www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 4 \"#$%FõLFOBSEËSUHFO ÖRNEK 6 \"#$%FõLFOBSEËSUHFO D |AK| = |BK| B |CE| = |ED| | |AB =CS | |OE =CS A5 E5 | |C x | |OA =CS 13 K k F AC =CS A 12 O 12 C 2k 10 10 xE 10 D B | |:VLBSEBLJWFSJMFSFHÌSF BD LBÀCJSJNEJS | |:VLBSEBLJWFSJMFSFHÌSF #' LBÀCJSJNEJS \"&#ÑÀHFOJOEF1JTBHPSUFPSFNJOEFO \"#$%FöLFOBSEÌSUHFOPMEVôVOEBOm ( % = 90° EJS COD ) | BE |2 +2 = 132 j |BE| = 12 $0%ÑÀHFOJOEFNVöUFöFNÑÀMÑEFO 'BôSMLNFSLF[J 3k = 12 j k = 4 |$%| =CSEJS |#'| =CSCVMVOVS 0IBMEF$0%ÑÀHFOJOEF1JTBHPSUFPSFNJOEFO Y2 + 122 = 202 Y2 =jY=CS |BD| =Y=CSCVMVOVS ÖRNEK 5 D \"#$%FõLFOBSEËSUHFO ÖRNEK 7 \"#$%FõLFOBSEËSUHFO A 2k |BE| = |EC| B |BF| = |FG| F |CF| = |FD| |AE| = |DE| 4k 2k | |GA =CS K 6F | |C AC =CS 12 8 | |BD =CS B GK A G 12 3k E E C D | |:VLBSEBLJWFSJMFSFHÌSF GE LBÀCJSJNEJS | |:VLBSEBLJWFSJMFSFHÌSF &' LBÀCJSJNEJS \"#LFOBSOBQBSBMFMPMBDBLöFLJMEF[EK]EPôSVQBSÀBT- \"# LFOBSOO PSUB OPLUBT PMBDBL öFLJMEF , OPLUBTO OÀJ[FMJN BMBMN,'PSUBUBCBOPMEVôVOEBO|,'| =CSWF |KE| =CSPMVS[,'] // [\"$]WF[KE] // [BD]PMEVôVOEBO &,PSUBUBCBOPMEVôVOEBO|$'| = 2 |EK|PMVS m ( F%KE ) = 90°PMVS GB k = |&'|2 =2+2 12 4k |&'| =CSCVMVOVS #FO[FSMJLUFO|GE| =CSPMVS 4. 3 49 32 7. 10
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr &öLFOBS%ÌSUHFOEF¦FWSFWF\"MBO ÖRNEK 9 D \"#$%FõLFOBSEËSUHFO %m/*m A | |AH =CS AB 4 | |BH =CS H a :VLBSEBLJ WFSJMFSF E 5 HÌSF \" \"#$% LBÀ BC CJSJNLBSFEJS DH C \"#$%FõLFOBSEËSUHFO [AH] m [DC]JTF \"&#ÑÀHFOJOEFÌLMJUEF r¥FWSF \"#$% =B |)&|2 = | |r A ( ABCD ) =B AH |)&| = 2 5 \" \"#$% = 9.2 5 5 2 CVMVOVS ·4 = 36 2 br r A ( ABCD ) = a2 sin ( % ) ADC AC . BD ÖRNEK 10 r A (ABCD) = 2 A B \"#$%FõLFOBSEËSUHFO 6 [AC] a [BD] = {E} E [ AC ] a [ BF ] = { G } ÖRNEK 8 2 |DF| = |FC| x5 | |AC =CS A B G4 & 15 10 A^ EFG h =CS2 D FC | |:VLBSEBLJWFSJMFSFHÌSF ED LBÀCJSJNEJS 4 23 |%'| = |'$|WF |DE|= |BE| PMEVôVOEBO #$% ÑÀHFOJOEF (BôSMLNFSLF[JPMVSWF|($| =CS |EG| =CSEJS 6x \" %&$ = 30 = jY=CSCVMVOVS 2 D2E 2C \"#$%FõLFOBSEËSUHFO [ AE ] m [ DC ] ÖRNEK 11 | | | |DE = EC =CS DE K C \"#$%FõLFOBS EËSUHFO :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJNLBSF- 11 x–1 EJS [ EF ] m [ AB ] xx x+1 |EF| = |EC| | | | |DE = FB =CS \"%&ÑÀHFOJOEFQJTBHPSUFPSFNJOEFO |\"&|2 + 22 = 42 |\"&| = 2 3 A x F1B \" \"#$% = 4. 2 3 :VLBSEBLJWFSJMFSFHÌSF ¦ \"#$% LBÀCJSJNEJS =8 3 2 CVMVOVS [KB] // [&'|ÀJ[JMJSTF#,$EJLÑÀHFOJOEF 1JTBHPSCBôO- br UTZB[MSTBY2 + Y- 2 = Y+ 2 Y2 -Y= 0 jY=PMVS ¦ \"#$% ==CSCVMVOVS 8 3 9. 36 5 10. 10 11. 20
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 12 ÖRNEK 14 A k F kB ôFLJMEF WFSJMFO FõLFOBS EËSUHFO õFLMJOEFLJ LBSUPOEB k A 2A [ AD ]WF[ BC ]LFOBSMBS[ AC ]LËõFHFOJOJOÐ[FSJOFHFMF- E 3A 2k DFLõFLJMEFLBUMBOEóOEB%WF#OPLUBMBSTSBTZMB'WF &OPLUBMBSZMB¿BLõNBLUBES k D7 C 2A 7–x D 2k C F 7 | | | | | | | |\"#$%FõLFOBSEËSUHFO AF = FB AE = ED 7 x A ( ABCD ) =CS2 E 7–x & :VLBSEBLJWFSJMFSFHÌSF A^ EFC hLBÀCJSJNLBSFEJS A7 B :VLBSEBLJÑÀHFOMFSJOBMBOMBSTJOÑTMÑBMBOEBOLFOBSMB- ,BSUPOVOCJSLFOBSCSWF\"JMF$OPLUBMBSBSBTV[BL- SOO ÀBSQNZMB PSBOUMES WF Ñ[FSJOEF ZB[MEô HJCJEJS MLCJSJNEJS 0IBMEF\"= 32 j\"= 4 \" &'$ =\"=CS2 CVMVOVS | |:VLBSEBLJWFSJMFSFHÌSF &' LBÀCJSJNEJS |\"'| =CSWF|$&|=CSPMVS 7 -Y+Y+ 7 -Y= 9 Y=CVMVOVS ÖRNEK 13 ÖRNEK 15 A D C 3k E F D k B 3k A BH G | |\"#$%FõLFOBSEËSUHFO [ CH ] m [ AH ] DB =CS k C A (ABCD) = 8 3 br2 % \"#$%FõLFOBSEËSUHFO [ GF ] // [ BC ] &` [AD] :VLBSEBLJWFSJMFSFHÌSF m ( BCH ) LBÀEFSFDFEJS & =CS2 = BF A^ EFG h | | | |AB D C A^ ADB h = 8 3 = 4 3 2 2 :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJNLBSF- EJS 30° 4.h 4 3= H 2 \"'(%QBSBMFMLFOBSOEB\" \"'(% =\" &'( h 2 h=2 3 \" \"'(% =CS2 30° \" '#($ =CS2PMVS 60° 60° 60° \" \"#$% =CS2 CVMVOVS A BH 0IBMEF\"#)ÑÀHFOJOEFm ( H%BA ) = 60°PMVS :BOJ m ( % ) = 30° PMVS BCH 12. 12 13. 32 14.
TEST - 21 &öLFOBS%ÌSUHFO 1. DE C \"#$%FõLFOBS 4. A B \"#$%FõLFOBS EËSUHFO EËSUHFO % = % E \"#'FõLFOBS m ( DAE ) m ( EAC ) пHFO m ( A%ED ) = 54° % m ( ADC ) = 56° F AB DC % :VLBSEBLJ WFSJMFSF HÌSF m ( F%BE ) LBÀ EFSFDF- :VLBSEBLJWFSJMFSFHÌSF m ( ABC )LBÀEFSFDF- EJS EJS \" # $ % & \" # $ % & 2. A E B \"#$%FõLFOBS D C EËSUHFO D m ( A%DC ) = 70° E % m ( BEC ) = 80° AB C % \"#$%FõLFOBSEËSUHFO m ( % ) = 35° ACE BEC :VLBSEBLJ WFSJMFSF HÌSF m ( ) LBÀ EFSFDF- | | | | | |m(E%AD) = 25° AE = ED = EB EJS \" # $ % & % :VLBSEBLJWFSJMFSFHÌSF m ( ECB )LBÀEFSFDFEJS \" # $ % & 3. \"#$%FõLFOBSEËSUHFOJOEF \"%&пHFOJ\"&EPóSV- \"#$%FõLFOBSEËSUHFOJõFLMJOEFLBSUPOEB $OPL- UBTOO [ AB ] ZF HËSF TJNFUSJóJ PMBO & OPLUBT %\" TVCPZVODBLBUMBOODB%OPLUBT$OPLUBTJMF¿BL- õZPS EPóSVTVÐ[FSJOEFEJS AB AB D EC DC :VLBSEBLJ WFSJMFSF HÌSF m ( % ) LBÀ EFSFDF- :VLBSEBLJ WFSJMFSF HÌSF m ( % ) LBÀ EFSFDF- ABC DCB EJS EJS \" # $ % & \" # $ % & 1. B 2. $ 3. D 4. \" B D
&öLFOBS%ÌSUHFO TEST - 22 1. D C \"#$%FõLFOBS 4. A B \"#$%FõLFOBS EËSUHFO EËSUHFO A E [ AH ] m [ CH ] F [CF]WF[EG] | |AC =CS G B¿PSUBZ | |BD =CS DC | |AC =CS BH | |BD =CS | | :VLBSEBLJWFSJMFSFHÌSF $) LBÀCJSJNEJS | | :VLBSEBLJWFSJMFSFHÌSF EG LBÀCJSJNEJS \" # $ % & A) 2 B) 2 2 $ E) 5 D) 3 2 2. D C \"#$%FõLFOBS ,ËõFLPPSEJOBUMBS\" # $ EËSUHFO 0 PMBO \"#$% FõLFOBS EËSUHFOJ õFLMJOEFLJ G & 'WF#EPóSVTBM UBIUBOOPSJKJOFUSBGOEBTBBUZËOÐOEFEËOEÐ- E SÐMNFTJZMFPMVõBOFõLFOBSEËSUHFO\"h#h$h0PMBSBL |AE| = |ED| JTJNMFOEJSJMJZPS%BIBTPOSBCVFõLFOBSEËSUHFOTB- F | |BD =CS óBEPóSVCJSJNBõBóEPóSVCJSJNËUFMFOJZPSWF PMVõBOFõLFOBSEËSUHFO\"hh#hh$hh0hPMBSBLJTJNMFO- A B EJSJMJZPS ¥ \"#$% =CS #VOBHÌSF 0h#hh$hh\"hhFöLFOBSEÌSUHFOJOJOBMB- | | :VLBSEBLJWFSJMFSFHÌSF (' LBÀCJSJNEJS OLBÀCJSJNLBSFEJS \" # $ % & \" # $ % & 3. A \"#$%FõLFOBSEËSUHFO #JSËóSFODJZFOJBMEóQFSHFMJOJEFOFNFLJ¿JOËODF DFUWFMMF [KM] EPóSV QBS¿BTO ¿J[JZPS %BIB TPOSB B [ AC ] a [ BE ] = { F } QFSHFMJO TJWSJ ZFSJOJ , OPLUBTOB CBUSQ [KM] ZBS- E | DE | =| AE | ¿BQM¿FNCFS¿J[JZPS%BIBTPOSBQFSHFMJOTJWSJZF- | |F SJOJ . OPLUBTOB CBUSQ [ KM ] ZBS¿BQM CBõLB CJS EF =CS D ¿FNCFS ¿J[JZPS ¥FNCFSMFSJO LFTJN OPLUBMBSO 3 WF:PMBSBLJTJNMFOEJSJZPS C #VOB HÌSF ,3.: EÌSUHFOJ JMF JMHJMJ BöBôEBLJ- | | :VLBSEBLJWFSJMFSFHÌSF #' LBÀCJSJNEJS MFSEFOIBOHJTJEPôSVEVS \" # $ % & | |A) #JSLFOBS KM PMBOLBSF | |B) #JSLFOBS KM PMBOLBSF | |C)#JSLFOBS KM PMBOFõLFOBSEËSUHFO | |D)#JSLFOBS KM PMBOFõLFOBSEËSUHFO E) #JSEJLEËSUHFO 1. \" 2. $ 3. B 4. B D $
TEST - 23 &öLFOBS%ÌSUHFO 1. D C \"#$%FõLFOBS 4. D C \"#$%FõLFOBS EËSUHFO E EËSUHFO A G [ EF] m[ AB ] G | AF | = | FB | E FB | DE | = | AG | [ EG ] m[ AD ] | AD | =CS A FB | |EF =CS | |GE =CS :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- | |BC =CS LBSFEJS \" # $ % & :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJN- LBSFEJS \" # $ % & A B 2. D C E DC AB \"#$%FõLFOBSEËSUHFO [AE]WF[DE]B¿PSUBZ % % A^ & h = 12CS2 m ( ABC ) 5.m ( DAB ) AED \"#$%FõLFOBSEËSUHFO = :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- LBSFEJS A ( ABCD ) =CS2 YVLBSEBLJ WFSJMFSF HÌSF FöLFOBS EÌSUHFOJO \" # $ % & ÀFWSFTJLBÀCJSJNEJS A) 16 B) 16 2 C) 32 D) 32 2 & \"#()FõLFOBSEËSUHFOJõFLMJOEFLJLVNBõQBS¿BT '&WF%$EPóSVMBSCPZVODBLFTJMJODFPSUBZB¿LBO õFLJMEÐ[HÐOBMUHFOPMVZPS 3. ôFLJMEF WFSJMFO \"#$% FõLFOBS EËSUHFOJ õFLJMEFLJ AE B LVNBõ QBS¿BTOB FõLFOBS EËSUHFO õFLMJOEFLJ LV- | |NBõQBS¿BMBSEJLJMNJõUJS AD =CS AB 2 FC 4 30 br 6 H DG D 2n C %JLJMFOLVNBõQBS¿BMBSOOËM¿ÐMFSJÐTUÐOEFCFMJSUJM- * '&WF%$EPóSVMBSCJSCJSJOFQBSBMFMEJS EJóJHJCJCJSËSÐOUÐZMFCFMJSMFONJõUJS & ** A ( ABGH ) = 8.A ^ AFE h #BöMBOHÀUBLJ LVNBö QBSÀBTOO BMBOOO EJ- *** % = 60° LJMFO LVNBö QBSÀBMBSOO UPQMBN BMBOOB PSBO m ( HAB ) LBÀUS #VOB HÌSF ZVLBSEB WFSJMFOMFSEFO IBOHJMFSJ A) 5 B) 45 $ % 42 E) 40 EPôSVEVS 11 11 11 \" :BMO[** # :BMO[*** $ *WF** % **WF*** & * **WF*** 1. E 2. D 3. B 4. \" E E
www.aydinyayinlari.com.tr ÇOKEGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, %÷,%²35(&/ TANIM ÖRNEK 2 B 60° ,BSõMLM LFOBSMBS CJSCJSJOF EJL WF FõJU PMBO A EËSUHFOFEJLEÌSUHFOEFOJS F 60° E 30° 30° 60° 60° %m/*m DC A B | | | |\"#$%EJLEËSUHFO [ AC ] a [ BD ] = { E } AD = EC E |BF| = |FC| :VLBSEBLJWFSJMFSFHÌSF m ( % ) LBÀEFSFDFEJS BEF DC |\"%| = |&$|WF|&$|= |\"&| = |ED|PMEVôVOEBO \"#$%EJLEËSUHFO \"%&FöLFOBSÑÀHFOPMVS [BD] a [AC] = {E} |#'| = |'$|WF#&$FöLFOBSÑÀHFOPMEVôVOEBO |AE| = |EB| = |ED| = |EC|EJS m ( B%EF ) = 30°PMVS NOT: %JLEÌSUHFOQBSBMFMLFOBSOCÑUÑOÌ[FMMJL- MFSJOJTBôMBS ÖRNEK 1 ÖRNEK 3 AB D C 30° a 60° E 30° E 15° 75° a+30° A 15° a+30° 75° a+15° B F DC | | | |\"#$%EJLEËSUHFO [ AC ] a [ BD ] = { E } EB = BF | | | | | | | |ABCD EJLEËSUHFO DC = AE AC = AD % = 15° % m ( FBC ) EBC % :VLBSEBLJWFSJMFSFHÌSF m ( ) LBÀEFSFDFEJS BDC :VLBSEBLJWFSJMFSFHÌSF m ( ) LBÀEFSFDFEJS m ( E%BF ) = a°PMTVO0IBMEFm ( B%CE ) = a + 15°PMVS |\"$| = 2 |\"%|PMEVôVOEBOm( D%CA ) = 30°PMVSWF m ( B%FE ) = a + 30° 3a +=j a = m ( B%AE ) = % = 30° EJS \"#& JLJ[LFOBS ÑÀHFO PM- % m ( DCA ) m ( BDC ) = 180° - 90° - 55° = 35°CVMVOVS EVôVOEBO m % ) = 75° PMVS0IBMEF m ( % ) = 15° ( ABE EBC CVMVOVS 1. 2. 3.
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKEGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÖRNEK 4 ÖRNEK 7 D C \"#$%EJLEËSUHFO DC 5E [ AC ] a [ BD ] = { E } 2E K2 5 A 6 | |ED = (2x + CS A8 | |EC = Y- CS 4 | |B AB =CS B | |:VLBSEBLJWFSJMFSFHÌSF \"% LBÀCJSJNEJS | |\"#$%EJLEËSUHFO [ DE ]åm[ AC ] AE å=CS | |EC å=CS |ED| = |&$|PMEVôVOEBOY+ 1 =Y- 3 & 4 =YjY=CS :VLBSEBLJWFSJMFSFHÌSF A^ AEB hLBÀCJSJNLBSFEJS \"%#EJLÑÀHFOJOEFQJTBHPSUFPSFNJOEFO ²LMJEUFPSFNJOEFO|DE|2 = |\"%|2 +2 = 102 j |\"%|=CSCVMVOVS |DE| =CS ÖRNEK 5 [BK] m [\"$] öFLJMEF[BK]OÀJ[FSTFL D 20 C \"#$%EJLEËSUHFO |BK| = |DE| =CSPMVS a a [ CF ]åm[ BD ] \" \"&# = 2.4 = 4 br2 CVMVOVS 2 ||15 E DC å=CS b | |AD å=CS ba A F xB | |:VLBSEBLJWFSJMFSFHÌSF #' LBÀCJSJNEJS #$%WF$'#ÑÀHFOMFSJOJOCFO[FSMJôJOEFO ÖRNEK 8 x 15 225 45 D 17 C = x = = CSCVMVOVS a 15 20 20 4 17 88 ÖRNEK 6 a a A4G 8 B \"#$%EJLEËSUHFO A2 E 15 B k F [ AC ] a [ DG ] = { F } | |\"#$%EJLEËSUHFO [ ED ]B¿PSUBZ AD å=CS | DC |å=CS 16 k 16 | |AG =CS D E | |BG =CS & 2k | |BC =CS :VLBSEBLJWFSJMFSFHÌSF A^ ADE hLBÀCJSJNLBSFEJS 12 C % = m ( % ) PMEVôVOEBO $%& JLJ[LFOBS ÑÀHFO m ( CED ) CDE | |:VLBSEBLJWFSJMFSFHÌSF '& LBÀCJSJNEJS PMVS#$&ÑÀHFOJOEFQJTBHPSUFPSFNJOEFO 2 + |BE|2 = 172 j |BE| =CS \"('WF%'$ÑÀHFOMFSJOEFCFO[FSMJLUFO|'$| = 3 |'\"|EJS |\"&| = 17 -=CS WF|&$| = 2 |\"'| = 2 |'&|EJS A^ ADE h = 2.8 2 L 2 = 122+2 \"%$ÑÀHFOJOEF1JTBHPSUFPSFNJOEFO 2 = 8 br CVMVOVS 4k = 20 j |'&| = k =CSCVMVOVS 45 7. 4 4. 4
www.aydinyayinlari.com.tr ÇOKEGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, %m/*m C ÖRNEK 10 P D D C \"#$%EJLEËSUHFO AB [ DE ] a [ AB ] = { F } [ CE ] a [ AB ] = { G } \"#$%EJLEËSUHFOWF1 J¿CËMHFEFCJSOPLUB AE = 4 3 CS | | | | | | | | r PA 2 + PC 2 = PB 2 + PD 2EJS | |A F G B CE =CS ÖRNEK 9 | |BE =CS D E 6 E | |:VLBSEBLJWFSJMFSFHÌSF DE LBÀCJSJNEJS 8 ^ 4 3 h2 + 72 = 42 + |DE|2 A 97 =+ |DE|2 |DE| =CSCVMVOVS C \"#$%EJLEËSUHFO %JLEÌSUHFOEF¦FWSFWF\"MBO C 10 & J¿ CËMHFEF CJS %m/*m x OPLUB D B | DE |å=CS | AE |å=CS | |CE =CS | |:VLBSEBLJWFSJMFSFHÌSF BE LBÀCJSJNEJS AB \"#$%EJLEËSUHFO 2 + 102 =2 +Y2 =+Y2 r¥FWSF \"#$% = 2.a AD + AB k Y2 =jY= 8 2 CSCVMVOVS | | | |r A ( ABCD ) = AB AD EJS ÖRNEK 11 A 4E x B \"#$%EJLEËSUHFO %m/*m P |AB | = |EC| C | |6 x+4 6 AE =CS D | |AD =CS DC :VLBSEBLJWFSJMFSFHÌSF ¦ \"#$% LBÀCJSJNEJS AB |EB| =YCSPMTVO|\"#| = |&$|PMEVôVOEBO |&$| =Y+CSPMVSY2 +2 = Y+ 2 \"#$%EJLEËSUHFOWF1 EõCËMHFEFCJSOPLUB 1JTBHPSUFPSFNJOEFO | | | | | | | | r PA 2 + PC 2 = PB 2 + PD 2EJS Y2+=Y2 +Y+ Y= 20 jY= ¦ \"#$% = + =CSCVMVOVS 9. 8 2 10. 9 11.
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKEGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÖRNEK 12 ÖRNEK 14 D EC \"#$%EJLEËSUHFO D C 30° 75° 45° 45° 75° m ( E%AB ) = 30° x 45° 45° x 2x % = 15° Mx E5 F xK x m ( CBE ) 2x+5 x 45° x 60° 15° ¥ \"#$% =CS 45° 45° 30° 45° 2x 75° A A B B :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJNLBSFEJS \"#$%EJLEËSUHFO [ AE ] [ BF ] [ CF ] [ DE ]B¿PSUBZMBS |%\"|=YBMSTBL |\"&| =Y= |\"#|PMVS | AB |å+ | BC | =CS | EF |å=åCS ¦ \"#$% =Y :VLBSEBLJWFSJMFSFHÌSF \" \"#$% æLBÀCJSJNLBSFEJS =YjY= 3 \" \"#$% ==CS2 CVMVOVS [EM]WF [',] EPôSV QBSÀBMBSO ÀJ[FSTFL PMVöBO ÑÀHFO- MFSJLJ[LFOBSEJLÑÀHFOPMVSWF|ME| = |DM| = |.\"| =YCS |',| = |,$|= |BK| =YCSEJS Y++Y= 21 Y=jY=CS \" \"#$% ==CS2 CVMVOVS ÖRNEK 13 ÖRNEK 15 AF B ABCD EJLEËSUHFO D C // 4 // 4 [ DF ] m [ EF ] 3h F 2h K 6 M 25 Dx x E3C |DF| = |EF| 9 E | |BC =CS 3 | |EC =CS A B :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJNLBSFEJS | | | |\"#$%EJLEËSUHFO [ AC ] a [ ED ] = {F } BE å= EC | || AD |å=åCS AB =CS %'&ÑÀHFOJOEFNVIUFöFNÑÀMÑEFOY=CSPMVS & 0IBMEF|%$| =Y+ 3 =CSEJS :VLBSEBLJWFSJMFSFHÌSF A^ FEC hæLBÀCJSJNLBSFEJS \" \"#$% = 11.4 =CS2 CVMVOVS $'&WF%\"'ÑÀHFOMFSJOEFCFO[FSMJLUFO|',| = 2|.'|EJS I=j h =PMVS Aa & k = 6.10 = 30 2 CVMVOVS FEC 2 br 12. 13. 44 14. 104 30
www.aydinyayinlari.com.tr ÇOKEGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 16 CE ÖRNEK 18 D 15° #JSLBóEB\"#$%EJLEËSUHFOJOJ¿J[JQJ¿JOEFCJS&OPLUB- F 45° 6 | | | |T BMOZPS [ DE ] m [ CE ] AB = CS BC = CS WF 6 ¥ %&$ = CS PMEVôVOB HÌSF \" \"#$&% LBÀ CJ- SJNLBSFEJS 30° 45° K A 6 3 –6 B6 \"#$%EJLEËSUHFO [ DE ] a [ AE ] = { E } m ( E%AB ) = 30° A 8 B x E 7 | |% m ( AEB ) = 15° AD =CS y :VLBSEBLJWFSJMFSFHÌSF \" \"#$% æLBÀCJSJNLBSFEJS [EK] m [\",]PMBDBLöFLJMEF[EK]OÀJ[FSTFL D8 C % = 45° PMVS ¦ %&$ =Y+Z+=jY+Z= 10 m ( EBK ) Y+Z 2 = 2 Y2+YZ+Z2 = 100 \" \"#$% = 6^ 6 3 - 6 h = 36 2 3 - 36 br CVMVOVS +YZ= 100 YZ=jYZ= xy A^ ABCED h = 56 - = 56 - 9 = 47 CSCVMVOVS 2 ÖRNEK 17 5 C D 34 ÖRNEK 19 H G 5 *BEN\"#$%EJLEËSUHFOJOJ¿J[JOJ[ F 2 **BEN%JLEËSUHFOJOEõOEB[ AE ] a [ DC ] = { F }PMB- A B 3 DBLõFLJMEFCJS'OPLUBTBMO[ E | | | |***BEN AF = EF PMBSBLBMO[ \"#$%EJLEËSUHFO [ DE ] a [ CE ] = { E } *7BEN A ( ABCD ) =CS2PMBSBLBMO[ :VLBSEBLJ BENMBS J[MFZFO ÌôSFODJ \"#& ÑÀHFOJOJO | | | | | |CD å= CE å=CS AE = 15 br EB å= 2 CS BMBOOLBÀCJSJNLBSFPMBSBLCVMVS & AB :VLBSEBLJWFSJMFSFHÌSF A^ DEC hLBÀCJSJNLBSFEJS 45 |\"&|2 + |&$|2 = |ED|2 + |EB|2 3k ^ 15 h2 +2 = |ED|2 + 22 40 = |ED|2 + 4 |ED|2 = |ED| = 30 C D F 2k %$&ÑÀHFOJOEF[$)]OÀJ[FSTFL |%)| = |&)| =CSPMVS1JTBHPSUFPSFNJOEFO E |$)|2 + 32 =2 j |$)| =CS \" \"'# = A^ ABCD h 90 = 45 CS2CVMVOVS & A^ AFB h = 6.4 22 A^ DEC h = 2 2 \" \"#& =+ 30 =CS2 CVMVOVS = 12 br CVMVOVS 36 3 - 36 17. 12 47 19.
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKEGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÖRNEK 20 ÖRNEK 22 ,FOBSMBSCSWFCSPMBOCJS\"#$%EJLEËSUHFOJOJ¿J[J- ôFLJM*EFLFOBSV[VOMVLMBSWFSJMFOEJLEËSUHFOõFLMJOEF- OJ[\"#$пHFOJOJ[ AC ]EPóSVQBS¿BTCPZVODBLBUMBE- LJõFSJU%LËõFTJ [AB]Ð[FSJOF #LËõFTJEF[DC]Ð[FSJ- óN[EB#OPLUBTOOZFOJZFSJOJ#hOPLUBTPMBSBLBMO[ OFHFMFDFLõFLJMEFõFLJM**EFLJHJCJLBUMBOZPSWFË[EFõ õFLJMMFSPMVõVZPS [\"#h] a [ CD ] = { E }PMEVôVOBHÌSF A^ & hLBÀCJ- AEC D C SJNLBSFEJS A 10 B ôFLJM* a 8 A B a C' C D x 5 DE 10–x x a 9 B' 8 C N B' 4 3 ôFLJM** #h&$ÑÀHFOJOEF1JTBHPSUFPSFNJOEFO Aa 9–a 4 B D' M 2 + -Y 2 =Y2 a3 + 100 -Y+Y2 =Y2 41 d A' Y=j x = 5 ôFLJM**EFEJLEËSUHFOõFSJUJO#LËõFTJ#hJMF% LËõFTJEF %hJMFHËTUFSJMNJõUJS A^ AEC h = 8.41 = 164 CS2 CVMVOVS 5.2 5 #h %hOPLUBMBSOEBOHFÀFOEEPôSVTV[\"#]ZFEJLPM- EVôVOBHÌSF %h.#h/EÌSUHFOJOJOBMBOLBÀCS2EJS ÖRNEK 21 B2 + 32 = -B 2 1JTBHPSUFPSFNJOEFO B2 + 9 =-B+B2 \"#$%EJLEËSUHFOJõFLJMEFLJHJCJEËOEÐSÐMÐODF%&'( EJLEËSUHFOJFMEFFEJMJZPS B= 4 AB | |EH = 4 3 CS \" %h.#h/ = 4.3 | |HF = 2 3 CS =CS2CVMVOVS E 4 43 C 30° 23 8 30° 60° H F D 30° 63 G | |:VLBSEBLJWFSJMFSFHÌSF )$ LBÀCJSJNEJS )%&EJLÑÀHFOJOEF|DE|=CSWF|%)| =CSPMVS |)$| = 6 3 - CVMVOVS 164 21. 6 3 - 8 22. 12 20. 5
%JLEÌSUHFO TEST - 24 1. F 4. A F B A 10° B E 130° E DC DC \"#$%EJLEËSUHFO BC = 2 · EF | EF | = | FB | \"#$% EJLEËSUHFO [EC] m [CF] m ( A%EC ) = 130° :VLBSEBLJ WFSJMFSF HÌSF m ( % ) LBÀ EFSFDF- FEB m ( F%AB ) = 10° EJS :VLBSEBLJWFSJMFSFHÌSF m ( % ) LBÀEFSFDF- \" # $ % & AFC EJS \" # $ % & A 23 B F 2. A B 2 E x F 10° D C 4E D CG | |\"#$%EJLEËSUHFO AD =CS AB = 2 3 CS | CE | =CS % AGD :VLBSEBLJWFSJMFSFHÌSF m (D%AE)LBÀEFSFDFEJS | | | |\"#$%EJLEËSUHFO m ( ) = 10° BD = CG \" # $ % & :VLBSEBLJ WFSJMFSF HÌSF m ( % ) LBÀ EFSFDF- AED EJS \" # $ % & D C E 3. A E B 10 6 D 14 C AB | | | |\"#$%EJLEËSUHFO AD =CS EC =CS | | | | | | | |\"#$%EJLEËSUHFO AD = BE DC = AE | |DC =CS % = 20° m ( DCE ) :VLBSEBLJ WFSJMFSF HÌSF m (A%DE) LBÀ EFSFDF- :VLBSEBLJ WFSJMFSF HÌSF m ( D%AE ) LBÀ EFSFDF- EJS EJS \" # $ å % & \" # $ % & 1. $ 2. B 3. B 4. B E B
TEST - 25 %JLEÌSUHFO 1. D E C ABCD 4. D C ABCD EJLEËSUHFO EJLEËSUHFO | |15 17 AD =CS E | |AB =CS |AB| = |AE| A 23 | |B EB =CS // |DA| = |DE| A // B m (D%EB) = 120° :VLBSEBLJWFSJMFSFHÌSF m ( E%AB )LBÀEFSFDF- :VLBSEBLJWFSJMFSFHÌSF m ( C%DE )LBÀEFSFDF- EJS EJS \" # $ % & \" # $ % & D FC ABCD // EJLEËSUHFO 58° 2. E D F |DE| = |EB| 15° C |AE| = |FC| K // B m ( D%FE) = 58° 25° AE A :VLBSEBLJ WFSJMFSF HÌSF m ( % ) LBÀ EFSF- ADE B DFEJS \"#$%EJLEËSUHFO \" , ' &EPóSVTBM \" # $ % & | | | |BD=AE m ( % ) = 15° m ( % ) = 25° BDC KAD :VLBSEBLJWFSJMFSFHÌSF m (D%CE)LBÀEFSFDF- \"#$%EJLEËSUHFOJõFLMJOEFLJCËMHFOJO,OPLUBTO- EJS EBPUVSBO,BEJS .OPLUBTOEBLJFWFUBõOZPS \" # $ % & AB K M 3. D E C ABCD // EJLEËSUHFO DC // |DE| = |EF| ,BEJSJMLFWJOJO#LËõFTJOFPMBOV[BLMó ZFOJFWJ- F OFPMBOV[BLMóOBFõJUUJS,BEJShJOZFOJFWJOJO$LË- m (A%FB) = 110° õFTJOFPMBOV[BLMó #WF$LËõFMFSJBSBTV[BLMóB FõJUUJS AB ,BEJShJOZFOJFWJOJO\"LÌöFTJOFPMBOV[BLMô % :VLBSEBLJWFSJMFSFHÌSF m ( FEC )LBÀEFSFDF- | | | |LNWF MD = 2. \", PMEVôVOBHÌSF %WF$ EJS LÌöFMFSJBSBTV[BLMLLBÀLNEJS \" # $ % & \" # $ % & 1. B 2. E 3. \" 4. \" B B
%JLEÌSUHFO TEST - 26 1. E 4. D C ABCD 4 EJLEËSUHFO D // F C [ DE ] m [ EF ] // | |8 CF =CS | |A E 6B BF =CS AB | |BE =CS | | | |\"#$%EJLEËSUHFO \" $ &EPóSVTBM AC = CE & | | | |AB =CS AD å=CS :VLBSEBLJWFSJMFSFHÌSF A^ DEF hLBÀCJSJNLB- | | :VLBSEBLJWFSJMFSFHÌSF BE LBÀCJSJNEJS SFEJS \" # $ % & A) 13 B) 2 13 C) 3 13 D) 4 13 E) 6 13 A B 6 F E 2. D C ABCD G 8 C D A EJLEËSUHFO E | |ABCD EJLEËSUHFO [ FG ] // [ AD ] BC =CS F [CE] m [DE] | |DC =CS | |DE =CS | |B | | | | :VLBSEBLJ WFSJMFSF HÌSF &' + DG UPQMBN BE =CS LBÀCJSJNEJS | | | | :VLBSEBLJWFSJMFSFHÌSF \"# + #' UPQMBN \" # $ % & LBÀCJSJNEJS A) 5 5 B) 5 C) 8 5 \"õBóEBEJLEËSUHFOõFLMJOEFCJSCJSJOFFõEJLEËSU- D) 9 5 E) 10 5 HFO LBMBT BSBMBSOEB CPõMVL LBMNBZBDBL õFLJMEF õFLJMEFLJHJCJEJ[JMNJõUJS A 3. D C ABCD CB 9 4 EJLEËSUHFO D E x | |AE =CS õFLJMEFLJ\"WF#OPLUBMBSBSBTOEBLJV[BLMLJMF 5 B | |EC =CS $WF%OPLUBMBSBSBTOEBLJV[BLMLFöJUPMEVôV- | |DE =CS OB HÌSF CJS LBMBTO V[VO LFOBSOO V[VOMVôV- A OVO LTBLFOBSOOV[VOMVôVOBPSBOLBÀUS A) 3 B) 7 $ % 9 E) 6 | | :VLBSEBLJWFSJMFSFHÌSF EB LBÀCJSJNEJS 22 A) 10 B) 2 5 C) 3 5 4. E $ E D) 2 10 E) 3 10 1. D 2. \" 3. E
TEST - 27 %JLEÌSUHFO 1. A B ABCD 4. A B ABCD EJLEËSUHFO EJLEËSUHFO [ AE ] m [ BD ] E [ FE ] m [ CE ] F | |AD =CS | |C DF =CS | |DE =CS DE | |C EC =CS DF | | :VLBSEBLJWFSJMFSFHÌSF #$ LBÀCJSJNEJS | | :VLBSEBLJWFSJMFSFHÌSF EB LBÀCJSJNEJS A) 6 B) 2 10 C) 42 A) 3 5 B) 2 5 C) 4 2 D) 3 5 E) 4 3 D) 4 5 & 2. A B A G B \"#$%LBSF E F HK &()'EJLEËSUHFO E DC D C [HK] m [BC] |EF| = |EG| | |DF =CS | |AG =CS \"#$%EJLEËSUHFO [AC] m [CE] [ BE ] // [ AC ] | | :VLBSEBLJWFSJMFSFHÌSF ), LBÀCJSJNEJS | | | | | |AB = BC EC = 3CS \" # $ % & | | :VLBSEBLJWFSJMFSFHÌSF \"$ LBÀCJSJNEJS \" # $ % & 3. A B 5FS[J\"INFU \"#$%EJLEËSUHFOõFLMJOEFLJLVNBõ [FE] WF [HG] CPZVODB LBUMBOELUBO TPOSB # WF % G H OPLUBMBSOOZFOJZFSMFSJOJOBSBTOEPóSVTBMPMBDBL õFLJMEFCJSJQMFEJLJZPS E DF C AB | |\"#$%EJLEËSUHFO [ FA ] m [ BE ] DF =CS | |EC =CS FE | | :VLBSEBLJWFSJMFSFHÌSF #$ LBÀCJSJNEJS HG A) 8 B) 6 2 C) 4 5 DC D) 2 21 E) 3 10 | | | | | |%$ =N EB + ($ = NWFLBUMBNB TPOSBTEJLJMFOLTNOV[VOMVôVNPMEVôVOB HÌSF CBöMBOHÀUBLJ#WF%OPLUBMBSBSBTV[VO- MVLLBÀNFUSFEJS \" # $ % & 1. B 2. $ 3. E 4. D \" $
Dikdörtgen TEST - 28 1. A B ABCD 4. D C D E2 dikdörtgen [ DB ] m [ EC ] E | |8 EB = 2 br | |C DE = 8 br AB :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- | |ABCD dikdörtgen, AE = ( 3x + 1 ) br karedir? BE = x + 48 br, A ( ABCD ) = 112 br2 A) 40 B) 36 C) 30 D) 24 E) 20 4 YukaSEBLJWFSJMFSFHÌSF ¦ \"#$% LBÀCJSJN- dir? A) 58 B) 60 C) 68 D) 72 E) 78 5. \"#$%EJLEËSUHFOJõFLMJOEFLJLBSUPOFõLBSFMFSFBZ- 2. A E B ABCD SMNõUS A B dikdörtgen |DE| = |DC| Ç ( ABCD ) = 18 br DC D C A ( ABCD ) = 18 br2 4BSCPZBMLBSFTFMCÌMHFMFSJONFSLF[MFSJOJLÌöF % LBCVMFEFOÑÀHFOJOBMBOCS2PMEVôVOBHÌSF \"#$%EJLEÌSUHFOJOJOBMBOLBÀCJSJNLBSFEJS :VLBSEBLJ WFSJMFSF HÌSF m ( EDC ) LBÀ EFSFDF- dir? A) 240 B) 250 C) 280 D) 320 E) 360 A) 15 B) 30 C) 45 D) 60 E) 75 6. A B 3. D C ABCD EK M NF dikdörtgen H [ CA ] m [ DE ] | |E DE = 6 br DG C | |A B CE = 9 br | | | |ABCD dikdörtgen, [ EF ] // [ AB ], DG = GC | | | |AD = AE , A ( HGNM ) = 5 br2 & :VLBSEBLJWFSJMFSFHÌSF A(AEB) PSBO OF- dir? A (ABCD) YukarEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- karedir? A) 1 B) 3 C) 2 D) 3 E) 5 13 26 13 13 13 A) 18 B) 27 C) 36 D) 45 E) 54 1. \" 2. # 3. $ 65 4. # 5. D 6. $
TEST - 29 %JLEÌSUHFO 1. A 4. D C H B K K E D A FG B E FC \"#$%WF',)#EJLEËSUHFO & , $WF% , (EPó- \"#$%EJLEËSUHFO \" # &EPóSVTBM $ ' &EPóSV- | | | | | | | |SVTBM AG = BG DE = AE TBM [AF] m [EC] A^ & h = A^ & h A (FBHK) AEF BEC | EF | =CS | FC | =CS :VLBSEBLJWFSJMFSFHÌSF PSBOLBÀ- US A (ABCD) :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- 35 25 16 16 9 LBSFEJS A) B) C) D) E) 72 48 25 27 16 \" # $ % & 2. D CF D C ABCD E EJLEËSUHFO K A E [ DK ] m [ AE ] AB | | | | AB = AD B |EC| = |EB| ABCD EJLEËSUHFO % $ 'WF\" & 'EPóSVTBM :VLBSEBLJWFSJMFSFHÌSF A (DKEC) PSBOLBÀ- & =CS2 US A (ABCD) A^ EFB h & A) 31 B) 21 C) 18 D) 13 E) 3 :VLBSEBLJWFSJMFSFHÌSF A^ DCE hLBÀCJSJNLB- 52 28 29 20 4 SFEJS \" # $ % & D E C ABCD EJLEËSUHFO 3. D E C ABCD A [ EF ] m [ AB ] H EJLEËSUHFO K L |EL| = |LB| G A^ & h =CS2 FGK F K A^ & =CS2 |AF| = |FB| GEH h & F B EKL =CS2 A^ h & =CS2 A B A^ AKB h & :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- :VLBSEBLJWFSJMFSFHÌSF A^ HBC hLBÀCJSJNLB- LBSFEJS SFEJS \" # $ % & \" # $ % & 1. B 2. $ 3. B 4. \" D D
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ,\"3& 7ANnM ÖRNEK 2 B \"#$%LBSF 5ÐNLFOBSMBSCJSCJSJOFFõJUWFEJLPMBOEËSUHF- A ne LBSFEFOJS |AE| = |DE| % k m ( ECB ) = 60° %m/*m M E 2k 60° A B k 15° k 60° 75° 30° K D C // :VLBSEBLJWFSJMFSFHÌSF m ( % ) LBÀEFSFDFEJS / / ADE [EK] m [%$]WF[EM] m [\"%]ÀJ[FSTFLPMVöBOÑÀHFOMFSEF E |&$| = |\"%| =LPMVS DC 0IBMEF&%$JLJ[LFOBSÑÀHFOJOEF m ( % ) = 75° PMVS \"#$%LBSFJTF EDC r [ AC ] m [ BD ] % = 90° - 75° = 15° CVMVOVS r [ AC ]WF[ BD ]B¿PSUBZ m ( ADE ) r |AE| = |EC| = |DE| = | |BE EJS ÖRNEK 1 ÖRNEK 3 A B \"#$%LBSF #JSLBóEB\"#$%LBSFTJOJ¿J[JQ %$EPóSVTVOVOÐ[FSJO- 15° #&$FõLFOBS de [ AE] a [ BC ] = { F}PMBDBLõFLJMEFCJS&OPLUBTBM- 60° пHFO O[ 15° E 30° | | | |'& = 2 2 . %$ PMEVôVOB HÌSF m( B%AE ) LBÀ EF- 15° SFDFEJS 60° A B C a 15° D 2a :VLBSEBLJWFSJMFSFHÌSF m ( % ) LBÀEFSFDFEJS k F AED k2 #&$FöLFOBSÑÀHFOWF\"#$%LBSFPMEVôVOEBO k2 2a H k2 3a 2 a ak |\"#| = |BE|EJSWF|$&|= |%$|EJS D kC E \"#&WF$%&JLJ[LFOBSÑÀHFOMFSJOEF '$& EJL ÑÀHFOJOEF [$)] LFOBSPSUBZ EPôSVTV ÀJ[JMJSTF % = % =PMVS \"$)ÑÀHFOJJLJ[LJOBSÑÀHFOPMVSa = m ( AEB ) m ( DEC ) 0IBMEF m ( % ) = 30° CVMVOVS a =CVMVOVS AED 1. 2. 3.
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÖRNEK 4 ÖRNEK 6 D E \"#$%LBSF A B \"#$%LBSF 30° a C [ AE ] a [ BE ] = { E ] 90°–a m % ) = % a 90°–2a a+45° F ( DAE m ( FAB ) % m ( CBE ) = 15° | |EF = 4 2 CS 46 | |AB = 4 3 CS 42 4 K a+45° 26 15° 90°–a 45° 45° D E 4C 4 3 45° 45° B | |:VLBSEBLJWFSJMFSFHÌSF &$ LBÀCJSJNEJS A | |:VLBSEBLJWFSJMFSFHÌSF BE LBÀCJSJNEJS \"#'WF\"%&ÑÀHFOMFSJFöPMEVôVOEBO|\"&| = |\"'|PMVS [BK] m [\"$]ÀJ[FSTFL\",#ÑÀHFOJOEF m ( % ) = a PMTVO DAE |BK| = 2 6 CSPMVS &,#ÑÀHFOJOEF|BE| = 4 6 CSPMVS \"&'JLJ[LFOBSÑÀHFOJOEF m ( A%EF ) = m ( A%FE ) = a + 45° UJS0IBMEF'&$ÑÀHFOJJLJ[LFOBSEJLÑÀHFOPMVSWF |&$| =CSPMVS ÖRNEK 5 A 6 B \"#$%LBSF ÖRNEK 7 a 2 m ( B%AF ) = % D C \"#$%LBSF b m ( EFC ) 45° 15° F | |BF =CS 45° m % = 15° a ( ECD ) | |CF =CS E x |AE| = |EC| 60° 4 2x 4 2 | |ED = 2 3 - 2CS b 15°30° D EC | |:VLBSEBLJWFSJMFSFHÌSF DE LBÀCJSJNEJS AB \"#'WF'&$ÑÀHFOMFSJCFO[FSÑÀHFOMFSEJS | |:VLBSEBLJWFSJMFSFHÌSF \"& LBÀCJSJNEJS 2 6 j |&$| = 4 &%$ WF &%\" ÑÀHFOMFSJ Fö PMEVôVOEBO [DE] BÀPSUBZ = EC 4 3 PMVS 4 14 |DE| = x 3 - x = 2 3 - 2 DE = 6 - = br CVMVOVS Y=CS 33 |\"&| =Y=CSCVMVOVS 4. 4 6 14 4 7. 4 3
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 8 ÖRNEK 10 E A B \"#$%LBSF 9 12 a F b |AB| = |BF| Db aC b b | |EC =CS 12 a x | |DE =CS K x a 8 F a . D 6 E 2C K | |:VLBSEBLJWFSJMFSFHÌSF &' LBÀCJSJNEJS 9b #hEFO |\"'|hZF EJL JOEJSFMJN \"%& ÑÀHFOJOEF QJTBHPS UF- AB PSFNJOEFO \"#$%LBSF [ DE ] m [ CE ] [ AF ] m [ CE ] |\"&| = 10 | | | |ED =CS EC =CS | |:VLBSEBLJWFSJMFSFHÌSF \"' LBÀCJSJNEJS \"%&WF#,\"ÑÀHFOMFSJCFO[FSPMEVôVOEBO 6x %,\"WF%&$ÑÀHFOMFSJFöPMEVôVOEBO|KD| =CS = |\",| =CSPMVS 10 8 0IBMEF|\"'| = 12 + 9 =CSCVMVOVS Y= CS |\"'| = = CS |&'| = 10 - = CSCVMVOVS ÖRNEK 9 ÖRNEK 11 D 16 C \"#$%LBSF D C \"#$%LBSF 4k [ AC ] a [ DF ] = { E } x \"#,FõLFOBSпHFO 16 E K | |AF =CS | |AB =CS 3k | |BF =CS 60° 4 4 4 A 12 F4B 30° 4 60° 60° B A | |:VLBSEBLJWFSJMFSFHÌSF DE LBÀCJSJNEJS | |:VLBSEBLJWFSJMFSFHÌSF KD LBÀCJSJNEJS %&$WF\"&'ÑÀHFOMFSJCFO[FSÑÀHFOMFSPMEVôVOEBO \"%,ÑÀHFOJOEFDPTJOÑTUFPSFNJZB[MSTB Y2 = 42 + 42 -DPT= 32 - 32· 3 4 |&'| = 3 |DE|EJS 2 \"%'ÑÀHFOJOEF1JTBHPSUFPSFNJOEFO = 32 - 16 3 |%'|2 = 122 +2 j |%'| =CS x = 32 - 16 3 = 32 - 2 192 = 24 - 8 20 = ^ 2 6 - 2 2 h br CVMVOVS 7k = 20 j k = 7 |DE| = 4k = 80 br CVMVOVS 7 80 10. 21 11. 2 6 - 2 2 9. 7
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÖRNEK 12 ÖRNEK 13 #JSLBóEB\"#$%LBSFTJOJ¿J[JQ J¿CËMHFEF[ AK ] m [ BK ] \"#$%WF&',-CJSFSLBSFPMNBLÐ[FSF BMBOMBSPSB- OUÐS PMBDBLõFLJMEF,OPLUBTBMO[ #ÑZÑLLBSFOJOÀFWSFTJCSPMEVôVOBHÌSF LÑÀÑL LBSFOJOBMBOLBÀCJSJNLBSFEJS | | | | | |AK =CSWF BK =CSPMEVôVOBHÌSF KD LBÀ #ÑZÑLLBSFOJOÀFWSFTJCSJTFCJSLFOBSCJSJNEJS CJSJNEJS \"MBOJTFCJSJNLBSFEJS ,ÑÀÑLLBSFOJOBMBOJTFCS2PMVS A B b a 5 a5 M 7 K 12 b DC \",#WF\".%ÑÀHFOMFSJFöPMEVôVOEBO |.\"| =CS |MD|=CSWF|MK| =CSEJS |KD|2 = 122+ 72 = 193 D&MK 1JTBHPSUFPSFNJOEF |KD| = 193 br CVMVOVS Karede Çevre ve Alan ÖRNEK 14 B \"#$%LBSF A %m/*m 45° 3 % = 15° .. m ( EDC ) A B 32 3 M | |DE = 2 3 CS // 45° 3 // 30° 60° E // 15° 23 D C // :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJNLBSFEJS D C \"#$%LBSF [DM] m [\"$]ÀJ[FSTFLPMVöBO%.&ÑÀHFOJOEF | |r¥ \"#$% = AB | |r A ( ABCD ) = AB 2 |DM| =CSPMVS \".%ÑÀHFOJOEF|%\"| = 3 2 CSEJS \" \"#$% = ^ 3 2 h2 = 18 2 CVMVOVS br NOT: ,BSF EJLEÌSUHFO WF QBSBMFMLFOBSO CÑ- UÑOÌ[FMMJLMFSJOJTBôMBS 12. 193 70 13. 3 14.
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 15 C \"#$%WF&'(\"LBSF ÖRNEK 17 B \"#$%LBSF D |EF| = |FC| A [ AE] m [ CE ] | |AB = ^ 3 2 + 3 hCS y2 y a |DF| = |FC| 2k k 5 | |EF =CS E x Fy xx x A x Gy B bF k Dk ba C 3 :VLBSEBLJWFSJMFSFHÌSF \" \"('& LBÀCJSJNLBSFEJS E |\"(|=YCSWF|BG|=ZCSPMTVO :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJNLBSF- EJS 1JTBHPSUFPSFNJOEFO|'$| = y 2 |&'| = |'$| |%'| = L CS PMTVO \"%' WF '&$ ÑÀHFOMFSJ CFO[FS PMEV- x=y 2 ôVOEBO 3k x+y=3 2+3 j k = 3 5 br = y+y 2=3 2+3 k k5 Z=CS AD = 6 5 br x=3 2 A^ ABCD h = ^ 6 5 h2 = 180 2 CVMVOVS br A^ AGFE h = ^ 3 2 h2 = 18 2 CVMVOVS br ÖRNEK 16 ÖRNEK 18 A 18 B \"#$%LBSF DE C \"#$%LBSF F 6 12 | DE | = | AG | =CS ECGF VE KMNA 45° K | AB | =CS KM G G EJLEËSUHFO 2k | |BC =BCS 12 2A F 45° A k D 6 E 12 C AN B :VLBSEBLJWFSJMFSFHÌSF \" \"('# LBÀCJSJNLBSFEJS :VLBSEBLJWFSJMFSFHÌSF LBSFOJOJÀFSJTJOEFOJLJEJL- EÌSUHFO ÀLBSMSTB LBMBO öFLMJO ÀFWSFTJ LBÀ CJSJN [GK] // [%$]PMBDBLöFLJMEF[GK]OÀJ[FMJN#VEVSVN- PMVS EB[GK| =CSPMVS(,'WF'%&ÑÀHFOMFSJCFO[FSPMEV- :VLBSEBLJöFLJMEFCFMJSUJMFOLFOBSMBSBHÌSF öFLMJOÀFW- ôVOEBO|('| = 2 |'&|PMVS SFTJEFôJöNF[:BOJBCSPMVS \" %(' =\" %'& =\"PMTVO 12.6 \"= 2 \"= \"= \"= 24 18 2 \" \"('# = 2 - 24 = 138 CS2 CVMVOVS 71 17. B
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÖRNEK 19 ÖRNEK 21 #JS LBóEB BMBO CS2 PMBO CJS \"#$% LBSFTJOJ ¿J[JOJ[ A 32 B \"#$%LBSF | |CE m [ AE ] PMBDBL õFLJMEF LBSFOJO EõOEB CJS & BM- 45° [ DB ] m [ BF ] | | | |O[ CE OJO AD LFOBSOLFTUJóJOPLUBZB'JTNJOJWFSJ- 45° 45° 4 | | | | DE = EF OJ[m ( D%FC ) = 75° 6 2k F | |BF = 3k | |#VOBHÌSF \"& V[VOMVôVLBÀCJSJNEJS E A 62 B DC 6 12 62 | |:VLBSEBLJWFSJMFSFHÌSF \"# LBÀCJSJNEJS 15° 45° 30° [#$]BÀPSUBZPMEVôVOEBO BÀPSUBZUFPSFNJOEFO E F 4 BD 75° = DC 2k 3k |BD| =CSWF\"#$%LBSFTJOEF|\"#| = 3 2 CSCVMVOVS [\"$]LÌöFHFOJÀJ[JMJSTF m ( % ) = 60° PMEVôVHÌSÑMÑS EAC |\"$| =CSPMEVôVOEBO|\"&| =CSCVMVOVS --ÑÀHFOJOEFO ÖRNEK 20 ÖRNEK 22 *BEN#JS\"#$%LBSFTJOJ¿J[JOJ[ \"#$%LBSFTJõFLMJOEFLJUBSMBOOJ¿CËMHFTJOEFCJSOPLUB- ZBCJSLB[L¿BLMQ UBSMBOOLËõFMFSJOFCJSJQZBSENZMB **BEN\"%LFOBSÐ[FSJOEFCJS&OPLUBTBMO[ CJSMFõUJSNFJõMFNJZBQMZPS ***BEN [ EF ] m [ FC ]PMBDBLõFLJMEFLBSFOJOJ¿CËMHF- AB TJOEFCJS'OPLUBTBMO[ K *7BEN [ FH ] m [ AB ] DC ,B[LJMF\" #WF$LÌöFMFSJBSBTOEBLJHFSJMFOJQMFSJO | | | | | |7BEN DE =CS AH =CSWF HB =CSBMO[ V[VOMVLMBS TSBTZMB N N WF N PMEVôVOB HÌ- SF LB[L JMF % LÌöFTJ BSBTOEBLJ JQJO V[VOMVôV LBÀ Yukarıdaki adımları izleyerek ABCD karesini çizen NFUSFEJS | |biri FH uzunluğunu kaç birim olarak bulur? |,\"|2 + |,$|2 = | KB |2 + | KD |2 2 +2 =2 + | KD |2 A8 H3B | KD |2 = | KD | = 53 CSCVMVOVS x xx 83 M b aK 9–x a F b 11–x E 2 DC ,'$WF'.&ÑÀHFOMFSJCFO[FSÑÀHFOMFSPMEVôVOEBO 3 11 - x = jY=CSCVMVOVS 9-x 8 19. 20. 72 21. 3 2 22. 53
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 23 B ÖRNEK 24 A ôFLJMEF\"#$%LBSFTJõFLMJOEFLJLVNBõQBS¿BTWFSJMNJõ- UJS#VLVNBõQBS¿BTOEBпHFOõFLMJOEFJLJLVNBõQBS- // //K MK ¿BTLFTJMJZPS M AB a 45° Ca D CD 45°–a \"#$%LBSFTJ[KM]CPZVODBLBUMBOEóOEBPLMBHËTUFSJ- E 12 16 MFOõFLJMFMEFFEJMJZPS KP M P M DF C E.'. | | | |% m ( EBF ) DR C R C = 45° EB =CSWF BF =CSPMEVôV- OB HÌSF LFTJMFO JLJ LVNBö QBSÀBTOO UPQMBN BMBO %BIBTPOSB,.$%EJLEËSUHFOJUBNPSUBTOEBO[13]CP- LBÀCJSJNLBSFEJS ZVODBLBUMBOODBPLMBHËTUFSJMFOõFLJMFMEFFEJMJZPS \"#&ÑÀHFOJOJ #$LFOBSZMBÀLBöBDBLöFLJMEFZBQöUSS- PM 1 TBL \" #'&h = ppTJO 2 XY 1 2 = 48 2 CS2 CVMVOVS TZ = ·16·12· 22 RC 4POPMVõBOõFLJMEFOCFMJSUJMFOEJLEËSUHFOLFTJMJQ¿LBSM- ZPSWFUFLSBSB¿MZPS 4POEVSVNEBBÀMELUBOTPOSBPMVöBOöFLMJCVMVOV[ AB// // ZTZ YXY KM YXY ZTZ DC 23. A ZTZ B 73 24. 48 2 YX Y M K YX Y C D Z TZ
TEST - 30 ,BSF 1. A B \"#$%LBSF 4. A B \"#$%LBSF |AF| = |AD| F |BC| = |EA| E % = 75° % = 76° m ( BEC ) m ( EDA ) F DC D EC :VLBSEBLJ WFSJMFSF HÌSF m ( E%BC ) LBÀ EFSFDF- EJS :VLBSEBLJ WFSJMFSF HÌSF m ( % ) LBÀ EFSFDF- BAF \" # $ % & EJS \" # $ % & A B 2. E \"#$%LBSF A B |BE| = |AD| % = 20° m ( BAE ) D CE | | | |\"#$%LBSF % $ &EPóSVTBM AC = DE DC :VLBSEBLJ WFSJMFSF HÌSF m ( % ) LBÀ EFSFDF- EBC :VLBSEBLJ WFSJMFSF HÌSF m (B%CE) LBÀ EFSFDF- EJS EJS \" # $ % & \" # $ % & D C L 3. E \"#$%LBSF H AB = 4 2 CS E A | |B EC =CS A FB G DC \"#$%LBSF [ AL ] a [ DG ] = { E} [ DL ] a [ AL ] = {L} :VLBSEBLJ WFSJMFSF HÌSF m (D%EC) LBÀ EFSFDF- |CL| = |BG| EJS \" # $ % & % :VLBSEBLJ WFSJMFSF HÌSF m ( LEG ) LBÀ EFSFDF- EJS \" # $ % & 1. B 2. $ 3. B 74 4. \" D B
,BSF C \"#$%LBSF 4. E TEST - 31 1. D % # &EPóSVTBM D \"#$%LBSF m (C%EB) = m (C%BE) |DB| = |CE| C // // AB AB E :VLBSEBLJWFSJMFSFHÌSF m % LBÀEFSFDFEJS :VLBSEBLJ WFSJMFSF HÌSF m (C%ED) LBÀ EFSFDF- (DEB) EJS \" # $ % & \" # $ % & 2. \"#$%LBSF \"#(FõLFOBSпHFOWF\"(&'FõLFOBS D C \"#$%LBSF EËSUHFOEJS E $ & 'EPóSVTBM D C % % G m ( BAE ) = m ( ECB ) F F AB AB E :VLBSEBLJ WFSJMFSF HÌSF m ( C%EB ) LBÀ EFSFDF- :VLBSEBLJWFSJMFSFHÌSF m ( % ) LBÀ EFSFDF- EFD EJS EJS \" # $ % & \" # $ % & 3. A B \"#$%LBSF D C \"#$%LBSF F \" ' $ & D EPóSVTBM K \" . , $ C EPóSVTBM |CE| = |AD| |DE| = |EF| L % = 28° M m ( KBC ) 28° % m ( LBA ) E = 17° :VLBSEBLJ WFSJMFSF HÌSF m (A%FD) LBÀ EFSFDF- 17° EJS AB \" # $ :VLBSEBLJWFSJMFSFHÌSF m ( K%LB )LBÀEFSFDF- EJS % & \" # $ % & 1. D 2. \" 3. \" 4. $ B D
TEST - 32 ,BSF 1. A D 4. #JS LBóEB CJS LFOBS CS PMBO CJS \"#$% LBSF- TJ ¿J[JOJ[ ,BSFOJO EõOEB [ DE ] m [ EC ] PMBDBL F õFLJMEF CJS & OPLUBT BMO[ &$ LFOBS Ð[FSJOEF LE [ AF ] m [ EC ]PMBDBLõFLJMEFCJS'OPLUBTBMO[ K C B | | | |ED =CSPMEVôVOBHÌSF \"' LBÀCJSJNEJS \" # $ % & \"#$%LBSF [ EF ] m [ BD ] [ LK ] m [ BD ] D C \"#$%LBSF | | | | | |KL + FK + FE =12 CS |DE| = |AE| | |:VLBSEBLJWFSJMFSFHÌSF #$ LBÀCJSJNEJS |FC| = |BF| | |AB = 4 3 CS \" # $ 4 2 D) 6 E) 6 2 EF 2. A B \"#$%LBSF , J¿ CËMHFEF CJS AB OPLUB K % % | |AK =CS m ( EDA ) m ( FCB ) | |KB =CS = = 30° | |KD =CS | |:VLBSEBLJWFSJMFSFHÌSF &' LBÀCJSJNEJS C A) 4^ 3 - 1 h B) 4 3 - 3 C) 4 3 - 2 D D) 4 3 - 1 E) 4 3 | | :VLBSEBLJWFSJMFSFHÌSF ,$ LBÀCJSJNEJS A) 6 B) 2 10 C) 3 5 D) 4 3 E) 5 2 ôFLJMEF LBSF õFLMJOEFLJ LºóU UBN PSUBTOEBO IFS BENEBBõBóEBWFSJMEJóJHJCJLBUMBOZPS 3. D C \"#$%LBSF [ DE ]B¿PSUBZ | |BC = 4 2 CS BEN BEN AE B ,BUMBOBOLºóUUBOBENEBCJSLBSFTFMCËMHFLFTJ- MJQ¿LBSMZPS%BIBTPOSBLBUMBOBOLºóUB¿MZPSWF | | :VLBSEBLJWFSJMFSFHÌSF BE LBÀCJSJNEJS BMBOOEBCS2B[BMNBPMEVóVHËSÐMÐZPS A) 4^ 2 - 2 h B) 4^ 2 + 2 h C) 8^ 2 - 1 h #VOBHÌSF LFTJMJQÀLBSUMBOLBSFOJOCJSLFOBS LBÀCJSJNEJS D) 8^ 2 + 1 h E) 2 A) 2 B) 2 2 C) 3 D) 3 2 E) 5 1. E 2. $ 3. $ 4. B \" $
,BSF F \"#$%LBSF 4. A TEST - 33 1. [ AF ] m [ FB ] B \"#$%LBSF A B [ AE ] m [ BE ] E | |FD =CS |BC| = |ED| | |BF =CS | |E AE =CS DC | | :VLBSEBLJWFSJMFSFHÌSF %$ LBÀCJSJNEJS DC A) 2 15 B) 8 C) 6 2 D) 4 5 & | | :VLBSEBLJWFSJMFSFHÌSF \"' LBÀCJSJNEJS \" # $ % & D C \"#$%LBSF [ DE ] m [ CE ] 2. A B \"#$%LBSF [ EF ] m [ AB ] # &WF%EPóSVTBM E E m ( B%AE ) = 30° | |AF =CS | |BE =CS | |FE =CS A FB | | :VLBSEBLJWFSJMFSFHÌSF #' LBÀCJSJNEJS A) 1 B) 2 $ % & DC | | :VLBSEBLJWFSJMFSFHÌSF \"& LBÀCJSJNEJS \"MJ\"OPLUBTOEBO#ZF )BLBOhEB$OPLUBTOEBO% A) 8 2 B) 8 C) 4 3 ZFFOLTBZPMMBSLVMMBOBSBLHJEFDFLUJS CK D) 4 2 & B M P 3. AB A E D F \"MJ\"OPLUBTOEBO )BLBO$OPLUBTOEBOBZOI[- DC MBSMBIBSFLFUFEJZPSMBS % | | | | õFLJMEFCÑUÑOLBSFMFSFöLBSFWF MP = 2. KM EAD | |\"#$%LBSF m =CS EJS\"MJhOJOEBLJLBEB\"EBO#ZFHJUUJôJOFHÌ- ( ) = 45° AB SF )BLBOBZOI[MB$EFO%ZFLBÀEBLJLEBHJ- EFS | |AE =CS 10 85 8 85 | | :VLBSEBLJWFSJMFSFHÌSF &$ LBÀCJSJNEJS A) B) 8 C) \" # $ % & 106 106 D) 6 5 85 E) 106 1. B 2. \" 3. B 77 4. D $ \"
TEST - 34 ,BSF 1. D C \"#$%LBSF 4. A B \" \"%$& =\" &#$ E | |DC =CS AE B D CF | | :VLBSEBLJWFSJMFSFHÌSF \"& LBÀCJSJNEJS | | | |\"#$%LBSF [ AF ] a [ BC ] = { E } AB = EC | |EF = 13 CS \" # $ % & :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- LBSFEJS \" # $ % & 2. D C \"#$%LBSF A B \"#$%LBSF | | | |F F |AE | |= EF| EB = GH | | | | DE = EC | |AB =CS E | | | | CF = EF G A^ & h =CS2 H FGH AB D EC :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- :VLBSEBLJWFSJMFSFHÌSF \" #'&$ LBÀCJSJNLB- LBSFEJS SFEJS \" # $ % & \" # $ % & \"#$% LBSFTJ õFLMJOEFLJ UBIUB QBS¿BTOB õFLJMEFLJ FõLFOBSпHFOUBIUBMBSNPOUFMFONJõUJS AB 3. A B \"#$%LBSF [ DE ]B¿PSUBZ | |CE = 4^ 2 - 1 hCS E DC :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- DC LBSFEJS 0MVöBO UBSBM CÌMHFOJO ÀFWSFTJ CS PMEVôVOB \" # $ % & HÌSF CBöMBOHÀUB LVMMBOMBO UBIUBOO BMBO LBÀ CJSJNLBSFEJS \" # $ % & 1. $ 2. D 3. D 4. \" B $
,BSF TEST - 35 1. A B \"#$%LBSF 4. A B \"#$%LBSF 'PSUBOPLUB E F [ AE ] m [ EF ] [ DE ] m [ AF ] E [ EF ] m [ FC ] F DE = 4 5 br D | |AE =CS DC | |FC =CS :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJN- | |C EF =CS LBSFEJS :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- LBSFEJS \" # $ % & \" # $ % & 2. A B G AE B F E DC F & \"#$%LBSF A^ AFD h = A ( ABCD ) :VLBSEBLJWFSJMFSFHÌSF GE PSBOLBÀUS AB DH C A) 1 2 1 1 1 G B) C) D) E) \"#$%LBSF &'($EJLEËSUHFO 3 2 3 4 | | | | | |EB = AE HG =CS 3. ôFLJMEFLJ \"#$% LBSFTJOEFO NBLBT ZBSENZMB :VLBSEBLJWFSJMFSFHÌSF \" &'($ LBÀCJSJNLB- SFEJS ,-./LBSFTFMCËMHFTJLFTJMJZPS \" # $ % & A LB K M DN C ,BMBOпHFOMFSCJSCJSJOFZBQõUSMBSBLZJOFCJSLBSF- \"MBO ^ 6 + 4 2 h CJSJNLBSF PMBO CJS \"#$% LBSFTJ- TFMCËMHFZBQMBCJMJZPS OJ¿J[JOJ[%$LFOBS [ BD ]LËõFHFOJJMF¿BLõBDBL ,-./CÌMHFTJOJOBMBO\"CS2PMEVôVOEB LBSF- õFLJMEF LBUMBOEóOEB $ OPLUBT , OPLUBTOB EFOL OJOCJSLFOBS 7 2 CSPMEVôVOBHÌSF \"LBÀCJ- HFMNFLUFEJS SJNLBSFEJS | | #VOBHÌSF KB LBÀCJSJNEJS \" # $ % & A) 1 B) 2 C) 3 D) 2 E) 2 2 1. D 2. $ 3. E 79 4. B E B
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr %&-50÷% TANIM ÖRNEK 2 A 2k 5BCBOMBSPSUBLJLJJLJ[LFOBSпHFOJOUBCBOMBS- 8 E OOCJSMFõNFTJZMFPMVõBOEËSUHFOFEFMUPJE de- OJS %m/*m 3k A |AB| = |AC| B 8C D | | | |BD = CD JTF | | | |\"#%пHFO \"#$&EFMUPJE AB = BC =CS | | | | AE = ED \"#%$EFMUPJEUJS | |:VLBSEBLJWFSJMFSFHÌSF $% LBÀCJSJNEJS B C \"#%$EFMUPJEJTF \"#$&EFMUPJEJOEF[BE]BÀPSUBZPMEVôVOEBO E D r [ AD ] m [ BC ] 8 BD = r [ AD ]B¿PSUBZ 2k 3k r |BE| = |EC| |BD | =CS r [ AD ]TJNFUSJFLTFOJ |$%| = 12 -=CSCVMVOVS r m ( A%BD ) = % m ( ACD ) ÖRNEK 1 \"#$%EFMUPJE ÖRNEK 3 4B A A a a |AB| = |AD| 4 E [ AC ]LËõFHFO 130° % ) = 110° E D m ( ABC B 110° 110° % m ( AEC ) = 130° a 20° D7 C \"#$%ZBNVL [ AB ] // [ DC ] C | | | | | |\"#&%EFMUPJE AB = BE =CS DC =CS :VLBSEBLJWFSJMFSFHÌSF m ( % ) LBÀEFSFDFEJS | |:VLBSEBLJWFSJMFSFHÌSF &$ LBÀCJSJNEJS ECD % % \"#&% EFMUPJEJOEF #% BÀPSUBZ WF \"#$% ZBNVL PMEV- ABC ADC m ( ) = m ( ) PMEVôVOEBO ôVOEBO =+ m ( E%CD ) % = m ( % ) EJS m ( BDC ) CBD m ( E%CD ) = 20°PMVS E&KF EF1JTBHPSUFPSFNJOEFO #%$JLJ[LFOBSÑÀHFOPMEVôVOEBO|%$| = |#$|EJS |&$| = 7 - 4 =CSCVMVOVS 1. 2. 4 3. 3
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 4 \"#$%EFMUPJE %FMUPJEEF\"MBO %m/*m A |BC| = |CD| A 16 16 | |BC =CS B6 6D 60° | |AB =CS 60° O % m ( BCO ) = 30° B C E 12 12 30° 30° C D | |:VLBSEBLJWFSJMFSFHÌSF \"0 LBÀCJSJNEJS \"#%$EFMUPJEWF[AD] a [BC] = {E} #$%FöLFOBSÑÀHFOJOEF|OD| =CSEJS r A^ ABCD h = 1 BC . AD 2 \"0%ÑÀHFOJOEF1JTBHPSUFPSFNJOEFO |\"0|2 +2 =2 |\"0|2 = 220 |\"0| = 2 55 CVMVOVS ÖRNEK 5 ÖRNEK 6 A \"#$%EFMUPJE D K F |AD| = |AB| AE C D B |ED| = |EC| |AF| = |FB| E | |AC =CS B | |BD =CS | | | |\"#$%EFMUPJE [ AC ] a [ BD ] = { E } AB = AD C | | | | | | | |AC + BD =CS AC 2 + BD 2 =CS2 | |:VLBSEBLJWFSJMFSFHÌSF &' LBÀCJSJNEJS :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJNLBSF- EJS , OPLUBT \"% LFOBSOO PSUB OPLUBT PMBDBL öFLJMEF BM- |\"$|+ |BD| 2 = |\"$|2 + 2.|\"$|.|BD| + |BD|2 OSTB[,'] // [BD]PMVSWF m ( % ) = 90° EJS FKE [,']WF[KE]PSUBUBCBOPMEVôVOEBO 121 =+ 2|\"$|. |BD| |KE| =CS |\"$|.|BD| = |,'|=CS A^ ABCD h = AC . BD 2 |&'|2 =2+2 = &,'ÑÀHFOJOEF1JTBHPSUFPSFNJO- den |&'| =CSCVMVOVS 2 = 14 br CVMVOVS 4. 2 55 10 14
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÖRNEK 7 \"#$%EFMUPJE ÖRNEK 9 D 43 |CD| = |CB| | | | | | | | |AB = AD WF BC = CD PMBDBLõFLJMEF\"#$%EFM- 4 % 6 C m ( BAD ) = 120° UPJEJOJ¿J[JOJ[[ AC ] a [ BD ] = { E }PMTVO#$LFOBSÐ[F- 33 43 SJOEF[ EF ] m [ BC ]PMBDBLõFLJMEFCJS'OPLUBTBMO[ | |BC = 43 CS A 60° 3 | | | | | |BF =CS FC =CSWF AE = 3 5 CSPMEVôVOB 60° K | |AB =CS HÌSF \"#$%EFMUPJEJOJOBMBOLBÀCJSJNLBSFEJS 33 6 B :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJNLBSFEJS &#$ÑÀHFOJOEF²LMJEUFP- A \"#$%EFMUPJEJOEF[$\"]BÀPSUBZPMEVôVOEBO SFNJOEFO |&$|2 = % 3 5 |&$| = 4 5 CS m ( DAC ) = 60° PMVS0MVöBOÑÀHFOEF|DK| = 3 3 CSEJS |BE|2 = 2.10 B 2 5 E 2 5 D |BE| = 2 5 CS %,$ÑÀHFOJOEF1JTBHPSUFPSFNJOEFO ^ 3 3 h2 + KC 2 = ^ 43 h2 2 F 45 A^ ABCD h = 7 5 .4 5 8 2 |,$| =CS C =CS2 CVMVOVS A^ ABCD h = 7.6 3 = 21 3 CS2 CVMVOVS 2 ÖRNEK 10 \"#$%EËSUHFO A ÖRNEK 8 m ( % ) 2 90° ABC D 6 C 13 13 | | | |AB = AD =CS 60° 60° Da B | | | |BC = CD =CS 45° 6 11 11 A ( ABCD ) =CS2 32 6 60° C 45° | |:VLBSEBLJWFSJMFSFHÌSF \"$ LBÀCJSJNEJS A 32 B | | | |\"#$%EFMUPJE [ DA ] m [AB ] AB = AD = 3 2 CS m ( % ) = a° PMTVO ADC % = 105° A^ ABCD h = 13.11. sin a ·2 =TJOa m ( ABC ) 2 TJOa = 132 :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJNLBSF- 12 - 5 EJS sin a = j cos a = 13 13 (a >PMEVôVOEBODPTaOFHBUJGUJS [DB]OÀJ[FSTFLPMVöBOÑÀHFOMFSEF & EFDPTJOÑTUFPSFNJ ADC \" \"#$% =\" %\"# +\" %#$ PMVS |\"$|2 = 132+ 112 + 2.13.11· 5 2 13 3 2 .3 2 + 6 . 3 = ^ 9 + 9 3 hbr2 CVMVOVS = 290 + 110 = 400 24 |\"$| =CSCVMVOVS 7. 21 3 9 + 9 3 9. 70 10. 20
Deltoid TEST - 36 1. A ABCD deltoid 4. A ABCD bir deltoid B |AB| = |AD| x |AB| = |AD| m ( A%DC ) = 115° B % = % E m (BAC) m (CAD) 5 D % = 80° | |BD = 24 br E m ( BEC ) D % = 90° m ( ABE ) | |EC = 5 br Ç ( ABCD ) = 66 br C C :VLBSEBLJ WFSJMFSF HÌSF m ( % ) kaç derece- | |:VLBSEBLJWFSJMFSFHÌSF AB kaç birimdir? BCE dir? A) 20 B) 18 C) 15 D) 13 E) 12 A) 60 B)65 C) 70 D) 75 E) 80 2. A ABCD deltoid 5. D 4 |BC| = |CD| A 2E |AB| = |BD| C B D % = 130° m ( ADC ) B | | | | | |ABCD deltoid, AD = AB , AE = 2 br | |DE = 4 br m ( A%DB ) = % m ( ACB ) C | |:VLBSEBLJWFSJMFSFHÌSF EC kaç birimdir? % A) 4 B) 5 C) 6 D) 7 E) 8 :VLBSEBLJWFSJMFSFHÌSF m ( BCD ) kaç derece- dir? A) 30 B) 36 C) 40 D) 45 E) 50 3. D 6. A ABCD deltoid [ EF ] m [ AD ] 32 [ EF ] // [ CD ] A C 10 8 I IAF = 8 br E B I IFD = 2 br F I IAB = 10 br 32 E 2 B D I IABCD deltoid, AC = 11 br, [AB] m [AD] C I I I IAD = AB = 3 2 br I I:VLBSEBLJWFSJMFSFHÌSF EC kaç birimdir? I I:VLBSEBLJWFSJMFSFHÌSF CD kaç birimdir? A) 6 B) 7 C) 8 D) 9 E) 10 A) 9 B) 8 C) 7 D) 6 E) 5 1. D 2. C 3. C 83 4. A 5. E 6. E
TEST - 37 Deltoid 1. D 6 C ABCD yamuk , 4. A ABCD deltoitd [ AB ] // [ DC ] 10 I IAB = 10 br BE F DEFC bir deltoid D I IBC = 12 br 12 3 I DCI = I CFI 2 2 = 172 br2 + AE I IB DC = 6 br AE CE I IFB = 3 br I I :VLBSEBLJWFSJMFSFHÌSF EB kaç birimdir? C A) 7 B) 8 C) 9 D) 10 E) 11 I I:VLBSEBLJWFSJMFSFHÌSF BE kaç birimdir? A) 8 B) 6 3 C) 5 3 D) 6 E) 4 3 2. A 4 B 4 5. A ABC üçgen C x F [AE] m [BD] D 11 E B D I I I IBE = ED = 6 br I IABCD bir deltoid, [AB] // [DE], DE = 11 br 6 6 I IDC = 3 br I I I IAB = BC = 4 br E I IEC = 8 br I I :VLBSEBLJWFSJMFSFHÌSF CE = x kaç birimdir? 8 A) 7 B) 6 C) 5 D) 4 E) 3 C 3. D I I:VLBSEBLJWFSJMFSFHÌSF AE kaç birimdir? 1 A) 4 6 B) 8 5 C) 12 3 KL D) 2 30 E) 2 15 2 AC 6. A ABCD deltoid 6 K E IAEI = IEBI M N B ICFI = IFDI 2 IBKI = IKDI D I IEF = 10 br B BD = 2 2 br ABCD deltoid, [CK] m [DA], [AL] m [DC] F I I I I[CM] m [AB], [AN] m [BC], DA = DC I I I I I I I IKD = 1 cm, LC = MB = 2 cm, CN = 6 cm C KL I I:VLBSEBLJWFSJMFSFHÌSF AC kaç birimdir? :VLBSEBLJWFSJMFSFHÌSF oranLBÀUS MN 4 3 8 7 A) 5 2 B) 7 2 C) 10 2 A) B) C) D) E) 2 D) 12 2 E) 14 2 3 2 3 3 1. C 2. A 3. A 84 4. D 5. E 6. E
Deltoid TEST - 38 1. D 4. A ABCD deltoid 13 20 43 m % = 150° A 24 B 150° (ABC) C 43 AB = AD = 4 3 br D AC = 2 39 br 13 20 B I I I I I IABCD deltoid, AB = AD = 13 br, DB = 24 br C I I I IBC = DC = 20 br :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- karedir? karedir? A) 20 3 B) 18 3 C) 16 3 A) 238 B) 242 C) 246 D) 248 E) 252 D) 12 3 E) 8 3 2. A ABCD deltoid 5. A ABCD deltoid E I AEI = 3.I ECI IABI = IADI B A ( BEC ) = 2 br2 T I ATI = 3.I TDI D I CKI = 3.I KDI D CP = 3. PB I I I IB PK C I IKT = 5 br C I IPT = 61 br :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- karedir? :VLBSEBLJ WFSJMFSF HÌSF \" \"#$ LBÀ CJSJNLB- redir? A) 8 B) 10 C) 12 D) 14 E) 16 A) 44 B) 42 C) 40 D) 36 E) 34 3. A ABCD deltoid 6. A ABCD deltoid BE IADI = IABI [BC] m [DC] 15° IBCI = ICDI IBAI = IBCI I I I IB D [AB] m [BC] O D DA = DC AC = 4 2 br I BDI = 2.I BCI m % = 15° I IC BO = 3 br (BCA) C :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- karedir? :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- karedir? A) 12 B) 12 3 C) 16 A) 10 B) 8 C) 6 D) 4 E) 2 D) 16 3 E) 24 3 1. E 2. E 3. B 85 4. D 5. C 6. B
KARMA TEST - 1 Çokgenler ve Dörtgenler 1. B 4. D C ABCD kare A | |DP = 2 br C 21 | |CP = 1 br P | |BP = 2 br D 2 K E AB F \" # $ % & 'EÐ[HÐOCJS¿PLHFOJOBSEõLLË- | | :VLBSEBLJWFSJMFSFHÌSF BC kaç birimdir? õFMFSJ [ BK ] a [ FK ] = {K}, m ( % ) = 1 44° BKF A) 5 B) 7 C) 2 2 :VLBSEBLJWFSJMFSFHÌSF CVÀPLHFOJOLFOBSTB- D) 10 E) 2 3 ZTLBÀUS A) 20 B) 24 C) 27 D) 30 E) 32 5. D ABCD yamuk C [AB] // [DC] 2. A K B 4 [EF] // [DA] L E 2 [DE] m [EF] DC | CE| = 2| EB| | | | |A F B ABCD paralelkenar , [ KL ] m [ AB ], DC = 4 FB % % DCA ACB | |DE = 12 br | | | |m = | |EF = 5 br ( ) m ( ), AB = 6 br, AL = 4 br | |LC = 2 br :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- karedir? & :VLBSEBLJWFSJMFSFHÌSF A^ AKL h kaç birimka- A) 200 B) 180 C) 169 D) 165 E) 145 redir? A) 2 B) 2 3 C) 4 D) 4 3 E) 6 6. A L 3. B P C 25° E D E D 15° K C AB | | | |\"%$&CJSEJLEËSUHFO AB = % = 25° DE , m ( BAD ) | |ABCD ve \",-1EJLEËSUHFOMFSJFõ EC = 2 br | | | |DE = 7 br, BC = 6 br % = 15° | |:VLBSEBLJWFSJMFSFHÌSF EL kaç birimdir? m ( BCD ) :VLBSEBLJWFSJMFSFHÌSF m ( % ) kaç derece- AED dir? A) 5 B) 4 C) 3 D) 2 E) 1 A) 30 B) 35 C) 40 D) 45 E) 50 1. D 2. B 3. B 86 4. A 5. D 6. B
Çokgenler ve Dörtgenler KARMA TEST - 2 1. E D 4. D C ABCD bir kare F4 A 15° m ( B%CE ) = 15° 60° FC 3 m % = 60° (CEF) E K | |FE = 3 br B A 6B | |CE = 4 br L | |AB = 3 6 br | |\"#$%&'EÐ[HÐOBMUHFO#-,$LBSF AB = 6 br | | :VLBSEBLJWFSJMFSFHÌSF AF kaç birimdir? & A) 3 3 B) 3 5 C) 5 :VLBSEBLJWFSJMFSFHÌSF A^ ACK h kaç birimka- D) 6 E) 7 redir? A) 21 B) 24 C) 27 D) 30 E) 36 2. D C 5. 1 A2 F D E 4 E O AB | | | | | |ABCD paralelkenar, ED = 1 br, EB = BC BC & A_ ABE i = 3 % A_ EBCD i 5 m ( EBC ) = 90° , | | :VLBSEBLJWFSJMFSFHÌSF AB kaç birimdir? ABCD dik yamuk, [ AB ] & OPLUBTOEB [ BC ], C OPLUBTOEB0NFSLF[MJ¿FNCFSFUFóFU [AD] // [ BC ] A) 5 B) 6 C) 7 D) 8 E) 9 | | | |[AB] m [BC], AE = 4 br , AF = 2 br 3. D F C :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- karedir? E GK H A) 45 B) 54 109 117 C) D) E) 60 22 AB \"#$%EJLEËSUHFO & = 4 br2 A^ FGK h Aa & k = 13 br2 , & = 10 br2 6. &OV[VOLFOBSDNPMBOCJSZBNVôVOEJôFS BKC A^ AHB h UÑN LFOBS V[VOMVLMBS CJSCJSJOF FöJUUJS #V ZB- & :VLBSEBLJWFSJMFSFHÌSF A^ EHG h kaç birimka- NVôVOÀFWSFTJDNPMEVôVOBHÌSF BMBOLBÀ cm2 dir? redir? A) 1 B) 2 C) 3 D) 4 E) 5 A) 13 B) 26 C) 30 D) 32 E) 36 1. C 2. A 3. A 87 4. E 5. D 6. D
KARMA TEST - 3 Çokgenler ve Dörtgenler 1. B 4. A KB ABCD paralelkenar // CA // [DK] m [KL] 3 3 [KM] m [DL] G D M L D 36° | |BL = 3 br 6 | |LC = 6 br | |KM = 3 br E C F & ABCDEF...... düzgün çokgen, maD%GFk = 36° :VLBSEBLJWFSJMFSFHÌSF A^ KDL h kaç birimka- redir? :VLBSEBLJWFSJMFSFHÌSF CVÀPLHFOLBÀLFOBS- MES A) 6 B) 9 C) 12 D) 18 E) 24 5. D C A) 12 B) 15 C) 18 D) 20 E) 24 | |2. ABCD bir yamuk, [AD] // [BC], BD = 24 br H | |AC = 10 br, [AD] ve [BC]OJOPSUBOPLUBMBSTSBT | |ile E ve F, EF = 13 br dir. A BE :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- ABCD ikizkenar yamuk [AB] // [DC], [BH] m [DE] karedir? | | | | | |AC = BE = 2. BH = 8 br A) 100 B) 110 C) 120 D) 130 E) 150 :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- 3. ôFLJM- EFLJ \"#$% EJLEËSUHFOJOEF [AB] LFOBS karedir? [BD] LËõFHFOJ Ð[FSJOF HFMFDFL CJ¿JNEF LBUMBOZPS A) 16 B) 16 3 C) 32 WFõFLJM-2 elde ediliyor. AD D) 32 3 E) 64 6. C ABCD deltoid 120° |CD| = |CB| B C % = 120° ôFLJM D m ( DCB ) E D B |AD| = |DE| 8 30° m ( A%DE ) = 30° A' F A E AD =3 B C ôFLJM DC AE | | | | | |A' E =CSPMEVôVOBHÌSF BC - DE GBSL :VLBSEBLJWFSJMFSFHÌSF PSBOLBÀUS kaç birimdir? BE A) 10 B) 8 C) 6 D) 4 E) 2 23 A) 1 B) 2 C) 3 D) E) 23 1. B 2. C 3. B 88 4. D 5. B 6. A
Çokgenler ve Dörtgenler KARMA TEST - 4 1. D C 4. D C G F A3 E 2B A EB % \"#$% CJS FõLFOBS EËSUHFO [DB] LËõFHFO [DE] ABCD paralelkenar, m ( DEG ) = 90° | | | |B¿PSUBZ, AE = 3 br, EB = 2 br % % :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCS2 dir? EDF FDG | | | |mak ma k = , AE = EB 80 2 | | | | | | | | | |EF = 3 br, BG = GC , ED + DG = 16 br C) A) 35 B) 25 2 9 :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- D) 50 100 2 karedir? E) 9 A) 40 B) 48 C) 56 D) 64 E) 72 2. ôFLJMEFLJ\"#$%EJLEËSUHFOJFõUVóMBEBOPMVõVZPS DC 5. D 10 C 6 AB A EB Çevre ( ABCD ) = 92 br dir. ôFLJMEF[DC] ZBSN¿FNCFSJO¿BQ :VLBSEBLJ WFSJMFSF HÌSF Fö EJLEÌSUHFOMFSEFO | | | |ABCD paralelkenar, DC = 10 br, AD = 6 br biSJOJOÀFWSFTJLBÀCJSJNEJS #VOBHÌSF \" \"#$% LBÀCJSJNLBSFEJS A) 24 B) 28 C) 32 D) 36 E) 40 3. D C ABCD kare A) 40 B) 45 C) 48 D) 50 E) 54 |EF| = |BF| E A FB 6. ,FOBSV[VOMVLMBSCSWFCSPMBOCJSEJLEËSUHFO :VLBSEBLJWFSJMFSFHÌSF m ( A%DF ) kaç derece- CJ¿JNJOEFLJCJSLBóUIFSIBOHJCJSLËõFHFOJOEFOCÐ- dir? LÐMFSFL JLJZF LBUMBOZPS WF UFL LBU LBMBO LTNMBS LFTJMJZPSWFLBóUUFLSBSB¿MZPS 0MVöBOöFLMJOBMBOLBÀCJSJNLBSFEJS 75 B) 38 77 79 81 A) C) D) E) A) 10 B) 15 C) 20 D) 30 E) 40 2 22 2 1. E 2. C 3. D 89 4. D 5. C 6. A
KARMA TEST - 5 Çokgenler ve Dörtgenler 1. D C ABCD dikEËSUHFO | |4. Bir ABC üçgeninde m(WA) = 90°, AB = 6 br | |AC = CS пHFOJO EõOB EPóSV BDEC karesi x [ DE ] m [ EL ] PMVõUVSVMVZPS'OPLUBTLBSFOJONFSLF[JEJS A3 E 5 | |:VLBSEBLJWFSJMFSFHÌSF AF kaç birimdir? | | | |AE = BL = 3 br A) 6 2 B) 7 2 C) 8 2 D) 9 2 E) 10 2 L | |3 CL = 5 br B | | :VLBSEBLJWFSJMFSFHÌSF EC kaç birimdir? A) 10 B) 6 3 C) 4 7 B D) 8 2 E) 12 5. ABCD deltoid H |BC| = |CD| A 15° 4 K 75° C [AC] ve [BD] N LËõFHFOMFS 2. D E C [HD] m [AB] D F % = 15° m ( % ) = 75° \" ,WF$EPóru- m(DAC) BCA | |sal, HK = 4 br AB :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- karedir? [ BE ]B¿PSUBZ [AC] m [CB], [CD] m [AD], A) 64 B) 60 C) 56 D) 52 E) 48 | | | |[DA] m [AB], AF = 5 br, FC = 3 br | | :VLBSEBLJWFSJMFSFHÌSF DE kaç birimdir? 6. ôFLJMEFLJ\"#$%QBSBMFMLFOBSOEB [AC] ve [DB]LË- A) 0,4 B) 0,5 C) 0,6 D) 0,8 E) 1 õFHFOMFSJ0OPLUBTOEBLFTJõNFLUFEJS AB 3. D 6 P3C ABCD, ATLE ve O F FCPK birer kare E 5 K E L F | |ED = 5 br | |DP = 6 br | |PC = 3 br DC A TB [AC] a [DF] = {E}, CF = 3 :VLBSEBLJWFSJMFSFHÌSF \" 5#',- LBÀCJSJN- BC 5 karedir? & A_ DEO i :VLBSEBLJWFSJMFSFHÌSF & PSBOLBÀUS? A_ EFC i A) 26 B) 27 C) 28 D) 29 E) 30 5 5 5 7 6 A) B) C) D) E) 8 7 9 9 7 1. D 2. A 3. C 90 4. B 5. A 6. C
Çokgenler ve Dörtgenler KARMA TEST - 6 1. E ABCD yamuk 4. \"#$ пHFOJOEF \" B¿TOO J¿ B¿PSUBZ [BC] yi D 5 C [ AB ] // [ CD ] OPLUBTOEBLFTNFLUFEJS K // F |CF| = |FB| | | | | | |AC - AB = BD ve m % ) = 60° D // (BAC 8 [ AE ] m [ FE ] B PMEVôVOBHÌSF m ( % ) kaç derecedir? A | |AD = 8 br ADC A) 90 B) 100 C) 110 D) 120 E) 130 | |EK = 5 br, A ( ABCD ) = 88 br2 | | :VLBSEBLJWFSJMFSFHÌSF ,' = x kaç birimdir? A) 7 B) 6,5 C) 6 D) 5,5 E) 5 5. A 10 2. ôFLJMEFLJ \"#$% EJLEËSUHFOJOEF [AC] LËõFHFOJ & 10 8 D WF'OPLUBMBSZMBпFõQBS¿BZBBZSMNõUS E m AB 9 // B E // n F // C D KC | | | |ABCD konveks CJSEËSUHFO AB = AD = 10 br | | | | | |DK = KC , [BF] m [AC], BC = 2 3 br | |:VLBSEBLJWFSJMFSFHÌSF &, kaç birimdir? | | | |% A) 3 2 B) 2 3 C) 2 3 D) 6 E) 3 m(ACB) = m ( B%DA ), AE = 8, BE = 9 br :VLBSEBLJWFSJMFSFHÌSF m PSBOLBÀUS n 4 5 3 9 9 A) B) C) D) E) 9 9 4 5 4 3. ôFLJMEFLJ \"#$%&' EÐ[HÐO BMUHFOJO NFSLF[J , OPLUBTES AB P S3 FK C 6. A B ABCD kare S1 S2 // K [EB] m [KC] EHD 7 E |AE| = |ED| // | |KD = 7 br S1, S2 ve S3J¿JOEFCVMVOEVLMBSLBQBMCËMHFMFSJO DC | | | |BMBOMBS [ KH ] m [ DE ], 3. AP = PF , S3 = 18 br2 :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJN- karedir? :VLBSEBLJ WFSJMFSF HÌSF 41 + 42 UPQMBN LBÀ birimkaredir? A) 44 B) 40 C) 36 D) 30 E) 28 A) 25 B) 27 C) 32 D) 36 E) 49 1. C 2. C 3. D 91 4. C 5. A 6. E
KARMA TEST - 7 Çokgenler ve Dörtgenler DE 1. C ABCD ... 4. A B D düzgün onikigen 4 | |A x E BD = 4 br F K | |:VLBSEBLJWFSJMFSFHÌSF AE kaç birimdir? BC A) 4 2 B) 4 3 C) 7 | | | |ABCD kare, BK = DE :VLBSEBLJWFSJMFSFHÌSF m ( A%KE ) kaç derece- dir? A) 150 B) 135 C) 120 D) 112,5 E) 105 D) 8 E) 12 2. A D 10° 120° 5. #JS LºóEB CJS \"#$% QBSBMFMLFOBS ¿J[JMJZPS %BIB E TPOSBQBSBMFMLFOBSOEõOEBCJS,OPLUBTBMOZPS BC [AK] a [DC] = { M }, [BK] a [DC] = {N}BMOQ%,$ | | | | | | | |ABCD paralelkenar, AE = BC , DE = AB ve ABK üçgenleri çiziliyor. % = 120° , % = 10° & = 20 br2 & = 9 br2PMEVôV- m(BCD) m(CDE) A^ ABK h WF A^ DKC h % OBHÌSF \" \"#$% LBÀCJSJNLBSFEJS CEA :VLBSEBLJWFSJMFSFHÌSF m ( ) BÀTLBç de- recedir? A) 18 B) 19 C) 20 D) 22 E) 24 A) 5 B) 10 C) 15 D) 17 E) 18 3. E [ KE ] m [ EA ] 6. #JSLºóEB\"#$%QBSBMFMLFOBS¿J[JMJZPS%BIBTPO- DF C ra %$LFOBSWF#$LFOBSÐ[FSJOEFTSBTZMB,WF | |CK = 5 br -OPLUBMBSOBMO[ [LK] m [ BC ], [ BL ]B¿PSUBZ 5 | | | |LA = 12 br, LK = 6 br dir. | |BK = 4 br K | |4 AB = 26 br A 26 | |B CD = 14 br :VLBSEBLJWFSJMFSFHÌSF m ( % ) kaç derece- DLA | |:VLBSEBLJWFSJMFSFHÌSF &, kaç birimdir? dir? A) 52 B) 54 C) 56 D) 12 E) 62 A) 75 B) 60 C) 45 D) 30 E) 15 5 5 5 5 1. B 2. C 3. E 92 4. E 5. D 6. D
Çokgenler ve Dörtgenler KARMA TEST - 8 1. A B 4. D G C F FH E AE B DC ABCD paralelkenar, [ BG ] ve [ CE ]B¿PSUBZ ABCD ikizkenar yamuk, [DF] m [AC], [BE] m [AC] | | | |[ FH ] m [ BC ], HC = 2 br, BC = 10 br | |DC = 20 br | | | | | |DF = 8 br, EB = 4 br, FE = 5 br % m ( ACD ) = 22, 5° :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJNLB- redir? :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- karedir? A) 140 B) 150 C) 152 D) 158 E) 160 A) 35 2 75 2 C) 42 2 B) 2 169 2 85 2 5. A E B ABCD D) E) EJLEËSUHFO D 4 2 F | DE| = 3|EF | | |EB = 2 br 2. C ABCD dik yamuk C B m % = % ) ( DEC ) 2.m ( AEB A | |AB = 2br | |AD = 10 br | |DC = 8 br DEF üçgeni [ DF ]CPZVODBLBUMBOODB%'$пHFOJ ED elde ediliyor. | | :VLBSEBLJWFSJMFSFHÌSF CE kaç birimdir? | | :VLBSEBLJWFSJMFSFHÌSF DC kaç birimdir? A) 9 B) 10 C) 12 D) 15 E) 20 A) 8 B) 9 C) 10 E) 12 E) 15 3. D KL . C 6. A 12 B ABCD M 6 EJLEËSUHFO D |BF| = |FC| G F AE GB |DE| = |EC| | | | | | | | |ABCD paralelkenar, 5. KL = DC , AB = 2. EG | |AD = 6 br A^ & h = 25 br2 EC EMG | |AB = 12 br :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJNLB- | | | | :VLBSEBLJWFSJMFSFHÌSF GE 2 + GF 2UPQMBN redir? kaç birimkaredir? A) 140 B) 138 C) 135 D) 130 E) 120 A) 25 B) 30 C) 35 D) 40 E) 45 1. D 2. B 3. A 93 4. E 5. C 6. A
<(1m1(6m/6258/$5 Çokgenler ve Dörtgenler 1. &õJU V[VOMVLUB EËSU UBIUB QBS¿BT CJSCJSJOF NPOUF 2. .FUFIBO JMF (ÐOEÐ[ BSBMBSOEB CJS PZVO PZOVZPS- FEJMFSFLõFLJM*EFLJLBSFFMEFFEJMFSFLEVWBSBNPO- MBS .FUFIBO \"#$% LBSFTJ õFLMJOEFLJ UBIUBOO FU- UFMFONJõUJS SBGOB CFMJSUJMFO ZËOEF CS V[VOMVóVOEB CJS UF- MJHFSHJOõFLJMEFTBSZPS5FMJOVDVOVOHFMEJóJOPL- AB UBZ , JMF JTJNMFOEJSJMJZPS (ÐOEÐ[ JTF .FUFIBO JMF [UZËOEFCSV[VOMVóVOEBCJSUFMJHFSHJOõFLJMEF TBSQ UFMJOV¿OPLUBTO.JMFJTJNMFOEJSJMJZPS AB D C DC ôFLJM–* B A 5BIUBOOÀFWSFTJCSPMEVôVOBHÌSF ,JMF. OPLUBMBSBSBTV[BLMLLBÀCJSJNEJS A) 9 2 B) 10 2 $ 4 13 D) & D 3. 4FMJO BõBóEBLJ ZBNVL õFLMJOEFLJ UBIUBOO CFMJSUJ- C MFOOPLUBTOBMB[FSUVUBSBL\"#LFOBSOOHËMHFTJOJ PMVõUVSVZPS ôFLJM-** CB # WF $ OPLUBMBSOEBLJ SBQUJZFMFS ¿LUóOEBO õFLJM **EFLJFõLFOBSEËSUHFONFZEBOBHFMNJõUJS#WF$ OPLUBMBSOOZFSEFOZÐLTFLMJóJCSB[BMNõUS #BöMBOHÀUBLJ LBSFOJO ÀFWSFTJ CS PMEVôVOB HÌSF JMLEVSVNEBLJWFTPOEVSVNEBLJDJTJNMF- SJOBMBOMBSPSBOLBÀPMBCJMJS \" # 4 $ 5 D) 2 E) 8 DA 3 3 3 | | | | | | | |AB =CS %$ =CS AD =CS #$ =CS PMEVôVOB HÌSF \"# LFOBSOO HÌMHFTJOJO CPZV %$LFOBSLBEBSPMEVôVBOEBLJVÀOPLUBTJMF# OPLUBTBSBTOEBLJV[BLMLLBÀCJSJNEJS A) 212 B) 42 $ 206 5 5 D) 41 E) 2 10 1. C 94 2. C 3. \"
Çokgenler ve Dörtgenler <(1m1(6m/6258/$5 1. \"MQFSEÐ[HÐOBMUHFOõFLMJOEFLJNBTBOO¿FWSFTJOJ 3. \"#$%EJLZBNVóVCFMJSUJMFOZËOEF\"#LFOBSUBCB- IFTBQMBNBLJ¿JOCJSCJSJOFEJLUBIUBZõFLJMEFLJHJ- OBEFóFDFLCJ¿JNEFEËOEÐSÐMÐZPS bi birbirine çiviliyor. BC AB K FC AD L | | | | | |CD =CS AD =CSWF AB = 16 br ol- ED EVôVOBHÌSF $OPLUBTJMFZBNVôVOEÌOEÑSÑM- ',LBMBTOOCPZVCS ,-LBMBTOOCPZVCSWF NFTJTPOVDVPMVöBO$OJOCVMVOEVôVZFOJOPL- -$LBMBTOOCPZVCSEJS UBBSBTOEBLJV[BLMLLBÀCJSJNEJS #VOBHÌSF NBTBOOÀFWSFTJLBÀCJSJNEJS A) 20 2 B) 12 5 C) 8 10 D) 10 6 E) 24 A) 42 B) 45 C) 48 D) 51 E) 58 4. ôFLJM * EF WFSJMFO \"#$% QBSBMFMLFOBS õFLMJOEFLJ LVNBõQBS¿BT[BD] boyunca kesiliyor. 2. \"õBóEB WFSJMFO EJLEËSUHFOMFS õFLJMEFLJ HJCJ LFTJM- A BA B NJõUJS * * DC DB ôFLJM* ** ** DC %BIBTPOSB*QBS¿B\"OPLUBT$OPLUBTOB%OPL- UBT#OPLUBTOBLBSõMLHFMFDFLõFLJMEFEJLJMJQ *** &#%$EËSUHFOJôFLJM**EFLJHJCJFMEFFEJMJZPS B :VLBSEBLJ WFSJMFSF HÌSF DJTJNMFSJO ÀFWSFMFSJ DC OBTMEFôJöJS I II III ôFLJM** E A) \"[BMS Artar Artar B) \"[BMS %FóJõNF[ Artar | | | |% C) Artar %FóJõNF[ Artar D) Artar Artar \"[BMS m ( DCA ) = 120°, DC = 10 br, BC = 6 br E) Artar Artar Artar | | :VLBSEBLJWFSJMFSFHÌSF BD kaç birimdir? A) 12 B) 14 C) 15 D) 16 E) 18 1. D 2. D 95 3. A 4. B
<(1m1(6m/6258/$5 Çokgenler ve Dörtgenler 1. A B 3. ôFLJM * EF WFSJMFO Ë[EFõ \"#$% WF ,-./ LBSFTJ E õFLMJOEFLJUBCMPMBSõFLJM**EFLJHJCJ$WF.LËõFMFSJ G ÐTUÐTUFHFMFDFLõFLJMEFEVWBSBNPOUFFEJMEJóJOEF JLJUBCMPCJSCJSJOJUBNBNMBZBSBLZFOJCJSUBCMPPMVõV- ZPS A D FC BD \"#$%LBSFTJõFLMJOEFLJLBSUPOEB C K | | | |[ AF ] a [ DE ] = { G } DF = FC & & & LN A^ AGD h = 2 br2 ve A^ AGE h + A^ DGF h = 17 br2 M EJS ôFLJM* :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- LBSFEJS? A) 28 B) 30 C) 32 D) 34 E) 36 2. ôFLJMEF\"#$%EJLEËSUHFOJOJO%$LFOBSZBZOHF- A FK SJMNFEFOËODFLJJQJEJS%$ZBZOOV[VOMVóV DNEJS L B AD D F DN E N C M ôFLJM** B DN C | | | |õFLJM**EF LF = '% =CSWFm(L%FD) = 120° PMEVôVOB HÌSF # JMF / LÌöFMFSJ BSBT V[BLML LBÀCSEJS A) 50 B) 50 3 C) 60 :BZPLJMFõFLJMEFHËTUFSJMEJóJHJCJHFSJMEJóJOEF D) 60 3 E) 120 | | | | | |AF =DN EF =DN BC =DNPMV- ZPS :VLBSEBLJWFSJMFSFHÌSF PLJMFHFSJMNJöIBMEFLJ JQJOV[VOMVôV JMLV[VOMVôVOVOLBÀLBUES A) 1 B) 3 C) 1 D) 3 E) 2 2 42 1. A 2. E 96 3. C
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