZBZ JMF BZO EÐ[MFNEF PMBO WF ¿FN- r A :BS¿BQCSPMBO CFSJMFZBMO[CJSPSUBLOPLUBTCVMVOBOEPóSVZB T r ÀFNCFSJOCJSUFôFUJEFOJS [ DE ] ¿BQM ZBSN ¥FNCFSJMFEPóSVOVOCVPSUBLOPLUBTOBUFôFU EFôNFOPLUBTEFOJS ¿FNCFS ¥FNCFSJO NFSLF[J JMF UFóFU EFóNF OPLUBTO CJSMFõUJSFOEPóSV UFóFUFEJLUJS xr K \"#$EJLпHFO r4 O merkez [\"#] m [\"$] O BD | |O E C ,$ = 4 br r 5WF,UFôFUEFôNFOPLUBMBSPMEVôVOBHÌSF Ad | |#5 YLBÀCJSJNEJS r4 = AB 4 + r 64 = & AB = 15 & x + 6 = 15 j x = 9 AB 10 r EUFóFUEPóSVTV ÖRNEK 9 r \"UFóFUEFóNFOPLUBT r 0\"m d T O7 merminin BMEô yol 20 25 ÖRNEK 7 [#\" 0 NFSLF[MJ O N A 15 OJõBOD O ¿FNCFSF \" OPLUB- 4 4 TOEBUFóFUUJS :BS¿BQCSPMBO¿FNCFSCJ¿JNJOEFLJCJSIBMLB\"OPLUB- A C TOEBOZFSFEJLCJSEPóSVMUVEBIBWBZBBUMZPS\"OPLUB- 2 | 0$| = 4 br TOEBOCSV[BLMLUBLJCJS/OPLUBTOEBCVMVOBOOJõBO- | #$| = 2 br DIBMLBZIBWBEBZLFOWVSNBZB¿BMõZPS/JõBODOOBU- xB UóNFSNJ IBMLBOONFSLF[JZFSEFOCSZÐLTFLUFZLFO IBMLBZB5OPLUBTOEBUFóFUHF¿JZPS | |:VLBSEBLJWFSJMFSFHÌSF \"# LBÀCJSJNEJS #VOBHÌSF NFSNJOJOBMEôZPMLBÀCJSJNEJS /JõBO- DOOCPZVHÌ[BSEFEJMNJõUJS 0\"m\"# ]0\"]=S= 4 0\"/ÑÀHFOJOEFO]0/] 05/ÑÀHFOJOEFO]5/] CS \"0#ÑÀHFOJOEF1JTBHPSUFPSFNJOEFO x2 + 42 = 62 x = 2 5 7. 2 5 4 8. 9 9. 24
www.aydinyayinlaricom.tr ¦&.#&37&%\"÷3& 5. MODÜL 11. SINIF ÖRNEK 10 ÖRNEK 11 [\"#] ¿BQM ZBSN x `;PMNBLÐ[FSF ZBS¿BQ Y- DNPMBO¿FNCFSJONFSLF[JOEFODN T ¿FNCFSJO¿BQCS V[BLMLUBCJSEEPóSVTVWFSJMJZPS E EPôSVTV JMF ÀFNCFSJO PSUBL OPLUBT PMNBEôOB r 6x3 EJS5 UFóFUEFóNF HÌSF ÀFNCFSJOZBSÀBQOOBMBCJMFDFôJFOCÑZÑLEF- Or OPLUBT WF \" # $ ôFSLBÀDNEJS Ar B 30° EPóSVTBMES ¦FNCFSWFEPôSVOVOPSUBLOPLUBTPMNBEôOEBOEPôSV r ÀFNCFSJLFTNF[ C 25 > 5x - 2 | | | | | |\"# = 2 #$ PMEVôVOBHÌSF 5$ =YLBÀCJSJNEJS 27 S jS >x % 5 YJOFOCÑZÑLUBNTBZEFôFSJ 05$ÑÀHFOJOEF m ( OCT ) = 30° S DN j]5$] Y r 3 = 6 3 br #JS¦FNCFSJMF#JS%PôSVOVO#JSCJSJOF(ÌSF %VSVNMBS %m/*m %Ð[MFNEFCJS¿FNCFSJMFCJSEPóSVOVOCJSCJSMFSJ- OFHËSFпGBSLMEVSVNVWBSES0NFSLF[MJ ZB- ÖRNEK 12 S¿BQV[VOMVóVSPMBO¿FNCFSJMFEEPóSVTVOV BMBMN EVSVNEEPóSVTV¿FNCFSJJLJGBSLMOPLUBEB O5 B LFTFS | 0\"| = r 60° T | |0) <SEJS 8H 6 O 120° 60° 30° . d C K 43 A 43 M H A 0NFSLF[MJDNZBS¿BQM¿FNCFSWFBSBMBSOEBB¿ EVSVNEEPóSVTV¿FNCFSFUFóFUUJS PMBO\"#WF\"$EPóSVMBSWFSJMJZPS0,m\"$ | |0) =SEJS | | | |0, =DN \", = 4 3 DNPMEVóVOBHËSF O a) ¦FNCFSJO\"#EPôSVTVOBV[BLMôFOB[LBÀDN EJS Hd b) ¦FNCFSJO \"# EPôSVTVOB V[BLMô FO ÀPL LBÀ EVSVN EEPóSVTV¿FNCFSJLFTNF[ DNEJS B # 0 \" )EPóSVTBM 0,. mmÑÀHFOj]0.] WF],.] 8 3 DN | 0\"| = r & | |0) >SEJS j].\"] 4 3 DNj]).] DN AHM mm O j]0)] DN r | |B ¦FNCFSJO \"# OBFOZBLOOPLUBTOOV[BLMô A | |j 5) = 10 - 5 =DN d | |C ¦FNCFSJO \"# OBFOV[BLOPLUBTOOV[BLMô H = 10 + 5 =DN | |r 0) >SEVSVNVOEB¿FNCFSJOEPóSVZBFOZB- LOOPLUBT\" FOV[BLOPLUBT#OPLUBTES 10. 6 3 5 11. 23 12. B C
11. SINIF 5. MODÜL ¦&.#&37&%\"÷3& www.aydinyayinlari.com.tr ¦FNCFSEF,JSJöJO²[FMMJLMFSJ ÖRNEK 13 %m/*m #JS ¿FNCFSJO NFSLF[JOEFO LJSJõF JOEJSJMFO EJL- AF 0NFSLF[MJ¿FNCFS NF LJSJõJPSUBMBS O 0.FSLF[ B [0'] m [\"#] [\"#],JSJõ DE [0&] m [%$] O |0&| = |0'| | |C \"# = ( 3x - 4 ) br AHB | |$% = ( x + CS | | | |:VLBSEBLJ WFSJMFSF HÌSF \"# + CD UPQMBN LBÀ CSEJS [0)] m [\"#] l I \")I = I )#I |OF|= |OE| j |\"#| = |DC| j 3x - 4 = x + 6 | | | | | | | |j x = \"# = 3x - \"# = 11 j \"# + CD = 22 #JS ¿FNCFSJO J¿JOEFLJ IFSIBOHJ CJS OPLUBEBO HF¿FOFOV[VOLJSJõ¿BQUS&OLTBLJSJõJTFCV ¿BQBEJLPMBOLJSJõUJS C 0.FSLF[ ÖRNEK 14 [\"#] m [$%] B x+4 1OPLUBTOEBOHF¿FO A ¥BQ DN PMBO õFLJMEFLJ ¿FNCFSEF <$%> LJSJõJ NFS- O FOV[VOLJSJõ [$%] 2x+1 LF[F <\"#> LJSJõJOEFO EBIB C ZBLOES AP B FOLTBLJSJõ [\"#] | |\"# = ( x + 4 ) cm D D #JS ¿FNCFSEF V[VOMVLMBS FõJU PMBO LJSJõMFSJO NFSLF[FV[BLMLMBSFõJUUJS | |$% = ( 2x + 1 ) cm B 0.FSLF[ :VLBSEBLJWFSJMFSFHÌSF YJOUBNTBZEFôFSJLBÀUS K AO D [0,] m [\"#] [CD]LJSJöJNFSLF[FEBIBZBLOPMEVôVOEBO [0)] m [$%] | | | |Sä CD > \"# jäY+ 1 > x + 4 H äY> 3 j x ` Z j x = 4 C ÖRNEK 15 |\"#| = |$%| l |0,| = |0)| 0NFSLF[MJ¿FNber #JS ¿FNCFSEF GBSLM V[VOMVLUBLJ JLJ LJSJõUFO [\"#]LJSJõ V[VOPMBOLJSJõNFSLF[FEBIBZBLOES | |O 0$ = 5 br r B 0.FSLF[ 5 h5 | |\"$ CS D H 1 O [0)] m [\"#] | |A B 6 HC 4 $# = 4 br [0,] m [$%] :VLBSEBLJWFSJMFSFHÌSF ÀFNCFSJOZBSÀBQLBÀCSEJS K A & & AHO OHC ve EFQJTBHPSCBôOUTOEBO C I2 + 25 =S2WFI2 + 1 = 25 |\"#| > |$%| l | |0)< |0,| EFOLMFNMFSJÀÌ[ÑMÑSTFjS= 7 6 13. 22 14. 4 15. 7
www.aydinyayinlaricom.tr ¦&.#&37&%\"÷3& 5. MODÜL 11. SINIF ÖRNEK 16 ÖRNEK 19 AH Cx [#%¿FNCFSFUFóFU O 0 NFSLF[MJ ¿FNCFSEF 0 # B BD m\"#WF $ %OPLUBMBSEPóSVTBM 10 6 Ba O | |BD =CS |0#| = |#$| = |$%| 10 D 0 NFSLF[MJ ¿FNCFSJO B EFO HF¿FO FO LTB LJSJõJO ZBS¿BQCSPMEVóVOB K 3a V[VOMVóV 8 2 br PMEVôVOB xa HÌSF $ EFO HFÀFO FO LTB | |HËSF BC LBÀCSEJS C LJSJöJOV[VOMVôVLBÀCSEJS a D L | | | |\")m\"#BMOSTB \") = HC WF 0%#)EJLEÌSUHFOPMVS | |& |OL| = | | | |0, =S=B BL = 4 2 AHO QJTBHPSEBO \") =CSj 8 + x = 10 j x =CS 0#-ÑÀHFOJOEFQJTBHPS ^ 4 2 h2 + 2 = 2 & a=2 a 9a 0$,ÑÀHFOJOEFQJTBHPS Y2+ 4a2 = 9a2 j x = 2 5 FOLTBLJSJö= 4 5 ÖRNEK 17 D C \"#$% LBSFTJOEF <#$> ÖRNEK 20 ¿FNCFSF & OPLUBTOEB UF- 4 r óFUUJS ôFLJMEFLJ PEBOO BMU WF ÐTU [FNJOMFSJ Fõ ¿FNCFS ZBZMB- 8–r O SõFLMJOEFEJS#VPEBZBHJSJõZBZONFSLF[JOEFODN E ,BSFOJOCJSLFOBSCSPM- V[BLMLUBLJ CJS LBQ JMF TBóMBONBLUBES 0EBOO ÐTUUFO H EVôVOB HÌSF ÀFNCFSJO HËSÐOÐNÐBõBóEBLJHJCJEJS 4r ZBSÀBQLBÀCSEJS B' A B [OH] m [\"%] |DH|= |)\"| = 4 A B | |OE m [BC] j |OE|=S O 60° A #VOBHÌSF |OH|= 8 -S O&HA EFQJTBHPS 30° 60° 30° 80 -S 2 + 42 =S2 jS= 5 3 H B ÖRNEK 18 ,BQ\"OPLUBTOEBONFOUFõFMJWF#OPLUBTOEBOPLZË- OÐOEFJUJMFSFLPEBOOJ¿JOFEPóSVFOGB[MBMJLB¿JMF d <\"#>E B¿MBCJMNFLUFEJS A #VOBHÌSF | \"#| = 8 br 4 2 |0$| = 3 |$%| a) 0EBZ PMVöUVSBO ÀFNCFS ZBZOO ZBSÀBQ LBÀ DNEJS O 3k D 0 NFSLF[MJ ¿FNCFr- C 2k | |b) \"#LBÀDNEJS EFEEPóSVTV%OPL- 5k 4 UBTOEB UFóFU PMEVóV- B | |OBHËSF CD LBÀCS | | | |\"# = \"#h PMEVôVOEBONFSLF[FV[BLMLMBSFöJUUJS#V EJS EVSVNEB[0\"]BÀPSUBZ E\"#j OD m\"#j | \"$| = | CB | = 4 m ( B%'AO ) = m ( O%AB ) = 60° & EFQJTBHPSjS= 5 | |a) O&AH EFO 0\" =S= 160 3 OCB | |j CD =CS & OAB | |b) EFO \"# = 160 3 16. 2 17. 5 18. 2 7 19. 4 5 20. a) 160 3 C 160 3
TEST - 1 ¦FNCFSJO5FNFM&MFNBOMBS 1. FB 0NFSLF[MJ¿FNCFSEF 4. D C ôFLJMEFLJ \"#$% LBSF- TJOJO J¿JOF \" NFSLF[MJ A [0'] m [\"#] [0&] m [%$] E O ¿FZSFL ¿FNCFS ¿J[JM- |\"#| < |$%| NJõUJS | |0& = ( 5 -L CS D EC | 0'| = 4 br AB | |OE >PMEVôVOBHÌSF LOJOCVMVOEVôVBSB- \"#$% LBSFTJOJO BMBO CJSJNLBSF PMEVôVOB MLOFEJS | |HÌSF CE LBÀCJSJNEJS \" # $ \" 8 - 4 2 B) 4 2 - 4 $ 4 - 2 2 % & D) 4 2 E) 2 2 5. E C F 2. K B 0NFSLF[MJ¿FNCFSEF D O A [0,] m [\"#] 7 [0-] m [$%] A 24 B H D | 0,| = | 0)| ôFLJMEFLJ$NFSLF[MJ¿FNCFSZBZ& ' #OPLUBMB- C SOEBOHF¿NFLUFEJS L | |[\"$] \"#$%EJLEËSUHFOJOJOLËõFHFOJ \"% =CJ- | | | |SJNWF \"# =CJSJNPMEVôVOBHÌSF \"' LBÀ | | | |)% = ( 3x + DN \"# = ( 2x + DN | | | |)- = 2 cm PMEVôVOBHÌSF 0, LBÀDNEJS CJSJNEJS \" # $ % & \" # $ % & 3. :BS¿BQ DN PMBO 6. #JSJNLBSFMFSFBZSMNõLBSFOJOJ¿JOEFGBSLMOPL- A B õFLJMEFLJ¿FNCFSEF UBCFMJSMFONJõUJS Bm [\"#]LJSJõUJS O | |\"# = B- 1 ) cm PMEVôVOBHÌSF BUBNTBZ- 0OPLUBTONFSLF[LBCVMFEFOCSZBSÀBQMCJS ÀFNCFS ÀJ[JMEJôJOEF CV OPLUBMBSEBO LBÀ ÀFN- TLBÀGBSLMEFôFSBMBCJMJS CFSJOEöOEBLBMS \" # $ % & \" # $ % & 1. \" 2. D 3. C 8 4. \" 5. D 6. \"
¦FNCFSJO5FNFM&MFNBOMBS TEST - 2 1. A ,-/0CJSEJLEËSUHFO 4. ¥FWSFTJ¿FNCFSõFLMJOEFPMBOCJSHËMEF1OPLUBT- L OBTBCJUMFONJõCJSCBMPOCVMVONBLUBES 0, = 4 cm | |K P | |4 0/ = 3 cm B O 3N õFLJMEFLJ0NFSLF[MJÀFNCFSZBZ\" - #OPLUB- (ËMF JTUFEJóJ OPLUBEBO HJSFCJMFO EPóSVTBM WF IFQ BZOZËOMÐIBSFLFUFEFOCJSZÐ[ÐDÐCVCBMPOVBMQ | |MBSOEBOHFÀNFLUFPMEVôVOBHÌSF #/ LBÀDN LZZB¿LNBLJ¿JOFOB[NZÐ[NFTJHFSFLUJóJOJ IFTBQMZPS EJS (ÌMÑOÀBQNPMEVôVOBHÌSF 1OPLUBTOO \" B) 3 $ D) 5 E) 3 LZZBV[BLMôFOB[LBÀNFUSFEJS 22 \" # $ % & 2. B ôFLJMEF 0 NFSLF[MJ D 2 ¿FZSFL ¿FNCFS WF E %$0& EJLEËSUHFOJ WFSJMNJõUJS | |\"$ =CJSJNWF 5. C \"WF%LËõFMFSJ¿FNCF- | |BE =CJSJN SJOÐ[FSJOEFPMBO D \"#$%EJLEËSUHFOJOJO A 4C O A [#$] LFOBS ¿FNCFSJ # :VLBSEBLJWFSJMFSFHÌSF %$0&EJLEÌSUHFOJOJO BMBOLBÀCJSJNLBSFEJS WF $ EFO GBSLM JLJ GBSLM OPLUBEBLFTNFLUFEJS \" # $ % & ¥FNCFSJOZBS¿BQCS | |B \"% = 8 br #VOB HÌSF \"#$% EJLEÌSUHFOJOJO ÀFWSFTJOJO BMBCJMFDFôJLBÀUBNTBZEFôFSJWBSES \" # $ % & 3. 0NFSLF[MJ¿FNCFSEF O B [0$] a [\"#] = { D } x | \"%| = | DB | = 3 cm 3D 3 | %$| = 1 cm A1 6. #JS ÀFNCFSEF V[VOMVôV 6 3 PMBO LJSJöJO NFS- C LF[FFOLTBV[BLMôDNPMEVôVOBHÌSF CV | |:VLBSEBLJWFSJMFSFHÌSF OD =YLBÀDNEJS ÀFNCFSJOÀBQLBÀDNEJS \" 2 2 B) 2 3 $ \" # $ % & D) 4 E) 5 1. C 2. E 3. D 9 4. \" 5. B 6. D
TEST - 3 ¦FNCFSJO5FNFM&MFNBOMBS 1. A B C 4. A ôFLJMEFLJ¿FNCFSEF D C [\"#]LJSJõ O1 O2 B | \"$| = 3|$#| ôFLJMEFLJ01 02NFSLF[MJ¿FNCFSMFS%OPLUBTOEB $OPLUBTOEBOHFÀFOFOLTBLJSJöJOV[VOMVôV UFóFUUJS[\"$LпÐL¿FNCFSF$OPLUBTOEBUFóFU | |DNPMEVôVOBHÌSF \"# LBÀDNEJS | | | |01D =CS 02D =CSWF [\"$ [0102 ] \" 8 3 B) 8 2 $ 6 3 | |PMEVôVOBHÌSF \"$ LBÀCSEJS D) 6 2 E) 4 3 \" # $ % & 2. A 0NFSLF[MJ¿FNCFSEF 5. ôFLJMEF0NFSLF[MJ D B DN WF DN ZBS- AC [\"0] #\"$ B¿TOO O ¿BQM JLJ ¿FNCFS WFSJM- B¿PSUBZ NJõUJS | |O \"# = ( 3x + 5 ) br | | | |\"# =DNPMEVôVOBHÌSF BD LBÀDNEJS | |B C \"$ = ( 2x + CS \" # $ % & | | | |:VLBSEBLJ WFSJMFSF HÌSF \"# + \"$ LBÀ CS EJS \" # $ % & 6. y – x + 4 = 0 3. 0NFSLF[MJ¿FNCFSEF O y – x + 16 = 0 A [\"0] %\"# B¿TOO AB B B¿PSUBZ 8 | \"#| = 8 br O %Ð[MFNEFPSUBL0NFSLF[MJJLJ¿FNCFSJOZBS¿BQMB- | $%| = 2 br SPSBOEJS C 2D [\"%] m [0$] Z- x + 4 =EPóSVTVCÐZÐL¿FNCFSF Z- x +=EPóSVTVLпÐL¿FNCFSF :VLBSEBLJWFSJMFSFHÌSF ÀFNCFSJOZBSÀBQLBÀ | | UFôFUPMEVôVOBHÌSF \"# LBÀCJSJNEJS CSEJS \" 2 2 # $ 2 6 \" # $ % & D) 4 6 E) 8 1. \" 2. D 3. E 10 4. \" 5. C 6. D
¦FNCFSJO5FNFM&MFNBOMBS TEST - 4 1. A 4. O OA B BDC 4 0NFSLF[MJ¿FNCFSEF \"#$пHFO [\"#] m [\"$] T 8C | | | | | | | |BD = %$ 0% =DN \"% =DN ôFLJMEF[$5 0NFSLF[MJ¿FNCFSF5OPLUBTOEBUF- :VLBSEBLJWFSJMFSFHÌSF ÀFNCFSJOÀBQLBÀDN | | | |óFU \"$m$5 #$ =DN $5 = 8 cm EJS :VLBSEBLJWFSJMFSFHÌSF ÀFNCFSJOZBSÀBQLBÀ \" # 10 5 $ DNEJS \" # 4 5 $ 4 3 D) 5 E) 4 2 D) 10 10 E) 15 2. C ôFLJMEFLJ 0 NFSLF[MJ 5. C B 2 ¿FNCFSEF E A D B [\"#] m [$%] K2 | | | |,$ = KB =CJSJN O6 | |KD =CJSJN D AF O :VLBSEBLJWFSJMFSFHÌSF ÀFNCFSJOZBSÀBQLBÀ 0NFSLF[MJ¿FZSFL¿FNCFS \"0#$LBSF CJSJNEJS \" 5 B) 2 5 $ | | | |%&0'EJLEËSUHFO #$ =DN DF =DN D) 3 5 & | | :VLBSEBLJWFSJMFSFHÌSF \"' LBÀDNEJS \" # $ % & 3. ôFLJMEFLJ 0 NFSLF[MJ ¿FNCFSEF AO 6. :BS¿BQDNPMBO¿FNCFSJMFBZOEÐ[MFNEF IFS- [\"0][#$] 17 IBOHJ пРEPóSVTBM PMNBZBO BMU GBSLM OPLUB BMO- | |#$ =DN ZPS #V OPLUBMBSO ¿FNCFSJO NFSLF[JOF V[BLMLMBS 30 | |0$ =DN DNEJS B C #VOB HÌSF CV OPLUBMBS LÌöF LBCVM FEFO ÑÀ- HFOMFSEFO LBÀ ÀFNCFSJO JÀ CÌMHFTJOEF ZFS BM- | | :VLBSEBLJWFSJMFSFHÌSF \"# LBÀDNEJS NB[ \" # 4 17 $ \" # $ % & D) 3 17 E) 2 17 1. \" 2. B 3. E 11 4. B 5. C 6. D
TEST - 5 ¦FNCFSJO5FNFM&MFNBOMBS 1. ôFLJMEF \"#$% LBSF- 4. d C TJOJO ¿FWSFM ¿FNCFSJ O D ¿J[JMNJõUJS K | BK | = |,$| AB ¦FNCFSJO ZBSÀBQ 5 2 DN PMEVôVOB HÌSF , ôFLJMEF0NFSLF[MJ ¿FNCFSWFEEPóSVTVWFSJMNJõ- OPLUBTOOÀFNCFSFV[BLMôFOB[LBÀDNEJS UJS%PóSVJMF¿FNCFSJOPSUBLOPLUBTZPLUVS0OPL- UBTOOEEPóSVTVOBPMBOV[BLMóDNEJS \" # $ 5 2 - 5 ¦FNCFSJO E EPôSVTVOB FO ZBLO PMBO OPLUBT- OOEPôSVZBPMBOV[BLMôYCJSJN FOV[BLOPL- D) 1 E) 2 UBTOOEPôSVZBPMBOV[BLMôZCJSJNPMEVôVOB HÌSF Y+ZLBÀCJSJNEJS 2. C 0NFSLF[MJ¿FNCFSEF \" # $ % & E [0%] m [\"#] 5. 4 [0&] m [\"$] O L | 0%| = 3 cm A3 | 0&| = 4 cm K | |\"$ =DN B D C B AD | |:VLBSEBLJWFSJMFSFHÌSF \"# LBÀDNEJS E \" 2 5 B) 2 6 $ % & #JSJN LBSFMFSF BZSMNõ Y CPZVUMBSOEB CJS EJL- EËSUHFOWFSJMNJõUJS 3. ,ËõFMFSJ 0 NFSLF[MJ &MJOEFLJ QFSHFM JMF , WF - OPLUBMBSOEBO HFÀFO DNZBS¿BQM¿FN- CJS ÀFNCFS ÀJ[NFL JTUFZFO &MJG QFSHFMJO TJWSJ A CFS Ð[FSJOEF PMBO VDVOVIBOHJOPLUBZBLPZNBMES C O \"$%#ZBNVóVWFSJM- 48 B NJõUJS \" \" # # $ $ % % & & 30 D | | | |[\"#][$%] \"# =DNWF $% =DN 6. #JSLFOBSDNPMBOEÑ[HÑOBMUHFOJOUÑNLF- PMEVôVOB HÌSF \"$%# ZBNVôVOVO ZÑLTFLMJôJ OBSMBSOBUFôFUPMBDBLöFLJMEFÀJ[JMFOÀFNCFSJO LBÀDNEJS ZBSÀBQLBÀDNEJS \" 4 3 B) 4 2 $ 3 2 \" # $ % & D) 4 E) 2 3 1. C 2. D 3. D 12 4. \" 5. C 6. \"
www.aydinyayinlaricom.tr ¦&.#&37&%\"÷3& 5. MODÜL 11. SINIF ¦&.#&3%&\"¦*-\"3m* ÷MJöLJMJ,B[BONMBS 11.5.2.1 : #JS¿FNCFSEFNFSLF[ ¿FWSF J¿ EõWFUFóFULJSJõB¿MBSOË[FMMJLMFSJOJLVMMBOBSBLJõMFNMFSZBQBS .FSLF[\"À ÖRNEK 1 D 0NFSLF[MJ¿FNCFS 7$1,0%m/*m 28° % ,ËõFTJ¿FNCFSJONFSLF[JOEFPMBOB¿ZB¿FN- E C CFSJOCJSNFSLF[BÀTEFOJS 25° m (AB) = 32° & #JS¿FNCFSEFCJSNFSLF[B¿OOËM¿ÐTÐCVNFS- F LF[B¿OOHËSEÐóÐZBZËM¿ÐTÐOFFõJUUJS m (DC) = 28° z % A y m (FE) = 25° O x #VOBHÌSF Y+ y +[ AB UPQMBN LBÀ EFSFDF- 32° EJS a O : merkez & O B x = m ( AB ) = 32° & y = m ( DC ) = 28° % z = m ( FE ) = 25° x + y + z = 85° r \"0#B¿TNFSLF[B¿ES ÖRNEK 2 %% C 0NFSLF[MJ¿FNCFS r m ( AOB ) = m ( AB ) = a D |$%| = |\"#| ¥FNCFSEFFõJUV[VOMVLUBLJLJSJõMFSJOCFMJSMFEJóJ & ZBZMBSFõUJS r m (CD) = 100° aB #VOB HÌSF A // B O % = a C 100° m ( OBA ) r a LBÀEFSFDFEJS // A && CD = AB & m ( CD ) = m ( AB ) = 100° D & m ( % ) = 100° AOB | || | & % 2a + 100 = 180 & a = 40° r \"# = $% l m ( CD ) = m ( AB ) ÖRNEK 3 ¥FNCFSJONFSLF[JOEFOLJSJõFEJLJOFO¿BQ CV LJSJõJOCËMEÐóÐZBZMBSPSUBMBS B 0 NFSLF[MJ S ZBS¿BQM ¿FN- D r3 r CFSWFSJMNJõUJS / / O O : Merkez A r xO r C AB EF = = CD = r r y r 32 z E r r2 r AB C D F %% #VOBHÌSF Y+ y +[ LBÀEFSFDFEJS | | | |r %$ m \"# l m(AC) = m(CB) x = Y+ y +[= %% y = [= | | | |r %$ m \"# l m(AD) = m(DB) 13 1. 85 2. 40 3. 270
11. SINIF 5. MODÜL ¦&.#&37&%\"÷3& www.aydinyayinlari.com.tr ÖRNEK 4 0NFSLF[MJ¿FNCFS 7$1,0%m/*m ) D #JS¿FNCFSEFBZOZBZHËSFO¿FWSFB¿MBSOËM- m (ADB) = 260° ¿ÐMFSJFõJUUJS O K 50° 1OPLUBTOEBOHFÀFOFOLTB a° T AP LJSJö[\"#]PMEVôVOBHÌSF a° // // A C B % LBÀEFSFDFEJS 2a° B m ( BOC ) % r m ( A%KB ) = m ( A%TB ) = m ( AB ) 1EFOHFÀFOFOLTBLJSJö[\"#]JTF[ OC ] m [\"#]WF 2 && #JS ¿FNCFSEF ¿BQ HËSFO ¿FWSF B¿OO ËM¿ÐTÐ m ( AC ) = m ( CB ) EJS K ) m ( ACB ) = 360 - 260 = 100 B <\"#>¿BQ AO % & m ( COB ) = 50° T ÖRNEK 5 r m ( A%KB ) = m ( A%TB ) = 180° = 90° 2 // // %Ð[HÐOCJSCFõHFOJOUÐNLË- õFMFSJOEFO HF¿FO CJS ¿FNCFS #JS¿FNCFSEFQBSBMFMJLJLJSJõJOBSBTOEBLBMBO a ¿J[JMJZPS ZBZMBSOËM¿ÐMFSJCJSCJSJOFFõJUUJS // O // #VOB HÌSF CFöHFOJO CJS AB LFOBSOO HÌSEÑôÑ NFSLF[ // BÀLBÀEFSFDFEJS CD &öJULJSJöMFSJOHÌSEÑôÑNFSLF[BÀMBSEBFöJUUJS %% 5a = r 7ABA / / 7CDA + m (AC) = m ( BD ) a = ¦FWSF\"À 7$1,0%m/*m ,ËõFTJ¿FNCFSJOÐ[FSJOEFPMBOWFLFOBSMBSCJ- SFS LJSJõ PMBO B¿ZB ¿FNCFSJO CJS ÀFWSF BÀT EFOJS #JS ¿FNCFSEF ¿FWSF B¿OO ËM¿ÐTÐ CV B¿OO HËSEÐóÐZBZËM¿ÐTÐOÐOZBSTOBFõJUUJS A B a° 2a° [AB] ve [BC] C CJSFSLJSJõ r \"#$B¿T¿FWSFB¿ES % r m ( % ) = m ( AC ) ABC 2 4. 50 5. 72 14
www.aydinyayinlaricom.tr ¦&.#&37&%\"÷3& 5. MODÜL 11. SINIF ÖRNEK 6 ÖRNEK 9 C 0NFSLF[MJ¿FNCFSEF E 0NFSLF[MJ¿FNCFSEF 3y O %% 20° m ( A%ED ) = 20° A m (AC) = 3y m (AB) = 6y B #VOBHÌSF 6y PMEVôVOB HÌSF m ( A%CB ) A O % LBÀEFSFDFEJS 40° m ( BCD ) = x LBÀEFSF- B x DFEJS C 3y + 6y =j y = D & % = 3y = 60° m ( ACB ) m ( AD ) = 40° ) m ( DAB ) = 180° + 40° = 220 x = 110° ÖRNEK 10 ÖRNEK 7 A ôFLJMEFLJ¿FNCFSEF D A 0NFSLF[MJ¿FNCFS B | BD | = | \"$| 40° % = 40° m % = a B m ( D%BA ) = 2a BOb m ( BAC ) ( ABO ) BC b % B B % = 4a m ( ACO ) = b m ( BAC ) #VOB HÌSF B + C UPQMBN C m ( A%CB ) = 5a LBÀEFSFDFEJS #VOBHÌSF m ( A%BC ) = bLBÀEFSFDFEJS &% & && m (BC) = m ( BOC ) = 80° m ( AD ) = 4a DB = AC & m ( AC ) = m (DB) a + b + 40 = 80 6a + 8a + 6a + 4a = 360° a + b = & m (BA ) = 10a b = 3a = 45° & m (BC ) = 8a & m (BD ) = 6a ÖRNEK 8 ÖRNEK 11 A 0NFSLF[MJ¿FNCFS A 0NFSLF[MJ¿FNCFSEF Bx 2x % = 40° % = 40° m ( ECD ) m ( OBC ) x % #VOB HÌSF m ( BAC ) = x #VOBHÌSF m ( % ) = x C ABE O 40° O E LBÀEFSFDFEJS // LBÀEFSFDFEJS C 40° // 40° 80° B D %% & m (AE) = 2x , m (DE) = 80° m ( BC ) = 2x° 2x += 180 x = % = 100° m ( COB ) % = 2X = 100° & x = 50° m ( COB ) 6. 60 7. 40 8. 50 15 9. 110 10. 45 11. 50
11. SINIF 5. MODÜL ¦&.#&37&%\"÷3& www.aydinyayinlari.com.tr ÖRNEK 12 ÖRNEK 15 A B 0NFSLF[MJ¿FNCFSEF A R ôFLJMEF 0 NFSLF[MJ x 35° P ¿FZSFL ¿FNCFSJO J¿JOF [\"#][$%] 45° x B 013$ LBSFTJ ¿J[JMNJõ- C O C UJS O % D m ( CBA ) = 35° #VOB HÌSF \"#3 BÀ- TOO ÌMÀÑTÑ LBÀ EF- #VOBHÌSF m ( % = x SFDFEJS CAB ) LBÀEFSFDFEJS && [OR]LBSFOJOLÌöFHFOJBÀPSUBZ AB ' CD & m ( AC ) = m ( BD ) = 70° & m ( % ) = 45° = m ( AR ) 180 + 70 POR x = = 125° 2x =j x = 2 ÖRNEK 13 30° F 60° 0NFSLF[MJZBSN ÖRNEK 16 K ¿FNCFS xB 0\"#$LBSF 100° B 0NFSLF[MJ¿FNCFS 45° C A 10° m (C%AO) = 10° BF = 2 . OA a C D 45° 50° 45° O AE 20° % = 50° m (ACB) :VLBSEBLJ WFSJMFSF HÌSF m ( F%BK ) = x LBÀ EFSFDF- O K #VOBHÌSF EJS m % = a LBÀEF- (OBC) |OB| = |BF| =S T SFDFEJS % & m (BF) = 60° m ( BC ) = 180° - 120° = 60° &% % ,#%&PMEVôVOEBOm (KD) + m (BE) = 90° [BT] çap, m ( TC ) = 2a = 180° - 60° % a = 60° m (KF) = 2x = 30° & x = 15° ÖRNEK 14 A :BOEBLJ¿FNCFSEF ÖRNEK 17 70° // 80° |\"%| = |%$| A 10° E ôFLJMEFLJ¿FNCFSEF x B \"#$%LBSF m ( E%AB ) = 10° D % m ( BAC ) = 70° #VOBHÌSF m ( A%DE ) =x LBÀ a % EFSFDFEJS B m (AB) = 80° // #VOB HÌSF m ( A%BD ) = a C LBÀEFSFDFEJS DC && m ( % ) = 20° & m ( % ) = 10° m ( AD ) = m ( DC ) = 2a° EB EDB & m ( % ) = 45° [DB]LÌöFHFO m ( BC ) = 140° ADB & m ( AB ) = 80° 80 + 140 + 4a = 360° 10 + x =j x = a = 35° 12. 125 13. 15 14. 35 16 15. 16. 60 17. 35
www.aydinyayinlaricom.tr ¦&.#&37&%\"÷3& 5. MODÜL 11. SINIF ÖRNEK 18 \" WF # OPLUBMBSOEB LFTJõFO 5FôFU,JSJö\"À ¿FNCFSMFSEFO CJSJOJO NFSLF[J 0 7$1,0%m/*m T OPLUBTES ,ËõFTJ¿FNCFSÐ[FSJOEFCVMVOBOWFCJSLFOB- m ( A%TB ) = 50° SCVLËõFEF¿FNCFSFUFóFU EJóFSLFOBS¿FN- 50° CFSJOLJSJõJPMBOB¿ZB¿FNCFSJOCJSUFôFU-LJSJö O ) BÀTEFOJS #VOBHÌSF m (AOB)LBÀEFSF- 5FóFU-LJSJõB¿TOOËM¿ÐTÐ CVB¿OOHËSEÐ- A 100° B óÐZBZËM¿ÐTÐOÐOZBSTOBFõJUUJS DFEJS T 5 UFóFUEFóNF m ( A%TB ) = 50° & m( % ) = 100° a° B OPLUBT AOB 2a° >;; ? ) #VEVSVNEBm ( AxB ) = 200°j m ( AOB ) = 360 - 200 = 160° ÖRNEK 19 . A A % 30° r m ( A%TB ) = m ( AT ) D 2 \"ZOZBZHËSFOUFóFU-LJSJõB¿TOOËM¿ÐTÐJMF ¿FWSFB¿TOOËM¿ÐTÐFõJUUJS a C T B EC a aA | | | | | |\"#$пHFOJOEF \"% = \"& = \"$ m(B%AE) = 30° #VOBHÌSF m ( % ) = a LBÀEFSFDFEJS DCB ]\"%]=]\"&]=]\"$]PMEVôVOEBO#VV[VOMVLMBSZBSÀBQ B \"hZNFSLF[LBCVMFEFOCJSÀFNCFS% & $OPLUBMBSOEBO r m ( % ) = % % ATB m ( BCT ) HFÀFS#VEVSVNEB m ( DE ) = 30° = 2a & a = 15° ÖRNEK 20 ÖRNEK 21 A 0 NFSLF[MJ ¿FNCFSEF [BF] ôFLJMEFLJ 0 NFSLF[MJ ¿FNCFS- x B ¿BQ [\"#][$&] D de [\"%¿FNCFSF\"OPLUBTO- B [0$][ EF ] m ( % ) = 10° EBUFóFUUJS OCE 2x A 3y C O E #VOBHÌSF m ( A%BF ) =x LBÀ % = 2x F D EFSFDFEJS O y + 10° m ( DAB ) m ( A%BC ) = 90° % 4y + 10 = 90 m ( BAC ) = 3y y = % C m ( BCA ) = y + 10° \"#0JLJ[LFOBSÑÀHFO m ( % ) = x = m( % ) #VOBHÌSF YLBÀEFSFDFEJS OAB OBA AB ' CE & % = x + 10 & & m ( COA ) & m ( AC ) = x + 10 m ( BA ) = 4x = 2y + 20 % OC ' EF & m ( % ) = m ( % ) = 10° & m ( CF ) = 20° 4x = 60 OCE CEF x = 15° m ( A%BF ) = x ÀFWSFBÀj ) = 2x m ( ACF ) x + 10 + 20 = 2x j x = 18. 160 19. 15 20. 30 17 21. 15
TEST - 6 ¦FNCFSEF\"ÀMBSm* 1. A 0NFSLF[MJ 4. D 0NFSLF[MJ¿FNCFS ZBSN¿FNCFS x C | \"%| = | %$| |\"#| = |0$| A 20° B % = 20° O m ( COB ) BOC & :VLBSEBLJ WFSJMFSF HÌSF m (AC) LBÀ EFSFDF- EJS \" # $ % & :VLBSEBLJWFSJMFSFHÌSF m ( D%AB ) = x LBÀEF- SFDFEJS \" # $ % & 2. B 0 NFSLF[MJ ¿FZSFL 5. C 0NFSLF[MJ¿FNCFS- a ¿FNCFS a de C D % 55° m ( OAC ) = 62° A O [\"#]¿BQ 62° B | $#| = | $%| A O % = 55° m ( ABC ) YVLBSEBLJ WFSJMFSF HÌSF m ( % ) =a LBÀ EF- OBC SFDFEJS % DCB :VLBSEBLJWFSJMFSFHÌSF m ( ) = a LBÀEF- \" # $ % & SFDFEJS \" # $ % & 3. C 6. #JSÐMLFEFZBQMBOTF¿JNTPOV¿MBSBLõBNDBOMZB- F A ZOEBB¿LMBONõUS4POV¿MBSEBJSFHSBGJóJOEFHËT- 40° B UFSFO57LBOBMIFSQBSUJOJOPZPSBOOGBSLMSFOLUF HËTUFSNJõUJS 110° Mavi .PS O ,SN[ Pembe ôFLJMEFLJ0NFSLF[MJEBJSFEJMJNJOEF m( % = 110° m ( % ) = 40° AOB ) OAC ) 4FÀJNJPSBOMBNBWJSFOHJOUFNTJMFUUJôJQBS- :VLBSEBLJWFSJMFSFHÌSF m (CFB)LBÀEFSFDF- UJLB[BOEôOBHÌSF HSBGJLUFLJNBWJSFOHJONFS- LF[BÀTLBÀEFSFDFPMBSBLWFSJMNJöUJS EJS \" # $ % & \" # $ % & 1. C 2. C 3. \" 18 4. D 5. B 6. C
¦FNCFSEF\"ÀMBSm* TEST - 7 1. D ôFLJMEFLJ<\"#> 4. D 0NFSLF[MJZBSN a ¿FNCFSEF aC ¿BQMZBSN¿FN- C E 150° berde O B <$%><\"&> A |%$| = |$#| m ( B%AE ) = 20° A B % m ( DCB ) = 150° :VLBSEBLJWFSJMFSFHÌSF m ( % = a LBÀEF- &% ADC ) m (CD) = 50°PMEVôVOBHÌSF m ( AEC ) = aLBÀ EFSFDFEJS SFDFEJS \" # $ % & \" # $ % & 5. ,NFSLF[MJ¿FNCFSEF 2. 0 NFSLF[MJ ¿FN- $UFóFUEFóNFOPLUBT berde % %% K B % m ( BCD ) m (AB) = 4m (BC) m( KAB ) = O C 3 Aa [\",][#$] A D C B % :VLBSEBLJWFSJMFSFHÌSF m ( BCD )LBÀEFSFDF- % EJS CAB ) :VLBSEBLJWFSJMFSFHÌSF m ( = a LBÀEF- SFDFEJS \" # $ % & \" # $ % & 3. B ôFLJMEFLJ 0 NFS- 6. 4FM¿VL ±óSFUNFO TOGOEBLJ ËóSFODJMFSJOJO UBIUB- LF[MJ ZHËSÐõB¿MBSOOFõJUPMNBTJ¿JOCJSPUVSNBEÐ[FOJ QMBOMZPS 5BIUBOO V[VOMVóVOV ZBS¿BQ LBCVM FEFO A 60° ¿FNCFSEF CJS¿FNCFSQMBOMBZQ ËóSFODJMFSJCV¿FNCFSJOÐ[FSJ- OFEFOLHFMFDFLOPLUBMBSBõFLJMEFLJHJCJZFSMFõUJSJZPS a 50° C % m ( OAB ) = 60° Tahta O% m ( OCB ) = 50° % 0UVSNBQMBOöFLJMEFLJHJCJPMEVôVOBHÌSF 4FM- :VLBSEBLJWFSJMFSFHÌSF m ( AOC ) = aLBÀEF- ÀVL²ôSFUNFOCJSÌôSFODJOJOHÌSÑöBÀTOLBÀ SFDFEJS EFSFDFPMBSBLCFMJSMFNJöUJS \" # $ % & \" # $ % & 1. B 2. B 3. C 19 4. B 5. C 6. \"
TEST - 8 ¦FNCFSEF\"ÀMBSm* 1. D 0NFSLF[MJ¿FNCFS 4. C ôFLJMEFLJ¿FNCFSEF a x C D [\"#][$%] E [\"#]¿BQ B |\"%| = |%$| |$&| = |BE| F B [&$][\"#] 50° m ( A%BE ) = 15° AO |\"&| = |ED| F 15° A % = 50° m ( ABD ) E :VLBSEBLJ WFSJMFSF HÌSF % = x LBÀ EF- :VLBSEBLJWFSJMFSFHÌSF m (D%CE) =aLBÀEFSF- m ( DEC ) DFEJS SFDFEJS \" # $ % & \" # $ % & 2. A 0NFSLF[MJ¿FNCFS 5. D 0NFSLF[MJ¿FNCFS C % = 40° [\"$] a [BD] = {E} 40° m ( ACB ) O B AaE O C % ( ABD 32° m ) = 32° B :VLBSEBLJWFSJMFSFHÌSF m % LBÀEFSFDF- :VLBSEBLJWFSJMFSFHÌSF m ( % = a LBÀEF- OAB DAC ) ( ) SFDFEJS EJS \" # $ % & \" # $ % & 6. ¶TUUFOHËSÐOÐõÐEBJSFPMBOCJSEPóVNHÐOÐQBTUB- TËODFEËSUFõEJMJNFBZSMZPS 3. A 0NFSLF[MJ¿FNCFS a B 45° m % = 45° O ( OBC ) 54° % m ( ODC ) = 54° D C %BIBTPOSBIFSEJMJNпLJõJBSBTOEBNFSLF[B¿- MBSFõJUPMBDBLõFLJMEFQBZMBõUSMZPS :VLBSEBLJWFSJMFSFHÌSF m (XA) = a LBÀEFSF- DFEJS #VOB HÌSF CJS LJöJZF EÑöFO QBTUB EJMJNJOJO \" # $ % & NFSLF[BÀTLBÀEFSFDFEJS \" # $ % & 1. B 2. D 3. E 20 4. D 5. D 6. E
¦FNCFSEF\"ÀMBSm* TEST - 9 1. A 4. A 0NFSLF[MJ¿FNCFS T C 20° E D [\"#]¿BQ O 77° % = 20° OE m ( ACD ) 55° |$&| = |ED| FB P KB 0 NFSLF[MJ ¿FNCFSEF 5& EPóSVTV ¿FNCFSF & ) :VLBSEBLJWFSJMFSFHÌSF m (CKB) LBÀEFSFDF- OPLUBTOEBUFóFU m ( % ) = 77° m ( % ) = 55° EJS TEA ABF :VLBSEBLJWFSJMFSFHÌSF m ( A%PF ) LBÀEFSFDF- \" # $ % & EJS \" # $ % & 2. F 5. 0NFSLF[MJ¿FNCFS Ax \" $ %EPóSVTBM O m ( B%CD ) = B C KE D % , NFSLF[MJ ZBSN ¿FNCFSEF \"%# пHFO [ BF A B m ( OAB ) = a | | | |¿FNCFSF\"OPLUBTOEBUFóFU \"# = \"% WF 70° C | | | |\"& = % LBÀ ED PMEVóVOB HËSF m ( FAD ) = x D :VLBSEBLJ WFSJMFSF HÌSF m ( O%AB ) = a LBÀ EF- EFSFDFEJS SFDFEJS \" # $ % & \" # $ % & 6. /B[M[\"#]¿BQM¿FNCFSJ¿J[JQ¿FNCFSJOÐ[FSJOEF CJS$OPLUBTJõBSFUMFZFSFL\"#$пHFOJOJ¿J[JZPS C 3. C D 0 NFSLF[MJ [\"#] AB ¿BQMZBSN¿FNCFS 36° O <0$> m <\"%> %BIB TPOSB BSLBEBõ \"ZMJOhF #V ¿FNCFSJO J¿JOEF A m ( D%AB ) = 36° CJS LFOBS [\"#] PMBO CFOJN ¿J[EJóJN пHFOF Fõ B CBõLBLB¿Ð¿HFO¿J[FCJMJSTJO EJZFTPSVZPS :VLBSEBLJWFSJMFSFHÌSF m ( % ) LBÀEFSFDF- OCB EJS \"ZMJOhJO EPôSV DFWBC BöBôEBLJMFSEFO IBOHJTJ PMNBMES \" # $ % & \" # $ % & 1. D 2. \" 3. B 21 4. E 5. B 6. C
11. SINIF 5. MODÜL ¦&.#&37&%\"÷3& www.aydinyayinlari.com.tr ¦&.#&3%&\"¦*-\"3** ÷MJöLJMJ,B[BONMBS 11.5.2.1 : #JS¿FNCFSEFNFSLF[ ¿FWSF J¿ EõWFUFóFULJSJõB¿MBSOË[FMMJLMFSJOJLVMMBOBSBLJõMFNMFSZBQBS ÷À\"À ÖRNEK 3 7$1,0%m/*m ¥FNCFSJO J¿JOEF LFTJõFO JLJ LJSJõJO PMVõUVSEVóV B [\"#] LJSJõJOJO V[VOMVóV ZBS- B¿MBSOIFSCJSJOFCV¿FNCFSJOCJSJÀBÀTEFOJS A ¿BQ V[VOMVóVOB FõJU PMBO #JS¿FNCFSEFJ¿B¿OOËM¿ÐTÐ CVB¿OOHËSEÐ- a % óÐZBZMBSOËM¿ÐMFSJUPQMBNOOZBSTOBFõJUUJS K ¿FNCFSde m ( CDE ) = 50° D [\"&] a [#$] = {K} 50° C E #VOB HÌSF % = a m ( AKB ) C A [\"#]WF[$%] LBÀEFSFDFEJS Ka CJSFSLJSJõ &% 60 + 100 a m (AB) = 60° & . m (CE) = 100° & a = = 80° B 2 D %ö\"À r\",% #,$ \",$ %,#CJSFSJ¿B¿ES 7$1,0%m/*m %% ,ËõFTJ¿FNCFSJOEõCËMHFTJOEF LFOBSMBS¿FN- m ( AD ) + m ( BC ) CFSJOJLJLFTFOJ CJSUFóFUCJSLFTFOJWFZBJLJUF- r % = óFUJPMBOB¿ZBCV¿FNCFSJOCJSEöBÀTEFOJS m ( AKD ) 2 ÖRNEK 1 #JS Eõ B¿OO ËM¿ÐTÐ HËSEÐóÐ ZBZMBSO ËM¿ÐMFSJ GBSLOOZBSTOBFõJUUJS B ôFLJMEFLJ¿FNCFSEF B ( ) x m (AKE) + m (BCD) = 272° A A C m ( % ) = 36° Ka BDA K aa #VOBHÌSF % =x F m ( EBD ) E 36° LBÀEFSFDFEJS C D D [,#WF[,%CJSFSLFTFO >;;? >;; ? m (AKE) + m (BCD) r#,%B¿TEõB¿ES a = = 136 & x + a + 36 = 180° & x = 8° %% 2 r m ( B%KD ) = m ( BD ) - m ( AC ) 2 ÖRNEK 2 T EK ôFLJMEFLJ¿FNCFSEF [&$] a [ BD ] = { F } Ka D A 80° m ( E%FD ) = A F ) B m (EKD) = B % [,5UFóFUWF[,#LFTFO #VOB HÌSF m ( BAC ) = a C r5,#B¿TEõB¿ES LBÀEFSFDFEJS %% & 2a + 90° r % = m ( TB ) - m ( AT ) m (BC) = 2a° & 80 = & a = 35° m ( TKB ) 2 2 1. 8 2. 35 22 3. 80
www.aydinyayinlaricom.tr ¦&.#&37&%\"÷3& 5. MODÜL 11. SINIF 7$1,0%m/*m ÖRNEK 5 [#\"WF[#$CJSFSUFóFU %õB¿ JLJUFóFUJOPMVõUVSEVóVCJSEõB¿JTFEõ A B m( % = 50° B¿ËM¿ÐTÐJMFEõB¿ZËOÐOEFLJZBZËM¿ÐTÐOÐO a ABC ) UPQMBNEJS 50° D m( % = 160° T DCE ) 160° C #VOBHÌSF m ( D%AB ) = a E LBÀEFSFDFEJS Ka & m (\\DC) = 40° m (AD) = 2a 2a + 40 + 50° = 180° L a = 45° [,5WF[,-CJSFSUFóFU r5,-B¿TEõB¿ES r m ( % ) + m ( $ ) = 180° ÖRNEK 6 TKL TL T C ôFLJMEFLJ B 40° ¿FNCFSEF x m ( % ) = 40° ACE K EO 30° A F D % m ( CAD ) = 30° L E #VOBHÌSF m ( A%BE ) =x LBÀEFSFDFEJS 0NFSLF[ %& [,5WF[,-CJSFSUFóFU m (AE) = 2x° m (BD) = 60° r % = % 40 = 2x - 60 & x = 70° m ( TKO ) m ( OKL ) %$ 2 r m (TE) = m (EL) %% r m ( TKO ) + m (TE) = 90° ÖRNEK 4 ÖRNEK 7 A A 0NFSLF[MJ D 30° [#\"WF[#$¿FNCF- E ¿FNCFS C re \" WF $ OPLUBMB- x 40° 30° m ( A%DB ) = 30° B OC SOEBUFóFUUJS D % ACB ) x B % = 30° m( = 40° m ( ADC ) #VOBHÌSF % = x LBÀ #VOBHÌSF m ( A%BE ) = x LBÀEFSFDFEJS m ( ABC ) EFSFDFEJS &% & m (AB) - m (EC) m (AB) = 80° ve 30 = PMEVôVOEBO 2 & m (AC) = 60° ve x + 60° = 180° % m (EC) = 20° x = 120° % m (AE) = 2x 2x + 80° + 20 = 180° & x = 40° 4. 120 23 5. 45 6. 70 7. 40
11. SINIF 5. MODÜL ¦&.#&37&%\"÷3& www.aydinyayinlari.com.tr ÖRNEK 8 ÖRNEK 11 #JSÀFNCFSJOBZOZBZMBSHÌSFOCJSJÀBÀTJMFCJSEö A ôFLJMEFLJ¿FNCFSEF BÀTOO UPQMBN PMEVôVOB HÌSF CV PSUBL ZBZ- MBSEBOCÑZÑLPMBOOÌMÀÑTÑLBÀEFSFDFEJS [#\"WF[#$CJSFSUFóFU a % = 30° m ( ABD ) 30° B a =PSUBLZBZMBS % HÌSFOJÀBÀ m ( ADC ) = 40° x a yi i = PSUBL ZBZMB- #VOBHÌSF S HÌSFO Eö BÀ PM- m ( D%AC ) = aLBÀEF- K C SFDFEJS 40° TVO D x >ZPMNBLÑ[FSF x + y = a ve x-y && =i m (KC) = 2a ve m (AC) = 180° - 30° = 150° 22 150 - 2a x + y = 2aWFY- y = 2i j x = a + i = 40 = 2 & a = 35° ÖRNEK 9 ÖRNEK 12 C ôFLJMEFLJ¿FNCFSEF B % A \"#$пHFOJOJOJ¿UFóFU a m ( CAE ) = 40° 40° ¿FNCFSJ¿J[JMNJõUJS DF 60° F 40° A % = 60° | DE | = | EF |WF m ( CFE ) D % = 40° m ( BAC ) E :VLBSEBLJWFSJMFSFHÌSF m ( % ) = a LBÀEFSFDFEJS #VOB HÌSF m ( A%CB ) LBÀ CBE % B E C EFSFDFEJS (CE) m & = 2a 4 & 2a - x = 80 & a = 50° % %% m ( BD) = x 2a + x = 120° m (DF) = 140° ve m (DE) = m (EF) = a° 2a + 140° = 360° & a = 110° #VEVSVNEB m ( % ) = 180 - 110 = 70° ACB ÖRNEK 10 60° B ôFLJMEFLJ¿FNCFSEF ÖRNEK 13 B 0¿FNCFSJONFSLF[J C 80° [#$][\"& D 13° m ( D%CA ) = 13° 80° 30° 47° O . % AE D x A m ( CDB ) = 30° E C % = 47° m ( BAC ) # UFôFU EFôNF OPLUBT PMEVôVOB HÌSF m ( B%AE ) = x #VOBHÌSF m ( B%CD ) LBÀEFSFDFEJS LBÀEFSFDFEJS %& m (DE) = 26° ve m (BD) = 2x° &% & m (BD) = m (EC) = 80° m (BC) - 26 & 47 = & m (BC) = 120° & 2 m (BC) = 60° 2x + 26° + 120° = 180° & x = 17° 140 - 80 x = = 30° 2 8. 110 9. 50 10. 30 24 11. 35 12. 70 13. 17
www.aydinyayinlaricom.tr ¦&.#&37&%\"÷3& 5. MODÜL 11. SINIF ÖRNEK 14 ÖRNEK 16 A \"#$пHFOJOEF [\"#] ¿BQM ZB- 70° [$%] m [\"#] E D SN¿FNCFS DF 45° [\"$] m [ BF ] b \"%$пHFO A F |BE| = |&$| a [$&]B¿PSUBZ % a m ( BAC ) = 70° B C x B // // C #VOBHÌSF %% E :VLBSEBLJ WFSJMFSF HÌSF m (ED) + m (BF) UPQMBN LBÀEFSFDFEJS % = x LBÀ m ( DEF ) EFSFDFEJS & m (DB) = 2b WFC+ 2a =j a + b = . %% [ BC ]ZJÀBQLBCVMFEFOÀFNCFS %WF&OPLUBMBSOEBO m (AE) + m (DF) HFÀFS&NFSLF[PMVS = 45° % 2 %% & m ( DF ) = x° & m (EA) + m (DF) = 90° %% j m (ED) + m (BF) = 90° & 70 = 180 - x (d› fl ac› ) 2 & x = 40° ÖRNEK 17 A B [\"#WF[\"$ ¿FNCFSF r 60° D E UFóFU r [\"#m <\"$ C |\"$| = |BE| & #VOB HÌSF m (CD) LBÀEFSFDFEJS ÖRNEK 15 A [%\"[#$] % 30° ]\"$]=]\"#]=SPMEVôVOEBO]#&]=SWFm (BE) = 60° DE j m ( K%BE ) = 30° j m ( B%AE ) = m ( B%EA ) = 15° [ EF ] m [\"%] %& j m ( CAE ) = 75°WFm (BD) = 30° && m (CD) + 30° = 90° j m (CD) = 60° [%\" [ EF ]WF[ DB UFóFU F C m( % = 30° ÖRNEK 18 B BAC ) B a [\"#UFóFU Ad C b [\"&] a [BD] = {F} :VLBSEBLJWFSJMFSFHÌSF m ( E%FD ) LBÀEFSFDFEJS K F m ( B%AE ) = m ( E%AD ) 50° E % m ( EFD ) = 50° & & & 360 - 60 c) m ( BC ) = 60° & m ( AB ) = m ( AC ) = = 150° 2 #VOB HÌSF m (CKD) D m ( A%DB ) = 210 - 150 (d› fl aç › ) = 30° LBÀEFSFDFEJS 2 #VEVSVNEBm ( E%FD ) = 60° b - a =D-Ej b +E= a +D a +D= JÀJBÀ B+D+ b +E= 200 x =-= 14. 40 15. 60 25 16. 17. 18.
11. SINIF 5. MODÜL ¦&.#&37&%\"÷3& www.aydinyayinlari.com.tr )(1/m6(/(5m1(<q1(/m. ÖRNEK 21 ,JSJöMFS%ÌSUHFOJ A \"$%'EËSUHFOJ¿FN- TANIM x B CFSMFSJ#WF&OPL- #ÐUÐOLËõFMFSJCJS¿FNCFSJOÐ[FSJOEFCVMV- 70° C UBMBSOEB LFTNFLUF- OBOEËSUHFOFLJSJöMFSEÌSUHFOJEFOJS EJSm ( % ) = 70° ,JSJõMFSEËSUHFOJOJOLBSõMLMB¿MBSOOUPQMB- ACD NEJS D F ED \"#$%LJSJõMFS EËSUHFOJEJS #VOBHÌSF m ( % ) = x LBÀEFSFDFEJS AC CAF [ BE] PSUBL LJSJöJ ÀJ[JMJSTF \"'&# WF #&%$ LJSJöMFS EÌSUHFOJ m( % = 180° - 70° = 110° BED ) % ) = 70° m ( BEF m( % + m( % = 180° BEF ) FAB ) 70 + x = 180° & x = 110° B r m ( B%AD ) + % = 180° ÖRNEK 22 m ( BCD ) E r % + % = 180° D \"#$%LBSF [ DE ] m [ EB ] m ( ADC ) m ( ABC ) x C A % m ( EBC ) = 25° ÖRNEK 19 #VOBHÌSF C ôFLJMEFLJ¿FNCFSEF 25° % = x LBÀEFSFDF- m ( DAE ) B m ( A%CF ) = 55° EJS 55° % = 15° B m ( BEA ) A 180–x° x Dx #VOBHÌSF F m ( B%DF ) = x LBÀEF- ,BSF CJS LJSJöMFS EÌSUHFOJEJS [ DB] ÀBQ PMBDBôOEBO 15° SFDFEJS ÀFNCFS&OPLUBTOEBOHFÀFS E %% m ( EC ) = 50°, m ( DE ) = 2x° 2x + 50 =j x = - x ++= x j x = ÖRNEK 23 A \"#$%EËSUHFO ÖRNEK 20 70° 65° % = 70° m ( BAC ) AE OD C ôFLJMEFLJ¿FNCFSEF % m ( DAC ) = 65° B [ ED ] m [#$] By x D % = 10° [\"#] m [\"$] m ( ACB ) |\"#| = |\"&| % m ( ACD ) = 35° #VOBHÌSF m ( A%DE ) LBÀEFSF- 10° 35° m ( A%DB ) = x° DFEJS C % = y° m ( CBD ) #VOBHÌSF x +ZLBÀEFSFDFEJS \"#%&LJSJöMFSEÌSUHFOJEJS[ EB ]ÀBQUS m ( B%AD ) + m( % ) = 180° BCD &% AE = AB & m ( AB ) = m ( AE ) = 90° PMEVôVOEBO\"#$%LJSJöMFSEÌSUHFOJ & m ( A%DE ) = 45° x = Z= Y+ y = 19. 125 20. 45 26 21. 22. 23.
¦FNCFSEF\"ÀMBSm** TEST - 10 1. D C ôFLJMEFLJ\"#$%EËSU- 4. A B HFOJOJO LËõFHFOMFSJ , OPLUBTOEB LFTJõ- 50° NFLUFEJS 60° K 45° x 70° B E A E xD C #&¿FNCFSF#OPLUBTOEBUFóFU % = 60° m ( AKD ) [\"#WF[%$¿FNCFSFUFóFU m ( B%AD ) = 50° WF % = 70° PMEVôVOB HÌSF m ( % ) =x m ( A%EB ) = 45° m ( ABE ) DAC % LBÀEFSFDFEJS #VOBHÌSF m ( ADC ) = x LBÀEFSFDFEJS \" # $ % & \" # $ % & 5. D C ôFLJMEF\"#$%LBSFTJ- OJO J¿JOF \" NFSLF[MJ 2. B E 50° ¿FZSFL ¿FNCFS WF F [#$] ¿BQM ZBSN ¿FNCFS¿J[JMNJõUJS [DF] a [$&] = {E} D A 55° C AB :VLBSEBLJõFLJMEF[\"#WF[\"$¿FNCFSFUFóFUUJS :VLBSEBLJWFSJMFSFHÌSF m (C%EF)LBÀ EFSFDF- EJS % = 50° % = 55° PMEVóVOBHËSF \" # $ % & m ( DBC ) m ( BCD ) m ( % ) LBÀEFSFDFEJS BAC \" # $ % & 6. 3. A 0 NFSLF[MJ ¿FN- ber E 20° % 30° x m ( ABC ) = 30° BD O C m % ) = 20° ( BAD %Ð[HÐOTFLJ[HFOõFLMJOEFLJCJSV¿VSUNBZTBóMBN- #VOBHÌSF m ( % ) = x LBÀEFSFDFEJS MBõUSNBLJ¿JOõFLJMEFLJJLJ¿UB¿BLMZPS ECA #VOBHÌSF CJSCJSJOJLFTFOÀUBMBSOPMVöUVSEVôV \" # $ % & EBSBÀLBÀEFSFDFEJS \" # $ % & 1. B 2. E 3. B 27 4. B 5. C 6. D
TEST - 11 ¦FNCFSEF\"ÀMBSm** TC 1. B 4. D A D P 28° K C E AF B ôFLJMEFLJ¿FNCFSEF [\"%] a [#$] = {K} m ( B%PD ) = 28°WF % + m ( P%DA ) = 70° ôFLJMEF \"#$% EJLEËSUHFOJOJO [%$] LFOBS [\"#] m ( PBC ) ¿BQMZBSN¿FNCFSF5OPLUBTOEBUFóFUUJS & PMEVôVOBHÌSF m (BD) LBÀEFSFDFEJS | | | | % & 'OPLUBMBSEPôSVTBMWF FB = 3 . \"' PM- EVôVOBHÌSF m (F%EB)LBÀEFSFDFEJS \" # $ % & \" # $ % & 2. B 5. A B [\"&]¿BQM¿FNCFSEF A 36° C F [\"#][$%] D C % = a D E m ( ACB ) [\"# ¿FNCFSF#OPLUBTOEBUFóFUUJS % = i m ( DFE ) | | | |#$ = $% m(B%AD) = PMEVóVOBHËSF :VLBSEBLJWFSJMFSFHÌSF a + iUPQMBNLBÀEF- % SFDFEJS m ( BCD ) = aLBÀEFSFDFEJS \" # $ % & \" # $ % & 3. C B [$%]WF[ BE ] 6. #JSWJEFPPZVOVLBSBLUFSJPMBO.JSJ¿FNCFSõFLMJO- 3a ¿FNCFS Ð[FSJO- EFEJS.JSJhOJOBó[¿FNCFSJOMJLZBZOHËSFDFL EFLJ ' OPLUBTO- õFLJMEFUBTBSMBONõUS F EB LFTJõNFLUF- 60° A EJS A K 2a D E B % = m ( % ) = 3a m ( % ) = 2a .JSJ ¿FNCFS õFLMJOEFLJ ZFNMFSJ Bó[ HJSJõJOF UFóFU m ( CAE ) ACD AEB PMBDBLõFLJMEFUPQMBZBSBLQVBOBMNBLUBES PMEVôVOBHÌSF aLBÀEFSFDFEJS ) #VOBHÌSF m ( AKB )LBÀEFSFDFEJS \" # $ % & \" # $ % & 1. \" 2. E 3. B 28 4. C 5. D 6. C
¦FNCFSEF\"ÀMBSm** TEST - 12 1. D C \"#$% LBSFTJ õFLJMEFLJ 4. T ¿FNCFSJOLJSJõMFSEËSUHF- 40° A OJ 50° m ( A%DE ) = E C AB D E x B :VLBSEBLJWFSJMFSFHÌSF m ( % ) LBÀEFSFDF- BAE EJS :BOEBLJõFLJMEF\"5EPóSVTV$NFSLF[MJ¿FNCF- SJOUFóFUJEJS \" # $ % & | | | | | | | |\"# = % \"$ BD = %$ m ( CAT ) = 50° PMEVôVOBHÌSF m ( A%BC ) =x LBÀEFSFDFEJS \" # $ % & 2. A E O 5. %BJSFõFLMJOEFLJNBTBOO\"OPLUBTOEBCVMVOBOJLJ C LBSODB BSBMBSOEBMJLCJSB¿JMFEPóSVTBMIBSF- 30° LFUFEFSFLZÐSÐNFZFCBõMZPS D A B 0 NFSLF[MJ ¿FNCFSEF [\"#] ¿BQ [&\" JMF [ ED % ¿FNCFSF UFóFU m ( DCB ) = 30° PMEVóVOB HËSF % LBÀEFSFDFEJS m ( DEA ) \" # $ % & 3. E #JSJODJ LBSODB TSBTZMB \" - B - & JLJODJ LBSODB JTFTSBTZMB\"- D -$- F -&OPLUBMBSOBVóSV- D ZPS #V IBSFLFUJO ÐTUUFO HËSÐOÐNÐ õFLJMEFLJ HJCJ- EJS 30° A B AB 25° C O a D F F C K E | | | |0NFSLF[MJ¿FNCFSEF \"% = 0$ öLJODJ LBSODBOO PMVõUVSEVóV LJSJõMFS BSBTOEBLJ % % = 30° PMEVóVOBHËSF m ( % ) = a m ( EAC ) EFC B¿MBS FõJU WF \"# &' PMEVóVOB HËSF m ( EKC ) LBÀEFSFDFEJS LBÀEFSFDFEJS \" # $ % & \" # $ % & 1. \" 2. B 3. C 29 4. D 5. E
TEST - 13 ¦FNCFSEF\"ÀMBSm** 1. D )(1/m6(/(5m1(<q1(/m. A P 72° 4. A 54° C 105° E O aB a D FC B ôFLJMEFLJ0NFSLF[MJ¿FNCFSF [1\" \"OPLUBTOEB ôFLJMEFLJ¿FNCFSMFS&WF'OPLUBMBSOEBLFTJõJZPS UFóFUWF[1# #OPLUBTOEBUFóFUUJS % ' $OPLUBMBSEPóSVTBM m ( D%AB ) = 105° % = 72°WFm % ) = 54° PMEVôVOBHÌSF m ( % ) = a LBÀEFSFDFEJS m ( DPB ) ( BAC ABC % \" # $ % & PMEVôVOBHÌSF m ( ABC ) = aLBÀEFSFDFEJS \" # $ % & 5. A B KO 2. C ôFLJMEF[1\" [15] C 50° WF[5$¿FNCFSF A \"WF$OPLUBMBSOEBLFTJõFO¿FNCFSMFSEFOCJSJOJO TSBTZMB \" # WF P 70° $ OPLUBMBSOEB % UFóFUUJS ABC ) NFSLF[J0OPLUBTm ( = 50° BD a ) T :VLBSEBLJWFSJMFSFHÌSF m ( AKC )LBÀEFSFDF- m ( A%PB ) % EJS WFm ( ADC ) = 70° = 50° \" # $ % & PMEVôVOBHÌSF m ( % ) = a LBÀEFSFDFEJS PTC \" # $ % & 6. A \"#$%& CFõHFOJ- // x B OJO ¿FWSFM ¿FN- D C CFSJWFSJMNJõUJS 3. E % = 120° m ( BAC ) E % m ( BCD ) D = 95° B 15° C // a |DE| = |$%| A O | | | |ôFLJMEFLJ0NFSLF[MJZBSN¿FNCFSEF \"% = $% :VLBSEBLJ WFSJMFSF HÌSF % ) = x LBÀ EF- m ( CDE WFm ( E%CA ) = 15° PMEVôVOBHÌSF m ( E%AD ) = a SFDFEJS LBÀEFSFDFEJS \" # $ % & \" # $ % & 1. D 2. \" 3. C 30 4. B 5. D 6. D
www.aydinyayinlaricom.tr ¦&.#&37&%\"÷3& 5. MODÜL 11. SINIF ¦&.#&3%&\"¦*-\"3*** ÷MJöLJMJ,B[BONMBS 11.5.2.1 : #JS¿FNCFSEFNFSLF[ ¿FWSF J¿ EõWFUFóFULJSJõB¿MBSOË[FMMJLMFSJOJLVMMBOBSBLJõMFNMFSZBQBS ·ÀHFOJO¦FWSFM¦FNCFSJ ÖRNEK 1 \"#$пHFOJOJO¿FWSFM¿FN- 7$1,0%m/*m A beSJOJONFSLF[J0OPLUBT x #JS пHFOJO п LËõFTJOEFO HF¿FO ¿FNCFSF CV B C m( % = 110° пHFOJO¿FWSFM¿FNCFSJEFOJS 110° BOC ) ¥FWSFM ¿FNCFSJO NFSLF[J BZO [BNBOEB пHF- O OJOLFOBSPSUBEJLNFMFSJOJOLFTJNOPLUBTES #VOBHÌSF a) %BSB¿MпHFOEF¿FWSFM¿FNCFSJONFSLF[Jп- K HFOJOJ¿CËMHFTJOEFEJS % ) = x m ( BAC A LBÀEFSFDFEJS 0NFSLF[ // m ( >;; ? ) = 110° , m ( >;; ? ) = 250° , m ( % ) = 125° O BAC BKC BAC / / //C ÖRNEK 2 // // 20°\"OBMJUJL EÑ[MFNEF WFSJMFO \" - # WF B $ - OPLUBMBSOO PMVöUVSEVôV \"#$ ÑÀHFOJOJO ÀFWSFM ÀFNCFSJOJO NFSLF[JOJO LPPSEJOBUMBSO CVMV- r 0¥FWSFM¿FNCFSJONFSLF[J OV[ r [0\"] [0#] [0$]¥FWSFM¿FNCFSJOZBS- B(3, 7) ¿BQES \"#$ EJL ÑÀ- HFO PMEV- b) %JLпHFOEF¿FWSFM¿FNCFSJONFSLF[JIJQPUFOÐ- ôVOEBO ÀFW- TÐOPSUBOPLUBTES SFM ÀFNCFSJO A NFSLF[J[ BC ] // LFOBSOO PS- // A(3,–5) UBOPLUBTES BC C(1, –5) A(3,–5) O Od 1+3 -5 + 7 n = ^ 2, 1 h , 22 % ÖRNEK 3 m ( BAC ) = 90°PMNBLÐ[FSF r 0OPLUBT¿FWSFM¿FNCFSJONFSLF[JEJS A D (FOJõ B¿M пHFOEF ¿FWSFM ¿FNCFSJO NFSLF[J пHFOJOEõCËMHFTJOEFEJS \"#$пHFOJOJO¿FWSFM¿FNCFSJ- A OJONFSLF[J0OPLUBTES C % m ( BAO ) = 20° BO 20° O % m ( B%AC ) > 90°PMNBLÐ[FSF B ACB r 0OPLUBT¿FWSFM¿FNCFSJONFSLF[JEJS #VOB HÌSF m ( ) LBÀ EF- C SFDFEJS ]0\"]= | OB | =Sj0\"#JLJ[LFOBSÑÀHFO j % = % = 20° m ( OAB ) m ( OBA ) % j m ( AOB ) = 140° j m ( A%CB ) = 70° 31 1. 125 2. 3. 70
11. SINIF 5. MODÜL ¦&.#&37&%\"÷3& www.aydinyayinlari.com.tr ÖRNEK 4 ÖRNEK 6 A \"#$ пHFOJOJO ¿FWSFM A D ¿FNCFSJOJO NFSLF[J 0 60° 8 OPLUBTES O 30° 4 [\")] m [#$] BC BH \"#$WF\"$%пHFO m ( A%BC ) = m ( A%DC ) | |\"0 = 8 cm | |0) = 4 cm C | | | |#VOBHÌSF \"$ + \"# UPQMBNLBÀDNEJS % = % = 60°PMEVóVOBHËSF m ( DAC ) 2.m ( BCA ) \")m#$PMEVôVOEBO\"#$JLJ[LFOBSÑÀHFOEJS | | | |DC =L \"# FöJUMJôJOJTBôMBZBOLSFFMTBZTLBÀUS ]\"#]=]\"$] ]0\"]= | OC | =DN ]0)]=DN AC AB & hEFQJTBHPSj | HC | = 4 3 & hEFTJOÑTUFPSFNJj = OHC ABC sin a sin 30° & A&DC hEFTJOÑTUFPSFNJj AC = DC ACH hEFQJTBHPSj]\"$]= 8 3 sin a sin 60° ]\"#]+]\"$]= 16 3 DN DC 4JOÑT5FPSFNJ #VFöJUMJLMFSEFOk = =3 TEOREM AB A \"#$ пHFOJOJO ¿FWSFM ÖRNEK 7 ¿FNCFSJOJO NFSLF[J 0 &WJWFPLVMVBZOZPMÐ[FSJOEFCVMVOBO.FSWFPLVMEBZLFO cO b OPLUBTES#VпHFOJO BOOFTJZMFIBCFSMFõJQCJSLBGFEFCVMVõNBQMBOZBQZPS R LFOBSV[VOMVLMBSB C Kafe D J¿B¿MBS \\A , [B , \\C B a C WF¿FWSFM¿FNCFSJOZB- S¿BQ3PMNBLÐ[FSF a = b = c = 2R PMVS ev sin (WA) sin (WB) sin (XC) 45° okul 60° ÖRNEK 5 A \"#$пHFO | |\"# =DN .FSWFZPMJMFMJL FWEFO¿LBOBOOFTJJTFZPMJMF | |7 6 MJL B¿ ZBQBDBL õFLJMEF EPóSVTBM IBSFLFU FEFSFL LBGF- ZFZÐSÐZPSMBS \"$ =DN \"OOFTJ N ZÑSÑEÑôÑOF HÌSF .FSWF LBGFZF LBÀ | |#$ = 8 cm NFUSFZÑSÑNÑöUÑS B8 C kafe BuOBHÌSF sin WA + sin WB PSBOLBÀUS sin XC \"#$ÑÀHFOJOEFTJOÑTUFPSFNJOEFO 867 j 8+6 7 == = sin A sin B sin C sin A + sin B sin C 45° 120° 60° ev okul sin A + sin B j =2 x 450 = & x = 150 6 m sin C sin 45 sin 120 4. 16 3 5. 2 32 6. 3 7. 150 6
¦FNCFSEF\"ÀMBSm*** TEST - 14 1. A 0 \"#$ пHFOJOJO 4. A \"#$ пHFOJOJO ¿FWSFM ¿FNCFSJOJO ¿FWSFM ¿FNCFSJ- 25° NFSLF[J O OJO NFSLF[J 0 OPLUBTES % ) = 25° 5x – 18 m ( OAB B C O m ( % ) = ^ 5x - 18 h° PMEVôVOB HÌSF Y EFôFSJ- ABC x BC OJOEFSFDFDJOTJOEFOBMBDBôFOLÑÀÑLUBNTB- % ZEFôFSJJMFFOCÑZÑLUBNTBZEFôFSJOJOUPQMB- :VLBSEBLJWFSJMFSFHÌSF m ( ACB ) = x LBÀEFSF- NBöBôEBLJMFSEFOIBOHJTJEJS DFEJS \" # $ % & \" # $ % & 2. A 0 \"#$ пHFOJOJO 5. B \"#$ пHFOJOJO ¿FWSFM ¿FNCFSJOJO x ¿FWSFM ¿FNCFSJOJO 30° NFSLF[J A x NFSLF[J,OPLUBT % = 30° 158° m ( A%KC ) = 158° O m ( BAO ) K C 5 | |%$ = 5 br BC :VLBSEBLJWFSJMFSFHÌSF m ( A%BC ) = x LBÀEF- SFDFEJS | |:VLBSEBLJWFSJMFSFHÌSF \"# =YLBÀCJSJNEJS \" # $ % E) 123 \" # $ % 5 2 E) 5 3 A 6. x C // 3. \"#$ пHFOJOJO ¿FWSFM ¿FNCFSJOJO NFSLF[J [#$] B // // OD LFOBSÐ[FSJOEFEJS .FSLF[JO [\"#]WF[\"$]LFOBSMBSOBV[BLMLMBS | | | | | |\"#%$EËSUHFO #0 = 0% = $% | |TSBTZMBDNWFDNPMEVôVOBHÌSF BC LBÀ 0 \"#$ ÑÀHFOJOJO ÀFWSFM ÀFNCFSJOJO NFSLF[J PMEVôVOBHÌSF m ( B%AC ) = x LBÀEFSFDFEJS CJSJNEJS \" # $ % & \" 10 B) 2 5 $ 2 10 D) 5 2 E) 4 5 1. \" 2. E 3. E 33 4. B 5. \" 6. C
TEST - 15 ¦FNCFSEF\"ÀMBSm*** 1. #JS\"#$пHFOJOEFm ( % ) = 30° 4. #JS\"#$пHFOJOJOLFOBSV[VOMVLMBSB C D J¿B¿- BAC MBS WA , WB , XC PMNBLÐ[FSF | |m (A%CB) = 105° #$ = 3 br PMEVôVOBHÌSF B+C+ 2c = 25 | |\"$LBÀCJSJNEJS 6 sin WA + 9 sin WB + 3 sin XC = 10 \" # 3 2 $ 3 3 % & 3 5 #VOBHÌSF CVÑÀHFOJOÀFWSFMÀFNCFSJOJOZBS- ÀBQLBÀCJSJNEJS \" 15 B) 10 $ 15 D) 10 E) 5 4 38 96 2. 30° A A 5. D a 30° 84 30° B DC BC \"#$ WF %#$ ÑÀHFOMFSJ JÀJO BöBôEBLJMFSEFO \"#$пHFO m ( B%AD ) = a m ( % ) = 30° DAC IBOHJTJLFTJOMJLMFEPôSVEVS | | | | | | | |\"# =CS \"$ =CS BD =%$ \" [#$]LFOBSOBBJUZÐLTFLMJLMFSFõJUUJS B) [#$]LFOBSOBBJULFOBSPSUBZMBSFõJUUJS PMEVôVOBHÌSF TJOaLBÀUS $ [#$]LFOBSOBBJUZÐLTFLMJLMFSFõJUUJS \" 3 B) 3 $ 4 D) 1 E) 1 D) ¥FWSFMFSJFõJUUJS 4 5 5 12 6 E) ¥FWSFM¿FNCFSMFSJPSUBLUS 3. #JS\"#$пHFOJOEFsin^ WA + WB h = 2 6. ¥FWSFTJCJSJNPMBO\"#$пHFOJOJOJ¿B¿MBS 3 WA , WB , XC PMNBLÑ[FSF sin WA + sin XC = 3 | |\"# = 12 br PMEVôVOBHÌSF CVÑÀHFOJOÀFWSFM sin WB ÀFNCFSJOJOÀBQLBÀCJSJNEJS | | | |PMEVôVOBHÌSF \"# + BC LBÀCJSJNEJS \" # $ % & \" # $ % & 1. B 2. \" 3. D 34 4. C 5. E 6. E
www.aydinyayinlaricom.tr ¦&.#&37&%\"÷3& 5. MODÜL 11. SINIF ¦&.#&3%&5&ó&57&6;6/-6,* ÷MJöLJMJ,B[BONMBS 11.5.3.1 : ¥FNCFSEFUFóFUJOË[FMMJLMFSJOJHËTUFSFSFLJõMFNMFSZBQBS %m/*m ÖRNEK 2mæB 9–a | |\"$ =DN a–2 a–2 | \"#| = 8 cm ¥FNCFSJO NFSLF[J JMF UFóFU EFóNF OPLUBTO- A | |#$ =DN EBOHF¿FOEPóSVUFóFUFEJLUJS . 0.FSLF[ 8D E 7. 5 5FóFU EFóNF O OPLUBT O r [05]:BS¿BQ Ba F 9–a C Td 9. r05m d #JS ¿FNCFSF ¿FNCFSJO EõOEBLJ CJS OPLUBEBO õFLJMEFLJ0NFSLF[MJÀFNCFS\"#$ÑÀHFOJOF% & ' JLJUFóFU¿J[JMFCJMJS7FCVUFóFUMFSJOUFóFUQBS¿B- MBSOOV[VOMVLMBSFõJUUJS | |OPLUBMBSOEBUFôFUPMEVôVOBHÌSF BF LBÀDNEJS A 5FôFUQBSÀBMBSOOFöJUMJôJOEFO | BD | =BPMTVO&öJUMJLMFSZFSMFöUJSJMJSTF | BD | = | BF | j 10 - a = a j a = 5 P ÖRNEK 3 B D 12 r [1\"]WF[PB]UFóFUQBS¿BMBS 12 r | 1\"| = | PB | xF E ÖRNEK 1 A 12–xx C \"#$% LBSFTJ WF [\"#] c dd A ¿BQM ZBSN ¿FNCFS WF- B D SJMNJõUJS\" #WF'OPL- a UBMBSUFóFUEFóNFOPL- E 12 a UBMBSES H b B c G bF C & ,BSFOJO CJS LFOBS V[VOMVôV CS PMEVôVOB HÌSF EFC %&$ÑÀHFOJOJOBMBOLBÀCJSJNLBSFEJS | |Çak =CS [ EF ] )OPLUBTOEB = 14 br \"# [\"$] % OPLUBTOEB [#$] ( OPLUBTOEB ¿FNCFSF UF- óFUUJS#VOBHÌSF Ça & kLBÀCJSJNEJS 5FôFUQBSÀBMBSOOFöJUMJôJOEFO ABC |CF|= |BC| = 12 | DC | = | ($| ]\"&]= |EF| = x ¦ $&' = | DC | + |$(| = 14 ]\"#]=]\"%]+ | #(| = 8 & DEC EFQJTBHPSj x = 3 ¦ \"#$ = 2 . 8 + 14 =CS A^ DEC h = 9.12 = 54 2 2 br 1. 30 35 2. 5 3. 54
11. SINIF 5. MODÜL ¦&.#&37&%\"÷3& www.aydinyayinlari.com.tr ÖRNEK 4 C \"#$% EJLEËSUHFOJOJO ÖRNEK 7 D J¿JOEFLJ ZBSN ¿FNCFS \"#$ пHFOJ [ DE] ¿BQM ZBSN ¿FNCFSF , WF - OPLUB 6 6 <#$>OB#OPLUBTOEB MBSOEBUFóFUUJS E . A 6 .6 <\"$>OB&OPLUBTOEB 2 AF B UFóFUUJS K 2 | | | |\"% = \"& =CSPMEVôVOBHÌSF AB 2 L 2 PSBOLBÀUS 30° 60° BD 2O 60° EC 2 EC & EFQJTBHPSEBOj | DC | = 6 3 | | | |[\"#] m [\"$] \", =DN BE =DNPMEVôVOBHÌ- ADC | | | |SF #, + LC LBÀDNEJS AB DC = AB = 6 3 & =3 EC 0NFSLF[ 0-\",LBSF S= ]#0]= 6 - 2 =CS & ÖRNEK 5 #VEVSVNEB KBO --ÑÀHFOJCVMVOVS BK = 2 3 \"#$%EËSUHFOJ[\"#]¿BQMZBSN¿FNCFSF\" #WF& & --ÑÀHFOJj CL = 2 23 OLC & CL = OPLUBMBSOEBUFóFUUJS 33 83 |#,]+ |CE| = 3 C E 9 4 5 D H9 44 A 2r B ÖRNEK 8 | | | |\"% =DNWF #$ =DN PMEVôVOBHÌSF ÀFNCF- ôFLJMEF \"#$пHFOJOJOJ¿JOF[#$]LFOBSOB5OPLUBTO- EBUFóFU [\"#]WF[\"$]LFOBSMBSOTSBTZMB%WF&OPLUB- SJOZBSÀBQLBÀDNEJS MBSOEBLFTFO\"NFSLF[MJ¿FNCFSZBZ¿J[JMNJõUJS \"#)%EJLEÌSUHFOJPMVöUVSVMEVôVOEB| \"%| = | HB | =DN %BIBTPOSB D&HC QJTBHPS | DH | =S= 12 A r #VEVSVNEBS= 6 Dr ÖRNEK 6 3 9T r B Dt zC \"#$%UFóFUMFSEËSUHFOJ E t z 1 | | | |\"# =B #$ =C | | | |$% =D \"% =E xC y b + d =CS B= 2c | | | | | |BD =DN #5 =DNWF &$ = 1 cm PMEVôVOa x | |HÌSF 5$ =YLBÀDNEJS Ax yB ]\"%]=]\"5]=]\"&]=S #VOBHÌSF BLBÀCSEJS & EFQJTBHPS S= 12 ABT 5FôFUQBSÀBMBSOOFöJUMJôJOEFO A&TC EFQJTBHPS Y= 5 ]\"#]+ |DC|=]\"%]+ |BC| a a +D= b +Ej a + = 15 j a =CS 2 4. 3 5. 6 6. 10 36 83 8. 5 7. 3
www.aydinyayinlaricom.tr ¦&.#&37&%\"÷3& 5. MODÜL 11. SINIF ÖRNEK 9 ÖRNEK 12 A \"#$%EËSUHFO A D 0NFSLF[MJ¿FZSFL¿FN- aa ber [#$¿FNCFSF$ 8 \"#m\"$ OPLUBTOEBUFóFU | |C \"# = 4 br i % = % ) | \"$| = 3 br B m ( BAC ) m ( CAD 15 10 D i a C T BO | | | | | |#$ =CS $% =CS \"% = 8 br PMEVôVOBHÌ- :VLBSEBLJ WFSJMFSF HÌSF ÀFNCFSJO ZBSÀBQ LBÀ CJ- | |SF \"$ LBÀCJSJNEJS SJNEJS % = % CVSBEBO m ( % ) = m ( % ) m ( DAC ) m ( DCT ) ABC ACD CVMVOVS #VEVSVNEB & + & D :BSN ÀFNCFSF UB- ACB ADC 15 AC A 3 a+3 NBNMBOEôOEB \" $ = & AC = 12 br 4 C aH &EPôSVTBMES B 10 8 2 | |0)\"#j OH =CS ÖRNEK 10 OE B =C %& | | | |CH = a j HE = B+ CS m (AB) + m (CD) = 180° A & EFÌLMJEj 4 =B B+ 3) j a = 1 | \"#| = 8 br COE C | |$% =CS | |& =S= D OHE EFQJTBHPSj OE 2 5 :VLBSEBLJWFSJMFSFHÌSF ÀFNCFSJOZBSÀBQLBÀCJS- ÖRNEK 13 [\"$] ¿BQM ¿FNCFS WF \"#$ NJEJS A [\"#]WF[CD]LJöJMFSJVÀVDBFLMFOJODF пHFOJWFSJMNJõUJS m ( % ) = 180° PMVS#VEVSVNEB[\"%]ÀBQWFm ( % ) = 90° 7 m( % = % ABC ABD 8 BAE ) m ( CAE ) CVMVOVS A&BD QJTBHPSEBO S 2 = 82 + 102 jS= 41 | |\"% =CS D | DB | = 1 br 1 ÖRNEK 11 C BE A 0NFSLF[MJ¿FNCFSJOZB- S¿BQCJSJNEJS :VLBSEBLJ WFSJMFSF HÌSF \"#$ ÑÀHFOJOJO BMBO LBÀ CJSJNLBSFEJS D 105° % = 37, 5° m ( ABC ) 75° C % [\"$]ÀBQ \"&m#$ \"#$JLJ[LFOBSÑÀHFOCVMVOVS O m ( ADC ) = 105° 37,5° | \"$| =CS [CD] m [\"%] PMEVôVOB HÌSF ODC A&DC EFQJTBHPS ]%$]= 15 B ÑÀHFOJOJOBMBOLBÀCJ- A^ ABC h = 8. 15 = 4 15 SJNLBSFEJS 2 %& % 2.m ( ABC ) = m (AC) = 75° j m ( AOC ) = 75° 0%$JLJ[LFOBSÑÀHFOCVMVOVS Aa & k = 1 ·10.10. sin 30° =CS2 ODC 2 9. 12 10. 41 11. 25 37 12. 2 5 13. 4 15
11. SINIF 5. MODÜL ¦&.#&37&%\"÷3& www.aydinyayinlari.com.tr ÖRNEK 14 ·ÀHFOJO÷À5FôFU¦FNCFSJ A \"%#пHFO 7$1,0%m/*m 6 \" , $OPLUBMBSEPó- #JSпHFOJOпLFOBSOBEBUFóFUPMBO¿FNCFSF 84 D SVTBM CVпHFOJOJÀUFôFUÀFNCFSJEFOJS | \"#| = 8 br A 0 NFSLF[MJ ¿FN- CFS \"#$пHFOJOF K | \",| = 4 br % & ' OPLUBMBSO- B | |\"% =CS EBUFóFUUJS C %% m (AB) = m (BC) | |:VLBSEBLJWFSJMFSFHÌSF BD LBÀCJSJNEJS F O E 0 \"#$ пHFOJOJO B J¿UFóFU¿FNCFSJOJO && % = m( A%DB ) m (AB) = m (BC) j m ( BAC ) NFSLF[JEJS DC #VEVSVNEB & + & ABK DBA 48 #JSпHFOJOJ¿UFóFU¿FNCFSJOJONFSLF[JCVп- = & BD = 12 br HFOJOJ¿B¿PSUBZMBSOOLFTJNOPLUBTES 6 BD A FE O ÖRNEK 15 A 0 NFSLF[MJ ZBSN B DC ¿FNCFSEF E [\"#] m [\"%] #JSпHFOJOJ¿UFóFU¿FNCFSJOJONFSLF[JOJO п- HFOJOLFOBSMBSOBV[BLMLMBSFõJUUJS#VV[BLML 3i [ EF ] m [ BD ] J¿UFóFU¿FNCFSJOZBS¿BQV[VOMVóVEVS i a B4 C 3 O1F 2D A | | | | | |OF =DN FD =DN BC =DNPMEVôVOBHÌ- FE 0 NFSLF[MJ S ZBS- | |SF \"# LBÀDNEJS O ¿BQM ¿FNCFSJO UF- óFU EFóNF OPLUB- | |[OE]ZBSÀBQÀJ[JMJSTF OE = rr MBS % & ' PMNBL | |& r Ð[FSF OEF EFQJTBHPSj EF = 2 2 B DC | |E&FD QJTBHPSj ED = 2 3 | 0%| = | 0'| = | 0&| =SPMVS %BIBTPOSB E&FD + B&AD CVMVOVS 22 23 10 6 = & AB = AB 10 3 10 6 38 14. 12 15. 3
www.aydinyayinlaricom.tr ¦&.#&37&%\"÷3& 5. MODÜL 11. SINIF ÖRNEK 16 ÖRNEK 18 A ôFLJMEF\"#$EJLпHF- #JSFöLFOBSÑÀHFOJOJÀUFôFUÀFNCFSJOJOZBSÀBQ rr OJOJO J¿ UFóFU ¿FNCFSJ CSPMEVôVOBHÌSF CVFöLFOBSÑÀHFOJOÀFWSFTJLBÀ FE WFSJMNJõUJS CJSJNEJS 3–r O 4–r B 3–r D 4–r C \"#$ FöLFOBS ÑÀHFO A PMEVôVOEBO \" 0 % | | | |\"# =DN \"$ = 4 cm PMEVôVOBHÌSF ÀFNCFSJO 30° EPôSVTBMES \"ZO [B- 30° ZBSÀBQLBÀDNEJS NBOEB 0 BôSML NFS- | |F E LF[JEJS \"% =CS O 4 #VEVSVNEB | | | |\"'0& LBSF \"' = \"& = S UFôFU QBSÀBMBSOO FöJUMJ- 60° D | |C \"# = 8 3 CVMVOVS A ôJOEFO ¦ \"#$ = 3.8 3 = 24 3 DN | BC | = 5 = 7 -SjS= 1 ÖRNEK 17 ÖRNEK 19 \"#$пHFO 0NFSLF[MJJ¿UFóFU¿FNCFSJпHFOF% ' ( 5ÐSLJZF IBSJUBTOEB \" # $ WF , JM¿FMFSJOJ JõBSFUMFZFO OPLUBMBSOEBUFóFUWF\" 0 &EPóSVTBMES .FMJT ,JM¿FTJOEFCVMVONBLUBES.FMJT,JM¿FTJOJO\" # $JM¿FMFSJOJCBóMBZBOLBSBZPMMBSOBFõJUV[BLMLUBPMEVóV- A OVIFTBQMZPS G A FO K C B B DE C | | | | | |\"# =DN \"$ =DN #$ = 14 cm PMEVôVOB [\"#] [\"$] WF [BC] LBSBZPMMBSOO TSBTZMB LN | |HÌSF DE LBÀCJSJNEJS LNWFLNPMEVôVOVÌôSFOFO.FMJThJO\"JMÀF- TJOFV[BLMôLBÀCJSJNEJS AB AC A \"#$ EJL ÑÀHFO rr CVMVOVS , \"#$ [OE]BÀPSUBZ = PMEVôVOEBO ED ÑÀHFOJOJO JÀ UF- ôFU ÀFNCFSJOJO BE CE NFSLF[JEJS WF \"&,%LBSFEJS | | | |BE = CE =DN | |DE =YPMTVO 160–r K 300–r _ EC = 10 - 2x B 160–r F 300–r C BD = BF = 6 - x b 8 = 10 - 2x x=1 5FôFUQBSÀBMBSOOFöJUMJôJOEFO b AF = AG = 6 + x ` & | |BC = 460 -S= 340 jS=CVMVOVS |\",| = 60 2 b GC = CD = 10 - x b a 16. 1 17. 1 39 18. 24 3 19. 60 2
11. SINIF 5. MODÜL ¦&.#&37&%\"÷3& www.aydinyayinlari.com.tr ·ÀHFOJO%ö5FôFU¦FNCFSJ ÖRNEK 21 0 \"#$ пHFOJOJO Eõ UFóFU ¿FNCFSJ- 7$1,0%m/*m H OJONFSLF[J O #JSпHFOJOCJSLFOBSOBEõBSEBO EJóFSJLJLF- 4 OBSOO EB V[BOUTOB UFóFU PMBO ¿FNCFSFEö A UFôFUÀFNCFSEFOJS A 0 NFSLF[ % & ' T UFóFUEFóNFOPLUB- B C 2K B EC MBSPMNBLÐ[FSF FD | | | |0)m\"# 0,m#$ \") =CS $, = 2 br 0 \"#$ пHFOJOJO O Eõ UFóFU ¿FNCFSJ- #VOBHÌSF OJONFSLF[JEJS | | | |a) #$ - \"#LB¿CJSJNEJS | |b) \"$LB¿CJSJNEJS %õUFóFU¿FNCFSJONFSLF[JCJSJ¿B¿PSUBZJMFJLJ | | | |a) [BO]BÀPSUBZPMEVôVOEBO BH = #,ES EõB¿PSUBZOLFTJNOPLUBTES | | | |\"# = Y PMVSTB BC = x + CVMVOVS #V EV- | | | |SVNEB BC - \"# =EJS D O A b) [\"0]WF[OC]BÀPSUBZPMEVôVOEBO | | | | | | | |\") = \"5 =CS $, = $5 =CS | |\"$ = 4 + 2 =CSCVMVOVS E ÖRNEK 22 K \"#$ пHFOJOJO Eõ UF- CF óFU ¿FNCFSMFSJOEFO A JLJTJOJONFSLF[J,WF5 B OPLUBMBSES 0NFSLF[ % & 'UFóFUEFóNFOPLUBMBSPMNBL | \",| = 8 br Ð[FSF [\"0] [#0]WF[$0]B¿PSUBZPMVS | |\"5 = 12 br ÖRNEK 20 BC A , \"#$ пHFOJOJO 48° K Eõ UFóFU ¿FNCFSJ- 84° OJONFSLF[J T 28° x m ( A%BK ) = 28° #VOBHÌSF 28° x % m ( KAC ) = 48° | |a) ,5LB¿CJSJNEJS B & C b) A^ AKT hLB¿CJSJNLBSFEJS :VLBSEBLJ WFSJMFSF HÌSF % = x LBÀ EFSFDF- m ( ACK ) EJS 5 ,EöUFôFUÀFNCFSJONFSLF[MFSJ \",m\"5CVMVOVS ,EöUFôFUÀFNCFSJOJONFSLF[JPMEVôVOEBO XA ve XC | |a) A&KT QJTBHPSEBO ,5 = 4 13 CS OJOEö XB OOJÀBÀPSUBZES b) & 8.12 2 += 2x jY CVMVOVS A^ AKT h = 2 = 48 br 20. 40 21. B C 22. a) 4 13 C
¦FNCFSEF5FôFUWF6[VOMVLm* TEST - 16 1. D C [\"#]WF[\"&]ZBSN 4. A ¿FNCFSFUFóFU 3 F E F \"#$%LBSF E | $&| = 2 br 5 B DC AB \"#$EJLпHFOJ [BD]¿BQMZBSN¿FNCFSF&OPL- | |:VLBSEBLJWFSJMFSFHÌSF \"& V[VOMVôVLBÀCJ- | | | |UBTOEBUFóFU \"& =CS &$ = 5 br PMEVôVOB | |HÌSF BC LBÀCJSJNEJS SJNEJS \" 2_ 2 + 1 i B) 2 2 + 1 $ 2 2 \" # $ % & D) 2_ 1 + 2 i E) 2_ 2 - 1 i 2. [\"# 0 NFSLF[MJ 5. A K C ¿FNCFSF # OPLUB- 45° A TOEBUFóFU 12 [\"$][0#] B |\"#| = 2|\"$| D 15° | |0# =DN O C 10 \",¿FNCFSF\"OPLUBTOEBUFóFU m ( % ) = 45° B KAB | |% m ( BDC ) = 15° WF \"# =CSEJS | |:VLBSEBLJWFSJMFSFHÌSF \"$ LBÀCJSJNEJS | |:VLBSEBLJWFSJMFSFHÌSF \"$ LBÀDNEJS \" 3 6 B) 6 2 $ \" # $ % & % & 3. D E C 'OPLUBT ('&% 6. ôFLJMEFLJ \"#$% EËSUHFOJ [\"#] ¿BQM 0 NFSLF[MJ F LBSFTJ JMF # NFS- 2 LF[MJ EËSUUF CJS ZBSN¿FNCFSF\" #WF5OPLUBMBSOEBUFóFUUJS ¿FNCFSJO PSUBL G OPLUBTES C T D 6 5 AB | |DG = 2 cmPMEVôVOBHÌSF \"#$%LBSFTJOJOCJS A OB LFO BSLBÀDNEJS | | | |\"% =CSWF #$ =CSPMEVôVOBHÌSF | |OC LBÀCJSJNEJS \" 4 + 2 2 B) 4 + 4 2 $ + 2 2 \" # 33 $ D) E) 71 D) 8 + 2 2 E) 8 + 4 2 1. \" 2. C 3. \" 41 4. B 5. E 6. D
TEST - 17 ¦FNCFSEF5FôFUWF6[VOMVLm* 1. 4. \"#$пHFOJOF \"OPLUBTOEBUFóFUCJS¿FNCFSWF- A SJMNJõUJS C 1 O A xT 3 4 2 P 12 DB C ôFLJMEF[1\" [1# [$%] 0NFSLF[MJ¿FNCFSFTSB- D B TZMB\" # 5OPLUBMBSOEBUFóFUUJS BD | | | | | |$5 =CJSJN 5% =CJSJNWF PD =CJ- | |SJNPMEVôVOBHÌSF 1$ =YLBÀCJSJNEJS | | | |\"% =CS \"$ = 3 br PMEVôVOBHÌSF DC \" # $ % & PSBOBöBôEBLJMFSEFOIBOHJTJEJS 2. A \" 3 B) 4 $ 2 3 E) 1 4 5 3 D) 5 DE BOC 5. A \"#$пHFOJOEF [\"#] m [\"$] [\"#]WF[\"$] 5 4L K 0NFSLF[MJ¿FNCFSF%WF&OPLUBMBSOEBUFóFUUJS | | | |\"# = CS WF \"$ = 21 br PMEVôVOB HÌSF ÀFNCFSJOZBSÀBQLBÀCJSJNEJS BD C \" # $ % & \"#$EJLпHFO [#$]¿FNCFSF%OPLUBTOEBUFóFU 3. [\"%] ¿BQM ZBSN ¿FNCFS \"#$ пHFOJOF \" WF & | | | |\", =CS \"- = 4 br PMEVôVOBHÌSF | | | |BD . CD ÀBSQNLBÀCJSJNLBSFEJS OPLUBMBSOEBUFóFUUJS \" # $ % & A D 12 x B EC 6. Z= x +WFZ= -x -EPóSVMBSOOLFTJNOPL- | | | | | |BE = &$ \"$ = 12 brPMEVôVOBHÌSF UBT,OPLUBTES#VJLJEPóSVZBUFóFUWFZBS¿BQ | |BD =YLBÀCJSJNEJS CJSJNPMBO¿FNCFSJONFSLF[J0OPLUBTES | | #VOBHÌSF 0, LBÀCJSJNEJS \" 4 3 B) 4 2 $ 3 3 \" # 4 3 $ 4 2 D) 2 3 E) 2 2 D) 4 E) 2 3 1. C 2. E 3. \" 42 4. B 5. D 6. C
¦FNCFSEF5FôFUWF6[VOMVLm* TEST - 18 1. C [\"#]¿BQMZBSN¿FNCFS 4. P A ôFLJMEF [1\" WF [1# 0 NFSLF[MJ \"#$ пHFO # UFóFU B O EFóNF OPLUBT WF # ' 12 ¿FNCFSF TSBTZMB D %EPóSVTBM C \"WF#OPLUBMBSO- EBUFóFU | |$% =CS [1\"m [PB EF | |0$ =CJSJm AB :VLBSEBLJ WFSJMFSF HÌSF #1\" ÑÀHFOJOJO BMBO LBÀCJSJNLBSFEJS | DE | = |\"&| = | DF | = | BF | |PMEVôVOBHÌSF BC | \" # $ % & LBÀCJSJNEJS \" 6 3 # $ D) 3 3 E) 5 2. O ôFLJMEFLJ 0 NFSLF[MJ 5. [\"#]¿BQM¿FNCFSJO¿BQCJSJNEJS EBJSFEJMJNJOEF 4 DC C [0&] \"NFSLF[MJEB- 60° EB AT JSF EJMJNJOF 5 OPLUB- A 2 TOEBUFóFU % DE | |B 0$ = 4 cm DAB ) | |5& = 2 cm \"&$%FõLFOBSEËSUHFO m ( = 60° PMEVôVOB | | :VLBSEBLJWFSJMFSFHÌSF OB LBÀDNEJS HÌSF \"&$% FöLFOBS EÌSUHFOJO ÀFWSFTJ LBÀ CJ- SJNEJS \" # $ % & \" # $ % & 3. ED CB KF O L 6. C [\"#]¿BQM¿FNCFSWF A A 3 \"#$пHFOJWFSJMNJõ- [ ,-]¿BQMZBSN¿FNCFSJONFSLF[J0 ¿BQ12 2 K H UJS CJSJNEJS0\"#$EJLEËSUHFO 0%&'LBSFWe B $)m\"% | | | |%$ = 0$ PMEVôVOBHÌSF \" 0\"#$ LBÀCJ- %% SJNLBSFEJS m (BC) = m (DB) | |D $, = 3 br \" 8 13 B) 9 7 $ 5 10 | |:VLBSEBLJWFSJMFSFHÌSF BC LBÀCJSJNEJS E) 2 11 D) 4 6 \" # $ % & 1. \" 2. C 3. B 43 4. E 5. D 6. D
TEST - 19 ¦FNCFSEF5FôFUWF6[VOMVLm* 1. 4. A \"#$ пHFOJOJO J¿ UF- A óFU ¿FNCFSJ WFSJMNJõ- UJS% & 'UFóFUEFó- P 60° O NFOPLUBMBSOOPMVõ- 12 C D F UVSEVóV %&' FõLF- B OBSпHFOJOJO¿FWSFTJ CJSJNEJS BE C ôFLJMEF[1\"WF[1# 0NFSLF[MJ¿FNCFSFTSBTZMB #VOB HÌSF \"#$ ÑÀHFOJOJO ÀFWSFTJ LBÀ CJSJN- EJS \"WF#OPLUBMBSOEB tFóFU m (A%PB) = 60°WF \" # $ % & | PB | = 12 cm | | :VLBSEBLJWFSJMFSFHÌSF \"$ LBÀDNEJS 5. \"OBMJUJLEÐ[MFNEFWFSJMFO\"0#EJLпHFOJOJOEõUF- \" 4 3 B) 6 3 $ óFU¿FNCFSJWFSJMNJõUJS D) 8 3 E) 24 y 2. A [#$] ¿BQM ZBSN L x 3 ¿FNCFS WF \"#$ B 4 пHFOJ WFSJMNJõUJS O A2 K D E | \"%| = | DB | | |-WF,UFóFUEFóNFOPLUBMBS \", =CS | |\"& = 4 br | |#- = 3 br PMEVôVOBHÌSF \"0#ÑÀHFOJOJOBMBO | |\"$ =CS LBÀCJSJNLBSFEJS BC \" # $ % & | | :VLBSEBLJWFSJMFSFHÌSF \"# LBÀCJSJNEJS \" 4 2 # $ 4 5 6. , \"#$пHFOJOJOEõUFóFU¿FNCFSJOJONFSLF[JEJS % & A x K | |3. \"#$пHFOJOEF [\"#] m [#$] \"# =CJSJNEJS 15° 35° ·ÀHFOJO JÀ UFôFU ÀFNCFSJOJO NFSLF[JOJO ÑÀHF- BC OJOLFOBSMBSOBV[BLMLMBSUPQMBNCJSJNPMEV- ôVOB HÌSF \"#$ ÑÀHFOJOJO ÀFWSFTJ LBÀ CJSJN- % = 35° % = 15° PMEVôVOB HÌSF EJS m ( ACK ) m ( ABK ) \" # $ % & % = x LBÀEFSFDFEJS m ( CAK ) \" # $ % & 1. D 2. C 3. \" 44 4. B 5. E 6. B
www.aydinyayinlaricom.tr ¦&.#&37&%\"÷3& 5. MODÜL 11. SINIF ¦&.#&3%&5&ó&57&6;6/-6,** ÷MJöLJMJ,B[BONMBS 11.5.3.1 : ¥FNCFSEFUFóFUJOË[FMMJLMFSJOJHËTUFSFSFLJõMFNMFSZBQBS 5FôFU¦FNCFSMFS ÖRNEK 1 %m/*m O1 O3 ¶¿ ¿FNCFS CJSCJSMFSJOF , 75° K M - .OPLUBMBSOEBUFóFU \"ZO EÐ[MFNEFLJ JLJ ¿FNCFS CJSCJSJOF J¿FSEFO UFóFUZBEBEõBSEBOUFóFUPMBCJMJSMFS L $ T m (KL) = 75° T % m (ML) = 50° O2 #JSCJSJOF UFóFU JLJ ¿FNCFSJO UFóFU OPLUBMBS WF & CV¿FNCFSMFSJONFSLF[MFSJEPóSVTBMES :VLBSEBLJWFSJMFSFHÌSF m (KM)LBÀEFSFDFEJS 0WF.NFSLF[MFS 5UFóFUOPLUBTPMNBLÐ[F- O1 02 03ÀFNCFSMFSJONFSLF[JPMTVO01 02 03ÑÀHFO SF % & m ( KL) = m (\\O ) = 75° m ( ML) = m (\\O ) = 50° a) 12 m ( & = m (\\O ) = a KM) 3 O r1 T 75 + 50 + a = 180°j a = M r2 0 . 5EPóSVTBM ÖRNEK 2 ¶¿¿FNCFSCJSCJSMFSJ- OF, -WF.OPL- | |0. = r2- r1 A UBMBSOEBUFóFUUJS m ( K%AL ) = 21° LB21° 36° m ( L%BM ) = 36° b) 42° 72° T 2a M O r2 r1 M Ka C 0 5 .EPóSVTBM :VLBSEBLJWFSJMFSFHÌSF m ( % ) LBÀEFSFDFEJS KCM | |0. = r2 + r1 ++ 2a = a = 45 1. 55 2. 33
11. SINIF 5. MODÜL ¦&.#&37&%\"÷3& www.aydinyayinlari.com.tr ÖRNEK 3 ÖRNEK 6 D C \"#$% LBSFTJ J¿FSJTJOF % K ôFLJMEFLJ ' NFSLF[MJ 9 T WF # NFSLF[MJ ¿FZSFL F ¿FNCFS % $ WF & NFS- 9 rr rr LF[MJ ZBSN ¿FNCFSMFSF ¿FNCFSMFS ¿J[JMNJõUJS 5 A rB 2M N TSBTZMB. ,WF/OPL- OPLUBT JLJ ¿FNCFSJO UFóFU 2 UBMBSOEBUFóFUUJS | |OPLUBTES \"# =CSPM- A 2 D 2C 2E 2B EVôVOB HÌSF LÑÀÑL | |\"# = 8 cmPMEVôVOBHÌSF 'NFSLF[MJÀFNCFSJOZB- ÀFNCFSJO ZBSÀBQ LBÀ SÀBQLBÀDNEJS CJSJNEJS % 5 #EPôSVTBM |FC| = 4 -S F&CE EFQJTBHPSEBO |DB| = 9 +S= 9 2 \"#$%LBSF -S 2 + 22 = S+ 2)2 j r = 4 S= 9 2 - 9 3 ÖRNEK 4 ÖRNEK 7 #JSCJSJOFJLJõFSJLJõFSEõUBO F [\"#]WF[\"$]¿BQ UFóFU PMBO \" # WF $ NFS- [FD] m <\"$> A r1 r2 B LF[MJ ¿FNCFSMFSJO ZBS¿BQ- 4 r1 r2 MBSTSBTZMBS1 S2 S3UÐS E |\"%| = |%$| | EF | = | ED | = 4 br r3 r3 | | | |\"# =CS \"$ =CSWF 4 | |#$ =CSPMEVóVOBHËSF C C A8 Da B S3LBÀCJSJNEJS | |:VLBSEBLJWFSJMFSFHÌSF BC LBÀCJSJNEJS S1 +S2 = 7 ]\"%]= |DC| j%NFSLF[j]\"%]= |DC| = |DF| = 8 S1 +S3 = 8 m ( A%EB ) = 90° j 42 = 8.a j a = ²LMJE S2 +S3 = EFOLMFNMFSJÀÌ[ÑMÑSTFS3 =CS |BC| = 8 - 2 = 6 ÖRNEK 5 ÖRNEK 8 C ôFLJMEFCÐZÐL¿FN- CFS EJLEËSUHFO JO п DR LFOBSOB FõPMBOJLJ LпÐL ¿FNCFS JTF # WF $ NFSLF[MJ ¿FNCFSMFS R R O2 r EJLE ËSUH FOJO JLJõFS CJSCJSMFSJOF EõUBO \" NFSLF[MJ K O1 R r 2r LFOBSOB WF CÐZÐL ¿FNCFSF EF J¿UFO UFóFUMFSEJS R . ¿FNCFSFUFóFUMFSEJS A C 3 \" # $ NFSLF[MJ ÀFNCFSMF- r r SJO ZBSÀBQMBS TSBTZMB AR B DN DNWFDNPMEVôVOB r 4 HÌSF \"#$ÑÀHFOJOJOÀFWSF- r TJLBÀDNEJS O3 rB | |\"% = 12 cm PMEVôVOBHÌSF LÌöFMFSJCVÀFNCFSMF- SJONFSLF[MFSJPMBOÑÀHFOJOBMBOLBÀDN2EJS ]\"$]= 9 - 3 = 6 | | | | | |\", = ,% =DN=3WF CB =S= 12 jS= ]\"#]= 9 - 4 = 5 |BC| = 3 + 4 = 7 O1 O2 O3ÑÀHFOJOJOZÑLTFLMJôJ 6 2 CJSJNEJS ¦ \"#$ = 6 +7 + 5 =CS 6.6 2 \" O1 O2 O3) = 2 = 18 2 3. 9 2 - 9 4. 5 5. 18 46 4 7. 6 8. 18 2 6. 3
www.aydinyayinlaricom.tr ¦&.#&37&%\"÷3& 5. MODÜL 11. SINIF ÖRNEK 9 ,FTJöFO¦FNCFSMFS 0 NFSLF[MJ ¿FNCFS $ %m/*m OPLUBTOEB[\"#]¿BQOB \"ZO EÐ[MFNEFLJ JLJ ¿FNCFS CJSCJSJOJ JLJ GBSLM OPLUBEBLFTFCJMJS O 3 D WF % OPLUBT OEB ZBSN K 53 ¿FNC FSFUFóFUUJS r1 r2 A M CB O1 O2 ¦FNCFSMFSJOZBSÀ BQMBSDNWFDNPMEVôVOBHÌ- L | |SF CB LBÀDNEJS 01WF02NFSLF[ ,WF-LFTJNOPLUBMBS .CÑZÑLÀFNCFSJONFSLF[JPMTVO & EFQJTBHPS | | | |01K = r1 02K = r2 OMC | | | |r r1 - r2 < 0102 < r1 + r2 |MC| =CS ]$#]= |MB| - |MC| = 8 - 4 =CS ÖRNEK 10 \"Z¿BFMJOEFLJJLJQFSHFMEFOCJSJOJOTJWSJVDVOV\"OPLUBT- OB EJóFSJOJOTJWSJVDVOV\"EBODNV[BLMLUBLJ#OPL- UBTOBZFSMFõUJSJZPS K 7$1,0%m/*m AB \"ZOEÐ[MFNEFJLJGBSLMOPLUBEBLFTJõFO¿FN- %BIB TPOSB PSUBL OPLUBMBS ZBMO[DB , OPLUBT PMBO JLJ CFSMFSJOLFTJNOPLUBTOEBO¿J[JMFOUFóFUMFSJCJS- GBSLM¿FNCFS¿J[JZPS CJSJOFEJLJTFCV¿FNCFSMFSFEJLLFTJöFOÀFN- #VOB HÌSF \"ZÀBhOO ÀJ[EJôJ JLJ GBSLM ÀFNCFSJO CJS- CFSMFSEFOJS CJSJOFFOV[BLJLJOPLUBTBSBTOEBLJV[BLMLLBÀCJ- SJNEJS K r1 r2 C AK D O1 O2 B | | | | 01WF02NFSLF[ 01K = r1 02K = r2 ÷LJ ÀFNCFSJO PSUBL OPLUBT ZBMO[DB , PMEVôVOEBO CV 01K m02K | | | |ÀFNCFSMFSUFôFUUJS \", =3 #, =SPMTVO r O1O2 = r21 + r22 | |\"# = R +S=DN &OV[BLJLJOPLUBMBS$WF% | |CD = 2R +S=DN 9. 4 10. 30 47
11. SINIF 5. MODÜL ¦&.#&37&%\"÷3& www.aydinyayinlari.com.tr ÖRNEK 11 ÖRNEK 14 C 0 WF . NFSLF[MJ ôFLJMEFLJ01WF02NFSLF[MJ¿FNCFSMFS\"WF#OPLUBMB- ¿FNCFSMFSJO LFTJN SOEBLFTJõNFLUFEJS Aa O OPLUBMBS$WF%EJS M 40° B maC%BDk = A D O1 O2 :VLBSEBLJWFSJMFSFHÌSF m ( C%AD ) = aLBÀEFSFDFEJS 12 3 D BC ) = 80° j ) = 280° j % ) = 140° m ()COD) m (CBD) m ( COD m (COD) = 2a = 140° & a = 70° % # $OPLUBMBSEPóSVTBM [%\" \"OPLUBTOEB02 mer- | | | |LF[MJ¿FNCFSFUFóFU BD =CJSJNWF #$ =CJSJN PMEVóVOBHËSF [\"#] LJSJöJOJOV[VOMVôVLBÀCJSJNEJS ÖRNEK 12 m ( A%BD ) = 90° ¦BQHÌSFOÀFWSFBÀ %Ð[MFNEFZBS¿BQMBSCSWFCSPMBOJLJ¿FNCFSEJL BuEVSVNEB m ( % ) = 90° LFTJõNFLUFEJS ABC #VOB HÌSF CV ÀFNCFSMFSJO NFSLF[MFSJ BSBTOEBLJ 0IBMEF \" 02 $EPôSVTBMES[%\"] m [\"$]EJS V[BLMLLBÀCJSJNEJS | |& 2 DAC EFÌLMJE \"# = 12.3 | |\"# =CS K 12 ¦FNCFSMFS EJL LFTJöUJ- 5 ôJOEFO O1 O2 O1,m O2, ÖRNEK 15 O1,02 ÑÀHFOJOEF QJ- TBHPS 01WF02NFSLF[MJ¿FNCFSMFS,WF-OPLUBMBSOEBLFTJõ- NFLUFEJS 52 + 122 = OO 2 j |O O | =CS K 12 12 2 O1 O2 ÖRNEK 13 DB . NFSLF[MJ ¿FNCFS 0 L O O1 NFSLF[MJ ÀFNCFSJO ZBSÀBQ CS PMEVôVOB HÌSF A NFSLF[MJ¿FNCFSJO M C | |,-LBÀCJSJNEJS NFSLF[JOEFO HF¿NFL- ¦FNCFSMFS CJSCJSJOJO NFSLF[JOEFO HFÀUJôJOEFO FöUJS #V UF \" % # WF $ 0 # EVSVNEB01,02WF01LO2ÑÀHFOMFSJFöLFOBSÑÀHFOEJS | |EPóSVTBM \"# =CS PMEVôVOB HÌSF . NFSLF[MJÀFNCFSJOZB- SÀBQLBÀCJSJNEJS | |& ,- 3 CS O KL [CD] m [\"#] ¦BQHÌSFOÀFWSFBÀ #VEVSVNEB$ . 1 EFO -30- =8 \"EPôSVTBMES m ( % ) = 90° ¦BQHÌSFOÀFWSFBÀ AOC | | | |OC = WF % = 90° PMEVôVOEBO \"#$ JLJ[LF- OB m ( AOC ) | | | | | |OBSÑÀHFO \"# = \"$ =CS CM =CS 11. 70 12. 13 13. 8 48 14. 6 15. 8 3
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