8. Sınıf Öğreniyorum Serisi Matematik Soru Bankası

["Uyguluyorum \u00dc\u00e7gende Yard\u0131mc\u0131 Elemanlar Test 68 1. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerden hangisinde k\u0131rm\u0131z\u0131 renk 3. ile \u00e7izilmi\u015f olan do\u011fru par\u00e7as\u0131 \u00fc\u00e7genin herhangi A bir kenar\u0131na ait y\u00fckseklik de\u011fildir? A) B) B K L MN C C) D) Yukar\u0131daki birimkareli k\u00e2\u011f\u0131tta verilen ABC \u00fc\u00e7ge- ninde BC kenar\u0131na ait olan kenarortay hangi nok- tadan ge\u00e7er? A) K B) L C) M D) N 4. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerden hangisinde \u00fc\u00e7genin her- hangi bir kenar\u0131na ait y\u00fckseklik \u00fc\u00e7genin d\u0131\u015f b\u00f6l- gesinde bulunabilir? 2. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerden hangisinde mavi renk ile A) Dar a\u00e7\u0131l\u0131 \u00fc\u00e7gen B) Dik a\u00e7\u0131l\u0131 \u00fc\u00e7gen \u00e7izilmi\u015f olan do\u011fru par\u00e7as\u0131 kesinlikle A a\u00e7\u0131s\u0131na C) E\u015fkenar \u00fc\u00e7gen D) \u0130kizkenar \u00fc\u00e7gen ait a\u00e7\u0131ortayd\u0131r? A) A B) A 5. K B CB C A C B C) C D) A C D A LM B Yukar\u0131daki noktal\u0131 k\u00e2\u011f\u0131tta verilen KLM \u00fc\u00e7geninde B L a\u00e7\u0131s\u0131na ait olan a\u00e7\u0131ortay hangi noktadan ge\u00e7er? A) A B) B C) C D) D 300 8. S\u0131n\u0131f","Test \u00dc\u00e7gende Yard\u0131mc\u0131 Elemanlar Uyguluyorum 68 6. Bir dik \u00fc\u00e7genin t\u00fcm kenarlar\u0131na ait y\u00fckseklikler 9. K nerede kesi\u015fir? LM A) \u00dc\u00e7genin d\u0131\u015f b\u00f6lgesinde B) \u00dc\u00e7genin i\u00e7 b\u00f6lgesinde Yukar\u0131da KLM \u00fc\u00e7geni bi\u00e7imindeki kartonun KL C) En uzun kenar\u0131n \u00fczerinde kenar\u0131 KM kenar\u0131 \u00fczerine \u00fcst \u00fcste gelecek bi\u00e7im- D) Dik a\u00e7\u0131n\u0131n k\u00f6\u015fesinde de katland\u0131\u011f\u0131nda olu\u015fan kat izi a\u015fa\u011f\u0131dakilerden hangisini ifade eder? 7. A\u015fa\u011f\u0131da birim kareli zemin \u00fczerinde verilen ABC A) K a\u00e7\u0131s\u0131na ait a\u00e7\u0131ortay \u00fc\u00e7genlerinden hangisinde, BC kenar\u0131na ait y\u00fck- B) L a\u00e7\u0131s\u0131na ait a\u00e7\u0131ortay C) LM kenar\u0131na ait kenarortay sekli\u011fin uzunlu\u011fu di\u011ferlerinden farkl\u0131d\u0131r? D) LM kenar\u0131na ait y\u00fckseklik A) A B) B B C C 10. A\u015fa\u011f\u0131daki DEF\u2206 , alan\u0131 16 br2 olan e\u015f karelerle olu\u015ftu- C) A A A rulmu\u015f zemin \u00fczerine \u00e7izilmi\u015ftir. B D) B D C F C E Buna g\u00f6re DEF \u00fc\u00e7geninde DE kenar\u0131na ait y\u00fck- seklik ka\u00e7 birimdir? A) 12 B) 14 C) 16 D) 18 8. I. E\u015fkenar \u00fc\u00e7gende bir kenara ait olan kenarortay ayn\u0131 zamanda y\u00fckseklik ve a\u00e7\u0131ortayd\u0131r. II. \u0130kizkenar \u00fc\u00e7gende tepe noktas\u0131na ait olan a\u00e7\u0131or- 11. Bir ABC \u00e7e\u015fitkenar \u00fc\u00e7geninde AB kenar\u0131 AC kenar\u0131- tay ayn\u0131 zamanda kenarortay ve y\u00fcksekliktir. n\u0131n \u00fczerine gelecek bi\u00e7imde katlan\u0131p tekrar a\u00e7\u0131l\u0131yor. III. Herhangi bir \u00fc\u00e7genin t\u00fcm a\u00e7\u0131lar\u0131na ait olan i\u00e7 Buna g\u00f6re olu\u015fan kat izi a\u015fa\u011f\u0131dakilerden hangi- a\u00e7\u0131ortaylar\u0131 \u00fc\u00e7genin i\u00e7 b\u00f6lgesinde kesi\u015fir. sini ifade eder? Yukar\u0131daki ifadelerden hangileri do\u011frudur? A) B a\u00e7\u0131s\u0131na ait a\u00e7\u0131ortay B) A a\u00e7\u0131s\u0131na ait a\u00e7\u0131ortay A) I ve II. B) I ve III. C) BC kenar\u0131na ait y\u00fckseklik C) II ve III. D) I, II ve III. D) AB kenar\u0131na ait y\u00fckseklik 8. S\u0131n\u0131f 301","Uyguluyorum \u00dc\u00e7gende Yard\u0131mc\u0131 Elemanlar Test 69 1. A\u015fa\u011f\u0131da kareli zeminde verilen ABC \u00fc\u00e7genlerin- 3. A\u015fa\u011f\u0131daki \u015fekilde |KL| = |KM| ve [KN] a\u00e7\u0131ortayd\u0131r. den hangisinde BC kenar\u0131na ait y\u00fckseklik ayn\u0131 K zamanda a\u00e7\u0131ortayd\u0131r? A) A B) C B L (4x+2)cm N M (3x+11)cm CA B C) B Buna g\u00f6re |LM| ka\u00e7 santimetredir? C D) A C A) 76 B) 78 C) 80 D) 82 A B 4. A D EF G C 55\u00b0 45\u00b0 20\u00b0 10\u00b0 20\u00b0 10\u00b0 2. K B 52\u00b0 \u015eekilde ABC a\u00e7\u0131s\u0131na ait a\u00e7\u0131ortay a\u015fa\u011f\u0131dakilerden N hangisidir? ? A) [BD] B) [BE] C) [BF] D) [BG] M L 5. Derece cinsinden i\u00e7 a\u00e7\u0131lar\u0131n\u0131n \u00f6l\u00e7\u00fcs\u00fc do\u011fal say\u0131 olan bir \u00fc\u00e7gende bir kenara ait olan y\u00fckseklik, ayn\u0131 za- manda a\u00e7\u0131ortayd\u0131r. Yukar\u0131daki \u015fekilde m(LNM\u2211 ) ka\u00e7 derecedir? Buna g\u00f6re bu a\u00e7\u0131ortay\u0131n ait oldu\u011fu a\u00e7\u0131n\u0131n \u00f6l\u00e7\u00fcs\u00fc a\u015fa\u011f\u0131dakilerden hangisi olamaz? A) 118 B) 116 C) 114 D) 112 A) 38\u00b0 B) 46\u00b0 C) 71\u00b0 D) 96\u00b0 302 8. S\u0131n\u0131f","Test \u00dc\u00e7gende Yard\u0131mc\u0131 Elemanlar Uyguluyorum 69 8. A\u015fa\u011f\u0131daki KLM \u00fc\u00e7geninde [KN] y\u00fckseklik, [KP] ise 6. a\u00e7\u0131ortayd\u0131r. P K T II I III R IV 70\u00b0 60\u00b0 M L Kareli zeminde verilen hangi nokta S noktas\u0131 ola- NP rak se\u00e7ilirse PRS \u00fc\u00e7geninin PR kenar\u0131na ait ke- Buna g\u00f6re m(NK\u2211P) ka\u00e7 derecedir? narortay T noktas\u0131ndan ge\u00e7er? A) I B) II C) III D) IV A) 5 B) 10 C) 15 D) 20 7. 9. D D\u0131 A BC EF Kareli zeminde verilen ABC \u00fc\u00e7geninde AB kenar\u0131na Yukar\u0131daki \u015fekilde DEF \u00fc\u00e7geninin D k\u00f6\u015fesi EF ke- ait y\u00fckseklik 15 cm\u2019dir. nar\u0131na paralel ok y\u00f6n\u00fcnde kayd\u0131r\u0131larak D\u0131EF \u00fc\u00e7geni elde ediliyor. Buna g\u00f6re bu \u00fc\u00e7genin alan\u0131 ka\u00e7 santimetrekare- dir? Buna g\u00f6re son durumda olu\u015fan \u015fekil i\u00e7in a\u015fa\u011f\u0131- dakilerden hangisi yanl\u0131\u015ft\u0131r? A) 45 B) 60 C) 75 D) 90 A) EF kenar\u0131na ait y\u00fckseklik de\u011fi\u015fmemi\u015ftir. B) EF kenar\u0131na ait kenarortay\u0131n uzunlu\u011fu artm\u0131\u015ft\u0131r. C) D a\u00e7\u0131s\u0131na ait a\u00e7\u0131ortay\u0131n uzunlu\u011fu de\u011fi\u015fmemi\u015ftir. D) DEF \u00fc\u00e7geninin alan\u0131 de\u011fi\u015fmemi\u015ftir. 8. S\u0131n\u0131f 303","\u00dc\u00e7gende Kenar Uzunluklar\u0131 Aras\u0131ndaki \u0130li\u015fki \u00dc\u00e7genin herhangi bir kenar\u0131n\u0131n uzunlu\u011fu, di\u011fer iki kenar\u0131n uzunluklar\u0131 toplam\u0131ndan k\u00fc\u00e7\u00fck, fark\u0131n\u0131n mutlak de\u011ferin- den b\u00fcy\u00fckt\u00fcr. Buna \u00fc\u00e7gen \u00e7e\u015fitsizli\u011fi denir. A cb |a \u2013 c| < b < a + c |a \u2013 b| < c < a + b C |b \u2013 c| < a < b + c a B \u00d6rnek: A 6 br 9 br Yandaki \u00fc\u00e7gende x do\u011fal say\u0131 de\u011ferlerini bulal\u0131m. |9 \u2013 6| < x < 9 + 6 3 < x < 15 \u20ba x de\u011ferleri 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 olabiir. B x br C 72 2. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerde verilenlere g\u00f6re x\u2019in alabi- lece\u011fi t\u00fcm do\u011fal say\u0131 de\u011ferlerini bulunuz. 1. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerde verilmeyen kenar uzunluk- lar\u0131n\u0131n (x) alabilece\u011fi t\u00fcm do\u011fal say\u0131 de\u011ferlerini a) D 5 br bulunuz. F a) A 10 br (x+2) br 8 br 4 br B x br C E (2x-1) br b) K b) 10 br C A 6 br M x br 7 br L 11 br c) K B c) D 9 br 8 br (x-1) br x br 15 br E F L (2x+1)br M 304 8. S\u0131n\u0131f","\u00dc\u00e7gende Kenar Uzunluklar\u0131 Aras\u0131ndaki \u0130li\u015fki NOT: Bir \u00fc\u00e7genin \u00e7izilebilmesi i\u00e7in kenar uzunluklar\u0131n\u0131n \u00fc\u00e7gen e\u015fitsizli\u011fini mutlaka sa\u011flamas\u0131 gerekir. \u00dc\u00e7genin kenarlar\u0131 aras\u0131nda \u00fc\u00e7gen e\u015fitsizli\u011fi kural\u0131 yoksa \u00fc\u00e7gen \u00e7izilemez. 3. A\u015fa\u011f\u0131da kenar uzunluklar\u0131 verilen \u00fc\u00e7genlerin \u00e7izilip \u00e7izilemeyece\u011fini bulunuz. a) 4 cm, 6 cm, 7 cm b) 8 cm, 8 cm, 11 cm c) 5 cm, 4 cm, 10 cm \u00e7) 9 cm, 12 cm, 2 cm d) 7 cm, 10 cm, 13 cm e) 8 cm, 10 cm, 18 cm NOT: \u0130ki \u00fc\u00e7genin birer kenar\u0131 \u00e7ak\u0131\u015f\u0131k olarak verildi\u011finde ve bu \u00e7ak\u0131\u015f\u0131k kenar\u0131n uzunlu\u011funun alabilece\u011fi de\u011ferler soruldu\u011funda iki \u00fc\u00e7gen i\u00e7in ayr\u0131 ayr\u0131 \u00fc\u00e7gen e\u015fitsizli\u011fi uygulan\u0131r. Ard\u0131ndan ortak olan de\u011ferler al\u0131n\u0131r. 4. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerde verilmeyen kenar uzunluklar\u0131n\u0131n (x) birim cinsinden alabilece\u011fi do\u011fal say\u0131 de\u011ferlerini bulunuz. A b) K a) 10 br 3 br 2 br 8 br B xC Lx N 3 br 5 br M 9 br 5 br D 5. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerde verilmeyen kenar uzunluklar\u0131n\u0131n (x), birim cinsinden alabilece\u011fi en b\u00fcy\u00fck ve en k\u00fc- \u00e7\u00fck do\u011fal say\u0131 de\u011ferlerini bulunuz. a) A b) K xM 11 br 10 br 4 br 2 br B xC 10 br N 7 br 9 br 8 br L D 8. S\u0131n\u0131f 305","\u00dc\u00e7gende Kenar Uzunluklar\u0131 Aras\u0131ndaki \u0130li\u015fki 6. A\u015fa\u011f\u0131daki \u00e7e\u015fitkenar \u00fc\u00e7gende x\u2019in alabilece\u011fi 9. A\u015fa\u011f\u0131daki \u015fekilde |BC|\u2019nun en k\u00fc\u00e7\u00fck do\u011fal say\u0131 do\u011fal say\u0131 de\u011ferlerinin toplam\u0131n\u0131 bulunuz. de\u011feri i\u00e7in x\u2019in alabilece\u011fi do\u011fal say\u0131 de\u011ferlerini A bulunuz. A 6 cm x cm B 8 cm C x 16 cm 7 cm 10 cm B C 7. A\u015fa\u011f\u0131daki ikizkenar \u00fc\u00e7gende x\u2019in alabilece\u011fi do- 10. A\u015fa\u011f\u0131daki \u015fekilde |KN|\u2019nun en k\u00fc\u00e7\u00fck do\u011fal say\u0131 \u011fal say\u0131 de\u011ferlerini bulunuz. de\u011feri i\u00e7in x\u2019in alabilece\u011fi do\u011fal say\u0131 de\u011ferlerini A bulunuz. K x 5 cm B C 8 cm x 11 cm L 14 cm N 5 cm M 8. A\u015fa\u011f\u0131daki \u015fekilde DEG \u00fc\u00e7geninin kenar uzunluk- 11. A\u015fa\u011f\u0131daki \u015fekilde verilen \u00fc\u00e7genlerin kenar uzunluk- lar\u0131 do\u011fal say\u0131 olmak \u00fczere \u00e7evre uzunlu\u011funun lar\u0131 santimetre cinsinden do\u011fal say\u0131d\u0131r. santimetre cinsinden alabilece\u011fi en b\u00fcy\u00fck ve en k\u00fc\u00e7\u00fck do\u011fal say\u0131 de\u011ferleri bulunuz. Buna g\u00f6re KMN \u00fc\u00e7geninin \u00e7evre uzunlu\u011funun alabilece\u011fi en b\u00fcy\u00fck ve en k\u00fc\u00e7\u00fck de\u011ferleri bu- D lunuz. 6 cm K G 7 cm 13 cm E 8 cm LN 3 cm F 10 cm M 306 8. S\u0131n\u0131f","\u00dc\u00e7gende Kenar Uzunluklar\u0131 Aras\u0131ndaki \u0130li\u015fki 12. A\u015fa\u011f\u0131daki \u015fekilde KLMN d\u00f6rtgeninin kenar uzun- 15. \u00c7evre uzunlu\u011fu 32 cm olan bir \u00fc\u00e7genin kenar luklar\u0131 santimetre cinsinden do\u011fal say\u0131 oldu\u011fu- uzunlu\u011funun santimetre cinsinden alabilece\u011fi en na g\u00f6re bu d\u00f6rtgenin santimetre cinsinden \u00e7evre b\u00fcy\u00fck tam say\u0131 de\u011feri ka\u00e7t\u0131r? uzunlu\u011funun en k\u00fc\u00e7\u00fck de\u011ferini bulunuz. K L 11 cm N M 13. A\u015fa\u011f\u0131daki \u00fc\u00e7genin santimetre cinsinden kenar 16. Kenar uzunluklar\u0131 santimetre cinsinden do\u011fal say\u0131 uzunluklar\u0131 do\u011fal say\u0131 oldu\u011funa g\u00f6re x\u2019in alabi- olan bir \u00fc\u00e7genin \u00e7evre uzunlu\u011fu 17 cm\u2019dir. lece\u011fi de\u011ferleri bulunuz. Buna g\u00f6re bu ko\u015fula uygun \u00e7izilebilecek ka\u00e7 A farkl\u0131 \u00fc\u00e7gen vard\u0131r? (2x + 3) cm (x + 1) cm B 10 cm C 14. A\u015fa\u011f\u0131daki \u00fc\u00e7genin santimetre cinsinden kenar 17. Kenar uzunluklar\u0131 santimetre cinsinden do\u011fal say\u0131 uzunluklar\u0131 do\u011fal say\u0131 oldu\u011funa g\u00f6re \u00fc\u00e7genin olan bir \u00e7e\u015fitkenar \u00fc\u00e7genin \u00e7evre uzunlu\u011fu 21 cm\u2019dir. santimetre cinsinden en b\u00fcy\u00fck \u00e7evre uzunlu\u011fu de\u011ferini bulunuz. Buna g\u00f6re bu ko\u015fula uygun \u00e7izilebilecek ka\u00e7 farkl\u0131 \u00fc\u00e7gen vard\u0131r? D (4x)cm F (x-2)cm 16 cm E 8. S\u0131n\u0131f 307","Uyguluyorum \u00dc\u00e7genin Kenar Uzunluklar\u0131 Aras\u0131ndaki \u0130li\u015fki Test 70 1. A 4. P 7 cm 11 cm x cm 2\u00a76 cm S B x cm C R 4\u00a76 cm \u015eekildeki PRS \u00fc\u00e7geninde x\u2019in alabilece\u011fi ka\u00e7 \u015eekildeki ABC \u00fc\u00e7geninde verilenlere g\u00f6re x a\u015fa- farkl\u0131 do\u011fal say\u0131 de\u011feri vard\u0131r? \u011f\u0131dakilerden hangisi olabilir? A) 2 B) 4 C) 14 D) 20 A) 10 B) 9 C) 8 D) 7 2. K 5. A\u015fa\u011f\u0131daki uzunluklar\u0131 verilen \u00e7ubuklardan han- 5 cm gisinin u\u00e7 uca eklenmesiyle bir \u00fc\u00e7gen olu\u015fturu- lamaz? M A) 8 cm, 10 cm, 12 cm 12 cm B) 6 cm, 8 cm, 10 cm L C) 5 cm, 7 cm, 9 cm \u015eekildeki KLM \u00fc\u00e7geninde |KL|\u2019nun santimetre D) 3 cm, 4 cm, 7 cm cinsinden alabilece\u011fi ka\u00e7 farkl\u0131 tam say\u0131 de\u011feri vard\u0131r? A) 7 B) 8 C) 9 D) 10 3. D 6. A\u015fa\u011f\u0131daki KLM \u00fc\u00e7geninin kenar uzunluklar\u0131 santi- metre cinsinden do\u011fal say\u0131d\u0131r. x cm K 10 cm 3 cm M E 10 cm F L 14 cm \u015eekildeki DEF \u00fc\u00e7geninde x\u2019in alabilece\u011fi en b\u00fc- Buna g\u00f6re bu \u00fc\u00e7genin \u00e7evre uzunlu\u011fu en az ka\u00e7 y\u00fck do\u011fal say\u0131 de\u011feri ka\u00e7t\u0131r? santimetredir? A) 13 B) 12 C) 11 D) 10 A) 29 B) 30 C) 31 D) 32 308 8. S\u0131n\u0131f","Test \u00dc\u00e7genin Kenar Uzunluklar\u0131 Aras\u0131ndaki \u0130li\u015fki Uyguluyorum 70 7. A 10. A 3,8 cm 7 cm 3 cm B x cm C C B 6,5 cm 8 cm 6 cm \u015eekildeki ABC \u00fc\u00e7geninin \u00e7evre uzunlu\u011funun D santimetre cinsinden alabilece\u011fi en b\u00fcy\u00fck tam \u015eekilde verilenlere g\u00f6re x\u2019in alabilece\u011fi en k\u00fc\u00e7\u00fck say\u0131 de\u011feri ka\u00e7t\u0131r? ve en b\u00fcy\u00fck tam say\u0131 de\u011ferleri toplam\u0131 ka\u00e7t\u0131r? A) 20 B) 21 C) 22 D) 23 A) 13 B) 14 C) 15 D) 16 11. K 8. A 5 cm 12 cm 2x 3x L x cm N 9 cm 14 cm B 10 cm C \u015eekildeki ABC \u00fc\u00e7geninde x\u2019in santimetre cinsin- M den alabilece\u011fi en b\u00fcy\u00fck do\u011fal say\u0131 de\u011feri ka\u00e7- \u015eekilde verilenlere g\u00f6re x\u2019in alabilece\u011fi iki basa- t\u0131r? makl\u0131 tam say\u0131 de\u011ferlerinin toplam\u0131 ka\u00e7t\u0131r? A) 12 B) 11 C) 10 D) 9 A) 110 B) 108 C) 91 D) 81 9. Kenarlar\u0131ndan birinin uzunlu\u011fu 13 cm olan bir 12. Bir kenar uzunlu\u011fu 17 cm olan bir \u00fc\u00e7genin \u00e7evre- sinin santimetre cinsinden alabilece\u011fi en k\u00fc\u00e7\u00fck \u00fc\u00e7genin di\u011fer iki kenar uzunlu\u011fu a\u015fa\u011f\u0131dakilerden tam say\u0131 de\u011feri ka\u00e7t\u0131r? hangisi olamaz? A) 4 ve 10 cm B) 5 ve 11 cm A) 36 B) 35 C) 34 D) 33 C) 6 ve 7 cm D) 7 ve 7 cm 8. S\u0131n\u0131f 309","Uyguluyorum \u00dc\u00e7genin Kenar Uzunluklar\u0131 Aras\u0131ndaki \u0130li\u015fki Test 71 1. 4 cm 3. D 5 cm 6 cm 8 cm 8 cm 10 cm 5 cm 18 cm A C Yukar\u0131da uzunluklar\u0131 verilen \u00e7ubuklarla olu\u015fturu- 7 cm labilecek bir \u00fc\u00e7genin \u00e7evresi en fazla ka\u00e7 santi- B metredir? \u015eekildeki ABCD d\u00f6rtgeninde |AB|\u2019nun santimetre cinsinden alabilece\u011fi en k\u00fc\u00e7\u00fck do\u011fal say\u0131 de\u011feri ka\u00e7t\u0131r? A) 1 B) 2 C) 3 D) 4 A) 36 B) 30 C) 24 D) 18 4. K 2. A\u015fa\u011f\u0131da bir zemine yerle\u015ftirilen kamera ayaklar\u0131n\u0131n M aras\u0131ndaki uzakl\u0131klar verilmi\u015ftir. 20 cm L \u015eekildeki KLM \u00fc\u00e7geninin \u00e7evre uzunlu\u011funun santimetre cinsinden alabilece\u011fi en k\u00fc\u00e7\u00fck do\u011fal say\u0131 de\u011feri ka\u00e7t\u0131r? A) 39 B) 40 C) 41 D) 42 x cm 40 cm 90 cm 5. \u0130ki kenar\u0131n uzunlu\u011fu 15 cm ve 8 cm olan bir \u00fc\u00e7ge- Buna g\u00f6re x\u2019in alabilece\u011fi de\u011ferlerden ka\u00e7 tanesi nin santimetre cinsinden \u00e7evre uzunlu\u011fu a\u015fa\u011f\u0131- tam kare say\u0131d\u0131r? dakilerden hangisi olabilir? A) 4 B) 5 C) 6 D) 7 A) 27 B) 30 C) 35 D) 46 310 8. S\u0131n\u0131f","Test \u00dc\u00e7genin Kenar Uzunluklar\u0131 Aras\u0131ndaki \u0130li\u015fki Uyguluyorum 71 6. Bir KLM \u00fc\u00e7geninin kenar uzunluklar\u0131 (x) cm, 9. Kenar uzunluklar\u0131 santimetre cinsinden do\u011fal say\u0131 olan bir \u00fc\u00e7genin \u00e7evre uzunlu\u011fu 24 cm\u2019dir. (x + 2) cm ve (x + 5) cm\u2019dir. Buna g\u00f6re bu \u00fc\u00e7genin bir kenar\u0131n\u0131n uzunlu\u011fu en Buna g\u00f6re x\u2019in santimetre cinsinden alabilece\u011fi \u00e7ok ka\u00e7 santimetredir? de\u011ferlerden biri a\u015fa\u011f\u0131dakilerden hangisi olamaz? A) 6 B) 5 C) 4 D) 3 A) 10 B) 11 C) 12 D) 13 10. K 7. A 6 cm 7 cm N BC 9 cm P 3 cm D L 4 cm 24 cm M \u015eekilde verilenlere g\u00f6re |AB|\u2019nun santimetre cin- \u015eeklide verilenlere g\u00f6re |LP|\u2019nun santimetre cin- sinden alabilece\u011fi en k\u00fc\u00e7\u00fck do\u011fal say\u0131 de\u011feri sinden alabilece\u011fi en b\u00fcy\u00fck tam say\u0131 de\u011feri ka\u00e7- ka\u00e7t\u0131r? t\u0131r? A) 9 B) 8 C) 7 D) 6 A) 12 B) 11 C) 10 D) 9 11. P R 8 cm T 8. \u00d6zde\u015f kibrit \u00e7\u00f6plerinin u\u00e7 uca eklenmesi ile bir \u00fc\u00e7gen olu\u015fturulacakt\u0131r. Olu\u015fturulacak \u00fc\u00e7genin bir kenar\u0131 i\u00e7in 8, di\u011feri i\u00e7in 14 S kibrit \u00e7\u00f6p\u00fc kullan\u0131lm\u0131\u015ft\u0131r. Buna g\u00f6re \u00fc\u00e7\u00fcnc\u00fc kenar i\u00e7in kullan\u0131lmas\u0131 gere- \u015eekilde verilenlere g\u00f6re PRST d\u00f6rtgeninin \u00e7evre ken kibrit \u00e7\u00f6p\u00fc say\u0131s\u0131 en fazla ka\u00e7t\u0131r? uzunlu\u011funun en k\u00fc\u00e7\u00fck tam say\u0131 de\u011feri ka\u00e7t\u0131r? A) 17 B) 19 C) 21 D) 23 A) 16 B) 17 C) 18 D) 19 8. S\u0131n\u0131f 311","\u00dc\u00e7gende A\u00e7\u0131 \u2013 Kenar Ba\u011f\u0131nt\u0131lar\u0131 Bir \u00fc\u00e7gende k\u00fc\u00e7\u00fck a\u00e7\u0131 kar\u015f\u0131s\u0131nda k\u0131sa kenar, b\u00fcy\u00fck a\u00e7\u0131 kar\u015f\u0131s\u0131nda uzun kenar bulunur. A cb Yandaki ABC \u00fc\u00e7geninde, m(A\uf8ff) > m(B)\uf8ff > m(C)\uf8ff ise a > b > c olur. B a C l Yandaki KLM \u00fc\u00e7geninde, \u00d6rnek: 75\u00b0 > 65\u00b0 > 40\u00b0 oldu\u011fundan K k > l > m olur. 75\u00b0 m 65\u00b0 k 40\u00b0 L M 73 c) K l M 1. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerin kenar uzunluklar\u0131n\u0131 k\u00fc\u00e7\u00fck- (x+20)\u00b0 ten b\u00fcy\u00fc\u011fe do\u011fru s\u0131ralay\u0131n\u0131z. a) m A k (2x-5)\u00b0 cb L 70\u00b0 50\u00b0 C Ba b) K \u00e7) A m l c(2x-10)\u00b0 b 65\u00b0 45\u00b0 M 115\u00b0 (x+15)\u00b0 C L k Ba NOT: Dik a\u00e7\u0131l\u0131 \u00fc\u00e7genlerde en uzun kenar NOT: Geni\u015f a\u00e7\u0131l\u0131 \u00fc\u00e7genlerde en uzun kenar 90\u00b0\u2019nin kar\u015f\u0131s\u0131nda bulunan kenard\u0131r. geni\u015f a\u00e7\u0131n\u0131n kar\u015f\u0131s\u0131nda bulunan kenard\u0131r. 312 8. S\u0131n\u0131f","\u00dc\u00e7gende A\u00e7\u0131 \u2013 Kenar Ba\u011f\u0131nt\u0131lar\u0131 c) K5\u00a73 cm 4\u00a78 cm L M 2. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerin i\u00e7 a\u00e7\u0131 \u00f6l\u00e7\u00fclerini b\u00fcy\u00fckten k\u00fc\u00e7\u00fc\u011fe s\u0131ralay\u0131n\u0131z. 9 cm a) A 8 cm 9 cm B 7 cm C \u00e7) 2-5 br R P b) D 3-3 br 1 br 42 E 8 cm S 6 cm F NOT: \u0130ki \u00fc\u00e7genin birer kenar\u0131 \u00e7ak\u0131\u015f\u0131k olarak verildi\u011finde ve bu \u00fc\u00e7genlerin kenar uzunluklar\u0131n\u0131n s\u0131ralamas\u0131 soruldu\u011funda iki \u00fc\u00e7genin a\u00e7\u0131lar\u0131na g\u00f6re ayr\u0131 ayr\u0131 s\u0131ralama yap\u0131l\u0131r. Ard\u0131ndan bu s\u0131ralamalar ortak olarak \u00e7\u00f6z\u00fcl\u00fcr. 3. A\u015fa\u011f\u0131daki \u015fekillerin en uzun kenarlar\u0131n\u0131 bulunuz. 4. A\u015fa\u011f\u0131daki \u015fekillerin en k\u0131sa kenarlar\u0131n\u0131 bulunuz. a) A a) A 50\u00b0 B 40\u00b0 75\u00b0 D B 40\u00b0 55\u00b0 D 55\u00b0 70\u00b0 b) C T C b) K V 50\u00b0 70\u00b0 50\u00b0 30\u00b0 P 65\u00b0 60\u00b0 L 70\u00b0 57\u00b0 64\u00b0 S 55\u00b0 N R M 8. S\u0131n\u0131f 313","\u00dc\u00e7gende A\u00e7\u0131 \u2013 Kenar Ba\u011f\u0131nt\u0131lar\u0131 5. A\u015fa\u011f\u0131daki \u00fc\u00e7gende K a\u00e7\u0131s\u0131 geni\u015f a\u00e7\u0131d\u0131r. 8. A\u015fa\u011f\u0131daki ABC ikizkenar \u00fc\u00e7geninin kenar uzunlukla- K r\u0131n\u0131 k\u00fc\u00e7\u00fckten b\u00fcy\u00fc\u011fe do\u011fru s\u0131ralay\u0131n\u0131z. A 6 cm 10 cm 110\u00b0 L x cm M C Buna g\u00f6re x\u2019in alabilece\u011fi do\u011fal say\u0131 de\u011ferlerini B bulunuz. 6. A\u015fa\u011f\u0131daki \u00fc\u00e7gende m(A\uf8ff) > m(B)\uf8ff \u2019dir. 9. A\u015fa\u011f\u0131daki KLM \u00fc\u00e7geninin kenar uzunluklar\u0131n\u0131 b\u00fc- A y\u00fckten k\u00fc\u00e7\u00fc\u011fe s\u0131ralay\u0131n\u0131z. K 4 cm 9 cm C B x cm 115\u00b0 55\u00b0 NL M Buna g\u00f6re x\u2019in alabilece\u011fi do\u011fal say\u0131 de\u011ferlerini bulunuz. 7. A\u015fa\u011f\u0131daki \u00fc\u00e7gende m(R\uf8ff) > m(P)\uf8ff \u2019dir. 10. A\u015fa\u011f\u0131daki \u00fc\u00e7gendre |AC| > |AB|\u2019dir. P A 12 cm 130\u00b0 5 cm S BC Buna g\u00f6re B a\u00e7\u0131s\u0131n\u0131n derece cinsinden alabilece- x cm \u011fi en k\u00fc\u00e7\u00fck do\u011fal say\u0131 de\u011ferini bulunuz. R Buna g\u00f6re x\u2019in alabilece\u011fi do\u011fal say\u0131 de\u011ferlerini bulunuz. 314 8. S\u0131n\u0131f","\u00dc\u00e7gende A\u00e7\u0131 \u2013 Kenar Ba\u011f\u0131nt\u0131lar\u0131 11. A\u015fa\u011f\u0131daki \u00fc\u00e7gende |AB| > |AC|\u2019dir. 14. A\u015fa\u011f\u0131daki \u015fekilde en k\u0131sa kenar\u0131 bulunuz. A AE 58\u00b0 52\u00b0 71\u00b0 40\u00b0 66\u00b0 D BC B C Buna g\u00f6re m(B\uf8ff)\u2019n\u0131n derece cinsinden alabilece\u011fi en b\u00fcy\u00fck do\u011fal say\u0131 de\u011ferini bulunuz. 12. A\u015fa\u011f\u0131daki \u00fc\u00e7gende |KL| > |KM|\u2019dir. 15. Bir DEF \u00fc\u00e7geninde m(D)\uf8ff < m(F\uf8ff)\u2019dir. K 80\u00b0 |DF| = 10 cm ve |DE| = 14 cm oldu\u011funa g\u00f6re M |EF|\u2019nun santimetre cinsinden alabilece\u011fi do\u011fal say\u0131 de\u011ferlerini bulunuz. L Buna g\u00f6re m(L)\uf8ff \u2019nun derece cinsinden alabilece\u011fi en b\u00fcy\u00fck do\u011fal say\u0131 de\u011ferini bulunuz. 13. A\u015fa\u011f\u0131daki \u00fc\u00e7gende m(P\uf8ff) > 60\u00b0\u2019dir. P 12 cm 12 cm 16. Bir KLM \u00fc\u00e7geninde m(K)\uf8ff < m(L\uf8ff) < m(M)\uf8ff \u2019dir. RS Bu \u00fc\u00e7genin kenar uzunluklar\u0131 santimetre cinsinden do\u011fal say\u0131 olup |LM| = 11 cm ve \u00e7evre uzunlu\u011fu Buna g\u00f6re |RS|\u2019nun santimetre cinsinden alabile- 40 cm\u2019dir. ce\u011fi en k\u00fc\u00e7\u00fck do\u011fal say\u0131 de\u011ferini bulunuz. Buna g\u00f6re |KM|\u2019nun santimetre cinsinden alabi- lece\u011fi en b\u00fcy\u00fck ve en k\u00fc\u00e7\u00fck de\u011ferlerin toplam\u0131n\u0131 bulunuz. 8. S\u0131n\u0131f 315","Uyguluyorum \u00dc\u00e7gende A\u00e7\u0131 Kenar Ba\u011f\u0131nt\u0131lar\u0131 Test 72 1. A 4. A\u015fa\u011f\u0131daki KLM \u00fc\u00e7geninde m(K)\uf8ff > m(L)\uf8ff \u2019dir. K cb 55\u00b0 65\u00b0 9 cm 14 cm B aC M L \u015eekildeki ABC \u00fc\u00e7geninin kenar uzunluklar\u0131n\u0131n s\u0131- x cm ralamas\u0131 i\u00e7in a\u015fa\u011f\u0131dakilerden hangisi do\u011frudur? A) c > b > a B) a > b > c Buna g\u00f6re x\u2019in alabilece\u011fi ka\u00e7 farkl\u0131 do\u011fal say\u0131 C) c > a > b D) a > c > b de\u011feri vard\u0131r? A) 7 B) 8 C) 9 D) 10 2. A\u015fa\u011f\u0131daki DEF \u00fc\u00e7geninin \u00e7evre uzunlu\u011fu 40 cm\u2019dir. D 14 cm F 15 cm 5. A 10 cm E BC Buna g\u00f6re bu \u00fc\u00e7genin i\u00e7 a\u00e7\u0131lar\u0131n\u0131n \u00f6l\u00e7\u00fclerinin s\u0131- ralan\u0131\u015f\u0131 a\u015fa\u011f\u0131dakilerden hangisinde do\u011fru veril- \u015eekildeki ABC \u00fc\u00e7geninde |AB|\u2019nun santimetre mi\u015ftir? cinsinden alabilece\u011fi en b\u00fcy\u00fck do\u011fal say\u0131 de\u011feri A) m(D)\uf8ff > m(E\uf8ff) > m(F)\uf8ff B) m(D\uf8ff) > m(F)\uf8ff > m(E\uf8ff) ka\u00e7t\u0131r? C) m(F\uf8ff) > m(D)\uf8ff > m(E)\uf8ff D) m(E\uf8ff) > m(D)\uf8ff > m(F\uf8ff) A) 10 B) 9 C) 8 D) 7 3. A 3\u00a75 cm 4\u00a73 cm 6. A\u015fa\u011f\u0131daki DEF \u00fc\u00e7geninde |DF| > |DE|\u2019dir. D BC 5\u00a72 cm 50\u00b0 \u015eekildeki ABC \u00fc\u00e7geninin i\u00e7 a\u00e7\u0131lar\u0131n\u0131n \u00f6l\u00e7\u00fclerinin EF s\u0131ralan\u0131\u015f\u0131 a\u015fa\u011f\u0131dakilerden hangisinde do\u011fru ve- rilmi\u015ftir? Buna g\u00f6re F a\u00e7\u0131s\u0131n\u0131n \u00f6l\u00e7\u00fcs\u00fc a\u015fa\u011f\u0131dakilerden hangisi olamaz? A) m(B)\uf8ff > m(A\uf8ff) > m(C)\uf8ff B) m(C)\uf8ff > m(B\uf8ff) > m(A\uf8ff) C) m(A\uf8ff) > m(C)\uf8ff > m(B)\uf8ff D) m(A\uf8ff) > m(B\uf8ff) > m(C\uf8ff) A) 66 B) 63 C) 55 D) 50 316 8. S\u0131n\u0131f","Test \u00dc\u00e7gende A\u00e7\u0131 Kenar Ba\u011f\u0131nt\u0131lar\u0131 Uyguluyorum 72 7. A 9. K 40\u00b0 C B 95\u00b0 N M 10\u00b0 110\u00b0 L 50\u00b0 \u015eekildeki ABC \u00fc\u00e7geninin kenar uzunluklar\u0131n\u0131n Yukar\u0131daki \u015fekilde en uzun kenar a\u015fa\u011f\u0131dakiler- s\u0131ralan\u0131\u015f\u0131 a\u015fa\u011f\u0131dakilerden hangisinde do\u011fru ve- den hangisidir? rilmi\u015ftir? A) [LN] B) [NM] C) [KL] D) [KM] A) |AB| = |AC| > |BC| B) |AC| = |BC| > |AB| C) |BC| > |AC| > |AB| D) |AC| > |AB| > |BC| 10. Kenar uzunluklar\u0131 santimetre cinsinden do\u011fal say\u0131 olan bir ABC \u00fc\u00e7geninde; |BC| = 18 cm ve m(A)\uf8ff > m(B\uf8ff) > m(C)\uf8ff \u2019dir. Buna g\u00f6re |AB|\u2019nin santimetre cinsinden alabile- ce\u011fi en b\u00fcy\u00fck de\u011fer ka\u00e7t\u0131r? A) 14 B) 15 C) 16 D) 17 8. A C 60\u00b0 70\u00b0 11. A\u015fa\u011f\u0131daki ABC \u00fc\u00e7geninde m(A)\uf8ff < m(B)\uf8ff < m(C\uf8ff)\u2019dir. A 40\u00b0 b 100\u00b0 D cC B Yukar\u0131daki \u015fekilde en uzun kenar a\u015fa\u011f\u0131dakiler- a den hangisidir? A) [AB] B) [AC] C) [BC] D) [BD] B \u00c7(ABC\u2206 ) = 75 cm ve a, b, c birer tam say\u0131 oldu\u011funa g\u00f6re c uzunlu\u011funun santimetre cinsinden alabi- lece\u011fi en k\u00fc\u00e7\u00fck de\u011fer ka\u00e7t\u0131r? A) 24 B) 25 C) 26 D) 27 8. S\u0131n\u0131f 317","Uyguluyorum \u00dc\u00e7gende A\u00e7\u0131 Kenar Ba\u011f\u0131nt\u0131lar\u0131 Test 73 1. A\u015fa\u011f\u0131da bir duvara dayal\u0131 olan \u00e7ubuk g\u00f6sterilmi\u015ftir. 3. E D 76\u00b0 1,5 m AC Buna g\u00f6re \u00e7ubu\u011fun duvara temas etti\u011fi noktan\u0131n, 38\u00b0 zeminden y\u00fcksekli\u011finin santimetre cinsinden alabilece\u011fi en b\u00fcy\u00fck do\u011fal say\u0131 de\u011feri ka\u00e7t\u0131r? B Yukar\u0131daki \u015fekilde en uzun kenar a\u015fa\u011f\u0131dakiler- den hangisidir? A) [AB] B) [EB] C) [BD] D) [DC] A) 151 B) 150 C) 149 D) 148 4. \u0130\u00e7 a\u00e7\u0131lar\u0131ndan ikisinin \u00f6l\u00e7\u00fcs\u00fc 56\u00b0 ve 41\u00b0 olan bir \u00fc\u00e7gen i\u00e7in a\u015fa\u011f\u0131dakilerden hangisi do\u011frudur? A) E\u015fkenard\u0131r. B) \u0130kizkenard\u0131r. C) \u00c7e\u015fitkenard\u0131r. D) Dik a\u00e7\u0131l\u0131d\u0131r. 2. A 80\u00b0 E 5. K 44\u00b0 88\u00b0 20\u00b0 30\u00b0 B 32\u00b0 D a b 60\u00b0 60\u00b0 40\u00b0 cP 50\u00b0 C LN M \u015eekilde verilenlere g\u00f6re en uzun kenar a\u015fa\u011f\u0131daki- \u015eekildeki KNP \u00fc\u00e7geninde a, b ve c kenar uzun- lerden hangisidir? luklar\u0131n\u0131n s\u0131ralan\u0131\u015f\u0131 a\u015fa\u011f\u0131dakilerden hangisinde A) [AB] B) [BE] C) [BD] D) [CD] verilmi\u015ftir? A) c > b > a B) c > a > b C) a > c > b D) a > b > c 318 8. S\u0131n\u0131f","Test \u00dc\u00e7gende A\u00e7\u0131 Kenar Ba\u011f\u0131nt\u0131lar\u0131 Uyguluyorum 73 6. A\u015fa\u011f\u0131daki DEF \u00fc\u00e7geninde [DG] a\u00e7\u0131ortayd\u0131r. 8. Bir DEF \u00fc\u00e7geninde m(F\uf8ff) > m(E)\uf8ff > m(D)\uf8ff \u2019dir. F Bu \u00fc\u00e7genin \u00e7evresi 24 cm oldu\u011funa g\u00f6re |DE|\u2019nun 40\u00b0 santimetre cinsinden alabilece\u011fi ka\u00e7 farkl\u0131 do\u011fal say\u0131 de\u011feri vard\u0131r? G A) 2 B) 3 C) 4 D) 5 D 50\u00b0 E 9. A 11 cm D C 60\u00b0 Buna g\u00f6re; I. |DG| = |FG| II. |FG| > |EG| III. |DF| > |EG| B yukar\u0131dakilerden hangileri do\u011frudur? \u015eekilde |BC|\u2019nun santimetre cinsinden alabilece- A) I ve II. B) II ve III. \u011fi en k\u00fc\u00e7\u00fck do\u011fal say\u0131 de\u011feri ka\u00e7t\u0131r? C) I ve III. D) I, II ve III. A) 10 B) 11 C) 12 D) 13 7. A\u015fa\u011f\u0131daki \u015fekilde e\u015fkenar \u00fc\u00e7gen bi\u00e7imindeki \u00fc\u00e7 kar- 10. tonun birer k\u00f6\u015felerinin birle\u015ftirilmesiyle olu\u015fan g\u00f6r\u00fc- n\u00fcm verilmi\u015ftir. 65\u00b0 45\u00b0 A C B Buna g\u00f6re bu kartonlar\u0131n \u00e7evre uzunluklar\u0131na Kareli zeminde verilen \u00fc\u00e7genin i\u00e7 a\u00e7\u0131lar\u0131n\u0131n \u00f6l- g\u00f6re s\u0131ralan\u0131\u015f\u0131 a\u015fa\u011f\u0131dakilerden hangisidir? \u00e7\u00fclerinin s\u0131ralan\u0131\u015f\u0131 a\u015fa\u011f\u0131dakilerden hangisinde verilmi\u015ftir? A) K\u0131rm\u0131z\u0131 > sar\u0131 > mor B) K\u0131rm\u0131z\u0131 > mor > sar\u0131 C) Mor > sar\u0131 > k\u0131rm\u0131z\u0131 D) Mor > k\u0131rm\u0131z\u0131 > sar\u0131 A) m(B\uf8ff) > m(C)\uf8ff > m(A)\uf8ff B) m(C)\uf8ff > m(A)\uf8ff > m(B)\uf8ff C) m(A\uf8ff) > m(C\uf8ff) > m(B)\uf8ff D) m(B\uf8ff) > m(A\uf8ff) > m(C)\uf8ff 8. S\u0131n\u0131f 319","Yeterli Say\u0131da Eleman\u0131 Verilen \u00dc\u00e7geni \u00c7izme \u00dc\u00e7 Kenar\u0131n\u0131n Uzunlu\u011fu Verilen \u00dc\u00e7gen Olu\u015fturma \u00dc\u00e7 kenar\u0131n\u0131n uzunlu\u011fu verilen bir \u00fc\u00e7gen, \u00fc\u00e7gen e\u015fitsizli\u011fine dikkat edilerek \u00e7izilir. Bunun i\u00e7in cetvel ve pergel kul- lan\u0131l\u0131r. \u00d6rnek: Kenar uzunluklar\u0131 8 cm, 6 cm ve 4 cm olan bir \u00fc\u00e7gen \u00e7izelim. 6 cm C 4 cm A B A B 8 cm 8 cm A 8 cm B 8 cm\u2019lik bir do\u011fru Pergel 6 cm a\u00e7\u0131larak Yaylar\u0131n kesi\u015fti\u011fi par\u00e7as\u0131 \u00e7izilir. A merkezli bir yay, 4 cm nokta A ve B noktalar\u0131 a\u00e7\u0131larak B merkezli bir ile birle\u015ftirilerek \u00fc\u00e7gen yay \u00e7izilir. olu\u015fturulur. 74 2. A\u015fa\u011f\u0131da verilen kenar uzunluklar\u0131na g\u00f6re tek bir \u00fc\u00e7gen \u00e7izilip \u00e7izilemeyece\u011fini belirleyiniz. \u00c7izi- 1. A\u015fa\u011f\u0131da kenar uzunluklar\u0131 verilen \u00fc\u00e7genleri cet- lebilen \u00fc\u00e7genlerin \u00f6n\u00fcndeki kutucu\u011fa \u201c\ufffd\u201d i\u015fareti vel ve pergel yard\u0131m\u0131yla \u00e7iziniz. koyunuz. a) 2 m, 4 cm ve 3 cm a) 5 cm, 7 cm, 10 cm b) 3 cm, 4 cm, 7 cm b) 4 cm, 5 cm ve 6 cm c) 6 cm, 6 cm, 5 cm \u00e7) 2 cm, 5 cm, 6 cm 320 8. S\u0131n\u0131f","Yeterli Say\u0131da Eleman\u0131 Verilen \u00dc\u00e7geni \u00c7izme \u0130ki kenar\u0131n\u0131n uzunlu\u011fu ve bu kenarlar\u0131n aras\u0131ndaki a\u00e7\u0131n\u0131m \u00f6l\u00e7\u00fcs\u00fc verilen \u00fc\u00e7geni olu\u015fturma. Bu \u015fart\u0131 sa\u011flayan tek bir \u00fc\u00e7gen \u00e7izilir. Bunun i\u00e7in cetvel ve a\u00e7\u0131\u00f6l\u00e7er kullan\u0131l\u0131r. \u00d6rnek: \u0130ki kenar\u0131n\u0131n uzunlu\u011fu 6 cm ve 5 cm, bu kenarlar\u0131n aras\u0131ndaki a\u00e7\u0131n\u0131n \u00f6l\u00e7\u00fcs\u00fc 55\u00b0 olan bir \u00fc\u00e7gen \u00e7izelim. AB A 55\u00b0 B C B C 6 cm 5 cm 5 cm 6 cm A 55\u00b0 A 6 cm B 6 cm 6 cm\u2019lik bir do\u011fru A\u00e7\u0131 \u00f6l\u00e7er kullan\u0131larak Bu \u0131\u015f\u0131n \u00fczerinde B ve C noktalar\u0131 par\u00e7as\u0131 \u00e7izilir. do\u011fru par\u00e7as\u0131 ile cetvel yard\u0131m\u0131yla birle\u015ftirilerek 55\u00b0\u2019lik a\u00e7\u0131 yapan bir 5 cm\u2019lik [AC] \u00fc\u00e7gen olu\u015fturulur. \u0131\u015f\u0131n \u00e7izilir. belirlenir. 75 1. \u0130ki kenar\u0131n\u0131n uzunluklar\u0131 5 cm ve 3 cm, bu kenarlar\u0131n aras\u0131ndaki a\u00e7\u0131n\u0131n \u00f6l\u00e7\u00fcs\u00fc 60\u00b0 olan \u00fc\u00e7geni \u00e7iziniz. 2. A\u015fa\u011f\u0131daki bilgilere g\u00f6re tek bir \u00fc\u00e7gen \u00e7izilip \u00e7i- c) |KL| = 8 cm, |KM| = 6 cm, m(LKM\u2211 ) = 50\u00b0 zilemeyece\u011fini belirleyiniz. \u00c7izilebilen \u00fc\u00e7genlerin \u00f6n\u00fcndeki kutucu\u011fa \u201c\ufffd\u201d i\u015fareti koyunuz. a) |AB| = 7 cm, |AC| = 10 cm, m(BAC\u2211 ) = 70\u00b0 \u00e7) |PR| = 5 cm, |PS| = 7 cm, m(PR\u2211S) = 60\u00b0 b) |DE| = 3 cm, |DF| = 6 cm, m(DE\u2211F) = 90\u00b0 8. S\u0131n\u0131f 321","Yeterli Say\u0131da Eleman\u0131 Verilen \u00dc\u00e7geni \u00c7izme Bir kenar\u0131n\u0131n uzunlu\u011fu ve bu kenar\u0131n iki ucundaki a\u00e7\u0131lar\u0131n \u00f6l\u00e7\u00fcs\u00fc verilen \u00fc\u00e7geni olu\u015fturma. Bu \u015fart\u0131 sa\u011flayan tek bir \u00fc\u00e7gen \u00e7izilir. Bunun i\u00e7in cetvel ile a\u00e7\u0131\u00f6l\u00e7er kullan\u0131l\u0131r. \u00d6rnek: A\u00e7\u0131lar\u0131ndan ikisinin \u00f6l\u00e7\u00fcs\u00fc 45\u00b0 ve 75\u00b0, bu iki a\u00e7\u0131s\u0131n\u0131 birle\u015ftiren kenar\u0131n uzunlu\u011fu 7 cm olan bir \u00fc\u00e7gen \u00e7izilir. C AB 45\u00b0 75\u00b0 45\u00b0 75\u00b0 7 cm A 7 cm B A 7 cm B 7 cm\u2019lik bir do\u011fru I\u015f\u0131nlar\u0131n kesi\u015fti\u011fi noktay\u0131 A ve par\u00e7as\u0131 \u00e7izilir. Do\u011fru par\u00e7as\u0131n\u0131n bir ucundan B noktalar\u0131 ile birle\u015ftirerek 45\u00b0\u2019lik, di\u011fer ucundan 75\u00b0\u2019lik a\u00e7\u0131 \u00fc\u00e7gen olu\u015fturulur. olu\u015fturulacak bi\u00e7imde \u0131\u015f\u0131nlar \u00e7iziniz. 76 1. A\u00e7\u0131lar\u0131ndan ikisinin \u00f6l\u00e7\u00fcs\u00fc 60\u00b0 ve 50\u00b0, bu iki a\u00e7\u0131s\u0131n\u0131 birle\u015ftiren kenar\u0131n\u0131n uzunlu\u011fu 5 cm olan \u00fc\u00e7geni \u00e7iziniz. 2. A\u015fa\u011f\u0131daki bilgilere g\u00f6re tek bir \u00fc\u00e7gen \u00e7izilip \u00e7i- c) m(D)\uf8ff = 45\u00b0, m(E\uf8ff) = 60\u00b0, |EF| = 8 cm zilemeyece\u011fini belirleyiniz. \u00c7izilebilen \u00fc\u00e7genlerin \u00f6n\u00fcndeki kutucu\u011fa \u201c\ufffd\u201d i\u015fareti koyunuz. a) m(A)\uf8ff = 90\u00b0, m(B\uf8ff) = 40\u00b0, |AB| = 7 cm b) m(DEF\u2211 ) = 80\u00b0, m(FD\u2211E) = 65\u00b0, |DF| = 6 cm \u00e7) m(K)\uf8ff = 50\u00b0, m(L\uf8ff) = 70\u00b0, |KM| = 10 cm 322 8. S\u0131n\u0131f","Test Yeterli Say\u0131da Eleman\u0131 Verilen \u00dc\u00e7geni \u00c7izme Uyguluyorum 74 1. A 4. A\u015fa\u011f\u0131da baz\u0131 elemanlar\u0131 verilen \u00fc\u00e7genlerden hangisi birden fazla \u00e7izilebilir? 5 cm 7 cm A) B) 5 cm 80\u00b0 B 6 cm C 4 cm 10 cm 7 cm 40\u00b0 60\u00b0 Yukar\u0131daki \u00fc\u00e7genin tek bir \u015fekilde \u00e7izilebilmesi i\u00e7in a\u015fa\u011f\u0131dakilerden hangisinin kesinlikle kulla- n\u0131lmas\u0131 gerekir? A) Cetvel ve pergel B) Pergel ve g\u00f6nye C) 9 cm D) C) Cetvel ve a\u00e7\u0131\u00f6l\u00e7er C) Pergel ve a\u00e7\u0131\u00f6l\u00e7er 80\u00b0 60\u00b0 80\u00b0 40\u00b0 60\u00b0 2. A\u015fa\u011f\u0131da baz\u0131 elemanlar\u0131 verilen \u00fc\u00e7genlerden 5. A hangisi tek bir \u015fekilde \u00e7izilebilir? A) m(A\uf8ff) = 100\u00b0, m(B)\uf8ff = 60\u00b0, m(C\uf8ff) = 20\u00b0 B) |DE| = 8 cm, |DF| = 11 cm, m(D\uf8ff) = 85\u00b0 C) |KL| = 12 cm, |KM| = 15 cm, m(L\uf8ff) = 50\u00b0 D) |PR| = 7 m, |PS| = 8 cm, |RS| = 15 cm 50\u00b0 17 cm BC 3. A\u015fa\u011f\u0131dakilerden hangisinde verilenlerle tek bir Yukar\u0131daki ABC \u00fc\u00e7geninin tek bir \u015fekilde \u00e7izile- \u00fc\u00e7gen \u00e7izilemez? bilmesi i\u00e7in a\u015fa\u011f\u0131dakilerden hangisinin bilinmesi A) m(A\uf8ff) = 50\u00b0, m(B\uf8ff) = 60\u00b0, |AB| = 14 cm yeterli de\u011fildir? B) m(K\uf8ff) = 45\u00b0, m(L\uf8ff) = 65\u00b0, |KM| = 9 cm A) m(B)\uf8ff B) m(C\uf8ff) C) |AB| = 5 cm, |BC| = 12 cm, |AC| = 13 cm C) |BC| D) |AC| D) |PR| = 11 cm, |RS| = 6 cm, m(S)\uf8ff = 70\u00b0 8. S\u0131n\u0131f 323","Uyguluyorum Yeterli Say\u0131da Eleman\u0131 Verilen \u00dc\u00e7geni \u00c7izme Test 74 6. K 9. A 17 cm 10 cm L 13 cm M BC Yukar\u0131daki KLM \u00fc\u00e7geninin sadece cetvel ve A\u015fa\u011f\u0131dakilerden hangisinde verilen elemanlar a\u00e7\u0131\u00f6l\u00e7er kullan\u0131larak tek bir \u015fekilde \u00e7izilebilmesi bilindi\u011finde \u015fekildeki ABC \u00fc\u00e7geni tek bir \u015fekilde i\u00e7in ayr\u0131ca hangi eleman\u0131n bilinmesi gerekir? \u00e7izilebilir? A) |KL| B) m(K)\uf8ff C) m(L)\uf8ff D) m(M\uf8ff) A) |AC| ve m(C)\uf8ff B) |BC| ve m(B)\uf8ff C) |AC| ve m(B)\uf8ff D) |BC| ve m(C)\uf8ff 10. 7. I. |DE| = 11 cm, |DF| = 12 cm, |EF| = 16 cm II. |KL| = 8 cm, m(K\uf8ff) = 75\u00b0, m(L) = 75\u00b0 A\u015fa\u011f\u0131daki \u00fc\u00e7genlerden hangisinin \u00e7iziminde \u015fe- kildeki ders arac\u0131 kullan\u0131labilir? III. m(P)\uf8ff = 45\u00b0, m(R)\uf8ff = 50\u00b0, m(S\uf8ff) = 85\u00b0 Yukar\u0131dakilerden hangisinde verilenlere tek bir \u00fc\u00e7gen \u00e7izilebilir? A) Yaln\u0131z I B) I ve II A) 6 cm B) C) I ve III D) I, II ve III 66\u00b0 7 cm 7 cm 8 cm 72\u00b0 C) D) 8. Sadece cetvel ve pergel kullan\u0131larak tek bir \u015fekil- 30\u00b0 10 cm de \u00e7izilebilecek DEF \u00fc\u00e7geni i\u00e7in a\u015fa\u011f\u0131dakilerden 50\u00b0 hangisinin bilinmesine gerek yoktur? 9 cm 8 cm 12 cm A) |DE| B) m(F\uf8ff) C) |DF| D) |EF| 324 8. S\u0131n\u0131f","Test \u00dc\u00e7genler Ba\u015far\u0131yorum 75 1. A\u015fa\u011f\u0131da bir mantar pano \u00fczerinde \u00fc\u00e7 adet raptiye ve ip ile yap\u0131lan etkinlik durumlar\u0131 verilmi\u015ftir. A A 15 cm 15 cm 7 cm B x-4 cm C B x cm C I.Durum II.Durum I. Durumda ip A noktas\u0131 \u00fczerinde bulunan raptiyeye ula\u015ft\u0131r\u0131lam\u0131yor. II. Durumda ise ayn\u0131 ip A noktas\u0131na ula\u015ft\u0131r\u0131larak bir ABC \u00fc\u00e7geni olu\u015fturulmu\u015ftur. Buna g\u00f6re x\u2019in alabilece\u011fi ka\u00e7 tam say\u0131 de\u011feri vard\u0131r? A) 18 B) 19 C) 20 D) 21 2. A\u015fa\u011f\u0131da \u00f6n y\u00fcz\u00fcn\u00fcn alan\u0131 400 cm2 olan kare bi\u00e7iminde bir karton g\u00f6sterilmi\u015ftir. ? Bu karton kenarlar\u0131n\u0131n orta noktalar\u0131ndan kesilerek \u00f6nce d\u00f6rt e\u015f par\u00e7aya ayr\u0131l\u0131yor. Ard\u0131ndan bu par\u00e7alardan biri, bir k\u00f6\u015fesi ve bir kenar\u0131ndan ge\u00e7ecek bi\u00e7imde \u015fekildeki gibi kesiliyor. Buna g\u00f6re son durumda kesilen par\u00e7an\u0131n uzunlu\u011funun (?) santimetre cinsinden alabilece\u011fi en k\u00fc\u00e7\u00fck do\u011fal say\u0131 de\u011feri ka\u00e7t\u0131r? A) 9 B) 10 C) 11 D) 12 8. S\u0131n\u0131f 325","Ba\u015far\u0131yorum \u00dc\u00e7genler Test 75 3. Ayn\u0131 uzunlukta olan \u00fc\u00e7 farkl\u0131 renkteki \u00e7ubuk a\u015fa\u011f\u0131daki gibi kendi i\u00e7lerinde e\u015fit par\u00e7alara ayr\u0131l\u0131yor. mor k\u0131rm\u0131z\u0131 mavi Buna g\u00f6re bu \u00e7ubuklardan, I. 1 mor, 1 k\u0131rm\u0131z\u0131 ve 1 mavi II. 2 mor ve 1 k\u0131rm\u0131z\u0131 III. 2 k\u0131rm\u0131z\u0131 ve 1 mavi yukar\u0131dakilerden hangileri tek ba\u015f\u0131na kullan\u0131larak bir \u00fc\u00e7gen olu\u015fturulabilir? A) I ve II. B) I ve III. C) II ve III. D) I, II ve III. 4. Nazl\u0131 \u015eekil I\u2019deki dikd\u00f6rtgen bi\u00e7iminde ABCD k\u00e2\u011f\u0131d\u0131n\u0131 D k\u00f6\u015fesinden AC k\u00f6\u015fegeni boyunca katlayarak \u015eekil II\u2019yi elde etmi\u015ftir. D CD C 35\u00b0 A B A? EB \u015eekil I D1 \u015eekil II Buna g\u00f6re son durumda \u201c?\u201d ile g\u00f6sterilen a\u00e7\u0131n\u0131n \u00f6l\u00e7\u00fcs\u00fc ka\u00e7 derecedir? A) 20 B) 25 C) 30 D) 35 326 8. S\u0131n\u0131f","Test \u00dc\u00e7genler Ba\u015far\u0131yorum 76 1. Yunus daire \u015feklindeki kartonlardan her birini kendi i\u00e7inde e\u015f daire dilimlerine ay\u0131r\u0131yor ve her bir dairenin birer dili- mini keserek \u00fc\u00e7gen \u015feklindeki bir kartonun k\u00f6\u015felerine yerle\u015ftiriyor. c a b Buna g\u00f6re son durumda olu\u015fan kartonun kenar uzunluklar\u0131 aras\u0131ndaki ili\u015fki a\u015fa\u011f\u0131dakilerden hangisinde verilmi\u015ftir? A) a > c > b B) a > b > c C) c > a > b D) c > b > a 2. A\u015fa\u011f\u0131daki krokide t\u00fcm yerle\u015fim yerleri aras\u0131ndaki uzakl\u0131klar metre cinsinden do\u011fal say\u0131d\u0131r. Ev (3x+5)\u00b0 25 m Okul (4x+10)\u00b0 (4x)\u00b0 Park Buna g\u00f6re ev ve park aras\u0131ndaki uzakl\u0131\u011f\u0131n alabilece\u011fi en k\u00fc\u00e7\u00fck de\u011fer ile okul ve park aras\u0131ndaki uzakl\u0131\u011f\u0131n alabilece\u011fi en b\u00fcy\u00fck de\u011ferin toplam\u0131 ka\u00e7 metredir? A) 49 B) 50 C) 51 D) 52 8. S\u0131n\u0131f 327","Ba\u015far\u0131yorum \u00dc\u00e7genler Test 76 3. A\u015fa\u011f\u0131da \u015eekil 1\u2019de \u00f6n y\u00fcz\u00fc mor arka y\u00fcz\u00fc ye\u015fil renkli olan ABC \u00fc\u00e7gen bi\u00e7imindeki k\u00e2\u011f\u0131t g\u00f6sterilmi\u015ftir. Bu k\u00e2\u011f\u0131t \u015eekil 2\u2019deki gibi KL boyunca C k\u00f6\u015fesi ile A k\u00f6\u015fesi \u00e7ak\u0131\u015facak bi\u00e7imde katlan\u0131yor. AA 65\u00b0 K 85\u00b0 CB x C B L \u015eekil 1 \u015eekil 2 Buna g\u00f6re son durumda x ile g\u00f6sterilen a\u00e7\u0131n\u0131n \u00f6l\u00e7\u00fcs\u00fc ka\u00e7 derecedir? D) 60 A) 45 B) 50 C) 55 4. A\u015fa\u011f\u0131da bir kuryenin kargo da\u011f\u0131taca\u011f\u0131 iki evin kargo \u015fubesine g\u00f6re konumlar\u0131 g\u00f6sterilmi\u015ftir. Kargo \u015eubesi a br c br I III II 1.Ev b br 2.Ev Kurye \u015fubeden \u00e7\u0131k\u0131p s\u0131ras\u0131yla I, II ve III do\u011frusal yollar\u0131n\u0131 kullanarak kargolar\u0131 b\u0131rak\u0131p tekrar \u015fubeye d\u00f6n\u00fcyor. a, b ve c de\u011ferleri 80 say\u0131s\u0131n\u0131n farkl\u0131 birer pozitif tam say\u0131 \u00e7arpan\u0131na e\u015fit oldu\u011funa g\u00f6re kuryenin ald\u0131\u011f\u0131 toplam yol en fazla ka\u00e7 birimdir? A) 140 B) 76 C) 46 D) 34 328 8. S\u0131n\u0131f","Pisagor Ba\u011f\u0131nt\u0131s\u0131 Dik \u00fc\u00e7gende 90\u00b0\u2019nin kar\u015f\u0131s\u0131ndaki kenara hipoten\u00fcs denir. \u00d6rnek: Bir dik \u00fc\u00e7gende dik kenarlar\u0131n uzunluklar\u0131n\u0131n kareleri toplam\u0131, hipoten\u00fcs uzunlu\u011funun karesine e\u015fittir. Bu e\u015fitli\u011fe Pisagor Ba\u011f\u0131nt\u0131s\u0131 denir. A b2 A hipboaten\u00fcs c2 c x2= 22+32 x2= 4+9 B C a2 + c2 = b2 3 cm x cm x2= 13 x= \u00e613 a2 B 2 cm C 77 \u00e7) P 2 cm S 1. A\u015fa\u011f\u0131daki dik \u00fc\u00e7genlerde verilmeyen kenar uzun- 8 cm x cm luklar\u0131n\u0131 bulunuz. a) A 5 cm x cm R d) T B 4 cm C 5\u00a72 cm x cm b) D 5 cm x cm V 10 cm Y e) A E 2 cm F 8 cm c) K x cm 4 cm x cm B L 6 cm M C 2\u00a73 cm 8. S\u0131n\u0131f 329","Pisagor Ba\u011f\u0131nt\u0131s\u0131 f) A \u0131) A x cm 2 cm D 3 cm D 7 cm cm x 4 cm B \u00e613 cm C B 2 cm C g) A x cm i) A 4 cm 6 cm D B 3\u00a75 cm x cm D 4 cm C B 4 cm 3 cm C \u011f) K x cm P j) 8 cm K L 5 cm 4 cm 4 cm x cm N L 3 cm N 2 cm M 5 cm M h) D k) P x cm T x cm 4 cm R 4 cm E H 12 cm 10 cm 3 cm 8 cm S 5 cm G F 330 8. S\u0131n\u0131f","Kenarlar\u0131na G\u00f6re \u00d6zel Dik \u00dc\u00e7genler 3-4-5 \u00dc\u00e7geni 5-12-13 \u00dc\u00e7geni 8-15-17 \u00dc\u00e7geni 7-24-25 \u00dc\u00e7geni 3k 5k 5k 13k 8k 17k 7k 25k 4k 12k 15k 24k Kenar uzunluklar\u0131 Kenar uzunluklar\u0131 Kenar uzunluklar\u0131 Kenar uzunluklar\u0131 3-4-5 ile orant\u0131l\u0131d\u0131r. 5-12-13 ile orant\u0131l\u0131d\u0131r. 8-15-17 ile orant\u0131l\u0131d\u0131r. 7-24-25 ile orant\u0131l\u0131d\u0131r. k = 1 ise 3-4-5 k = 1 ise 5-12-13 k = 1 ise 8-15-17 k = 1 ise 7-24-25 k = 2 ise 6-8-10 k = 2 ise 10-24-26 k = 2 ise 16-30-34 k = 2 ise 14-48-50 k = 3 ise 9-12-15 k = 4 ise 12-16-20 78 \u00e7) D x cm F 1. A\u015fa\u011f\u0131da \u015fekillerde verilmeyen kenar uzunlukla- 10 cm 26 cm r\u0131n\u0131 bulunuz. a) A 8 cm x cm E d) D B 6 cm C x cm 8 cm b) A 5 cm x cm E F e) K 15 cm B 12 cm C c) D 7 cm E x cm 48 cm x cm 25 cm F L 14 cm M 8. S\u0131n\u0131f 331","f) A x cm Kenarlar\u0131na G\u00f6re \u00d6zel Dik \u00dc\u00e7genler 8 cm D \u0131) K 30 cm 24 cm x cm L 10 cm N 18 cm M B 6 cm C g) 17 cm A i) K B 9 cm 50 cm D 60 cm 8 cm L 14 cm N x cm M C x cm \u011f) A j) P x cm 39 cm 16 cm x cm 20 cm RT B D 18 cm C 25 cm 60 cm S h) K 20 cm M k) P 25 cm x cm Nx cm R 24 cm L52 cm T 332 8. S\u0131n\u0131f 15 cm 7 cm S","Kenarlar\u0131na G\u00f6re \u00d6zel Dik \u00dc\u00e7genler NOT: \u00dc\u00e7 kenar uzunlu\u011fu verilen bir \u00fc\u00e7genin dik \u00fc\u00e7gen olup olmad\u0131\u011f\u0131n\u0131 anlamak i\u00e7in bu kenarlardan en uzun olan\u0131 hipoten\u00fcs olarak al\u0131n\u0131r. Ard\u0131ndan pisagor ba\u011f\u0131nt\u0131s\u0131 uygulan\u0131r. Pisagor ba\u011f\u0131nt\u0131s\u0131 sa\u011flan\u0131rsa bu \u00fc\u00e7gen dik \u00fc\u00e7gendir. 2. A\u015fa\u011f\u0131da kenar uzunluklar\u0131 verilen \u00fc\u00e7genlerden dik \u00fc\u00e7gen olanlar\u0131 belirleyerek alt\u0131ndaki kutucu\u011fa \u201c\ufffd\u201d i\u015fareti koyunuz. a) A b) A 4\u00a73 cm C c) A 4\u00a72 cm C 5 cm 6 cm \u00e633 cm 9 cm 4 cm 8 cm B B B C \u00ca61 cm \u00e7) 7 cm F d) D e) K D 3\u00a73 cm 10\u00a75 cm 6\u00a75 cm M 8 cm 10 cm \u00e615 cm L 8\u00a75 cm E 2\u00a73 cm F E 3. A\u015fa\u011f\u0131daki \u015fekilde verilmeyen kenar uzunluklar\u0131n\u0131 bulunuz. b) A 29 cm D a) A D 22 cm 13 cm 24 cm x cm E 15 cm B x cm C B 36 cm C 8. S\u0131n\u0131f 333","c) A Kenarlar\u0131na G\u00f6re \u00d6zel Dik \u00dc\u00e7genler 20 cm 20 cm 13 cm f) A 13 cm x cm x cm BD C B 10 cm D 4 cm C 24 cm \u00e7) M g) K 12 cm x cm 16 cm K x cm N 12 cm L 12 cm N 17 cm 17 cm M 12 cm L d) A x cm D h) A 7 cm B |AE|=? 5 cm 39 cm 36 cm C 5 cm D 4 cm E B 40 cm C e) P \u0131) S |KS|=? P 2 cm T 25 cm 5 cm x cm 3 cm M 4 cm N 3 cm K 5 cm L R 7 cm S 334 8. S\u0131n\u0131f","Kenarlar\u0131na G\u00f6re \u00d6zel Dik \u00dc\u00e7genler NOT: m(A\uf8ff) > 90\u00b0 ise 5. A\u015fa\u011f\u0131daki dikd\u00f6rtgenlerin bir k\u00f6\u015fegeninin uzun- a2 > b2 + c2 luklar\u0131n\u0131 bulunuz. A a) 30 br cb 16 br m(A)\uf8ff < 90\u00b0 ise B a C a2 < b2 + c2 4. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerde verilmeyen kenar uzun- b) 15 br luklar\u0131n\u0131n santimetre cinsinden alabilece\u011fi do\u011fal say\u0131 de\u011ferlerini bulunuz. 20 br a) A m( A\uf8ff )>90\u00b0 9 cm 12 cm Bx C c) 48 br b) m( L\uf8ff )>90\u00b0 14 br y K 12 cm L 16 cm M 6. A\u015fa\u011f\u0131daki \u00fc\u00e7genin birimkare cinsinden alan\u0131 ile birim cinsinden \u00e7evre uzunlu\u011fu fark\u0131n\u0131 bulunuz. A c) D 3x br 40 br m( F\uf8ff )>90\u00b0 13 cm 12 cm B 4x br C E zF 8. S\u0131n\u0131f 335","Koordinat Sisteminde Pisagor Ba\u011f\u0131nt\u0131s\u0131 Koordinat sisteminde \u00f6zellikle iki nokta aras\u0131 uzakl\u0131\u011f\u0131 hesaplamak i\u00e7in pisagor ba\u011f\u0131nt\u0131s\u0131n\u0131 kullanabiliriz. \u00d6rnek: Koordinat sisteminde K(\u20132,4) ile L(4,\u20134) noktalar\u0131 aras\u0131ndaki uzakl\u0131\u011f\u0131 bulunuz. y |KL|2 = 82 + 62 K4 |KL|2 = 64 + 36 |KL|2 = 100 8 br 4 x -2 O -4 |KL| = \u00ca100 = 10 6 br L 79 c) D(3,2) ve E(-1,-1) x 1. A\u015fa\u011f\u0131daki koordinat sistemlerinde verilen nokta- y lar aras\u0131ndaki uzakl\u0131klar\u0131 bulunuz. O a) A(-3,-3) ve B(2,3) y x O 2. A\u015fa\u011f\u0131daki noktalar\u0131n orijine uzakl\u0131klar\u0131n\u0131 bulunuz. a) A(3,\u20134) b) B(\u20133,5) b) K(-2,1) ve L(-5,-3) y x O NOT: Koordinat sisteminde A(x,y) ve B(x\u0131,y\u0131) noktalar\u0131n\u0131n aras\u0131ndaki uzakl\u0131\u011f\u0131 bulmak i\u00e7in a\u015fa\u011f\u0131daki ba\u011f\u0131nt\u0131 kullan\u0131labilir. |AB|2 = (x \u2013 x\u00d9)2 + (y \u2013 y\u00d9)2 336 8. S\u0131n\u0131f","Test Pisagor Ba\u011f\u0131nt\u0131s\u0131 K Uyguluyorum 77 4. M 1. A 8 cm 8 cm 8\u00a72 cm B 6 cm C L \u015eekildeki ABC \u00fc\u00e7geninde |AC| ka\u00e7 santimetredir? \u015eekilde KLM \u00fc\u00e7geninde |KM| ka\u00e7 santimetredir? A) 4 B) 6 C) 8 D) 10 A) 9 B) 10 C) 11 D) 12 5. A\u015fa\u011f\u0131daki do\u011fru par\u00e7alar\u0131ndan \u00fc\u00e7 tanesi kullan\u0131larak bir dik \u00fc\u00e7gen elde ediliyor. 2. A K 12 cm L 6 cm 4 cm M 15 cm N BC \u015eekildeki ABC \u00fc\u00e7geninde |BC| ka\u00e7 santimetredir? P 16 cm R A) 5\u00a72 B) \u00e651 C) 2\u00e613 D) \u00e653 S 20 cm T Buna g\u00f6re bunun i\u00e7in hangi do\u011fru par\u00e7as\u0131 kulla- n\u0131lmam\u0131\u015ft\u0131r? A) [KL] B) [MN] C) [PR] D) [ST] 3. A 13 cm B 12 cm C 6. \u00c7evre uzunlu\u011fu 24 cm olan karenin k\u00f6\u015fegen uzunlu\u011fu ka\u00e7 santimetredir? \u015eekildeki ABC \u00fc\u00e7geninde |AC| ka\u00e7 santimetredir? A) 5 B) 6 C) 7 D) 8 A) 12\u00a72 B) 12 C) 6\u00a72 D) 6 8. S\u0131n\u0131f 337","Uyguluyorum Pisagor Ba\u011f\u0131nt\u0131s\u0131 Test 77 7. 15 cm A 10. Koordinat sisteminde P(\u20134,7) noktas\u0131n\u0131n ba\u015flan- 9 cm g\u0131\u00e7 noktas\u0131na olan uzakl\u0131\u011f\u0131 ka\u00e7 birimdir? A) \u00e665 B) \u00e674 C) 3\u00e615 D) 5\u00e613 BC \u015eekildeki ABC \u00fc\u00e7geninin alan\u0131 ka\u00e7 santimetreka- redir? A) 36 B) 54 C) 72 D) 90 11. K 5 cm L \u00e619 cm M 10 cm N 8. A\u015fa\u011f\u0131da kenar uzunluklar\u0131 verilen \u00fc\u00e7genlerden \u015eekilde verilenlere g\u00f6re |KL| ka\u00e7 santimetredir? hangisi dik \u00fc\u00e7gen de\u011fildir? A) 2\u00e635 B) \u00ca141 C) \u00ca142 D) 12 A) 5 cm, 5 cm, 5\u00a72 cm B) 4 cm, 6 cm, 8 cm C) 3 cm, 3\u00a73 cm, 6 cm D) 8 cm, 15 cm, 17 cm 12. P 2 cm T 7 cm S 9. A 2\u00e611 cm 26 cm B D 10 cm C R 18 cm \u015eekilde verilenlere g\u00f6re |AB| ka\u00e7 santimetredir? \u015eeklide verilenlere g\u00f6re |RS| ka\u00e7 santimetredir? A) 40 B) 35 C) 30 D) 25 A) 9 B) 10 C) 11 D) 12 338 8. S\u0131n\u0131f","Test Pisagor Ba\u011f\u0131nt\u0131s\u0131 Uyguluyorum 78 1. A 4. K 1 cm B 7 cm C \u015eekildeki ABC \u00fc\u00e7geninde |AC| ka\u00e7 santimetredir? A) 9 B) 8 C) 5\u00a72 D) 4\u00a73 L M Kareli zeminde verilen KLM \u00fc\u00e7geninin kenar uzunluklar\u0131na g\u00f6re s\u0131ralan\u0131\u015f\u0131 a\u015fa\u011f\u0131dakilerden hangisinde verilmi\u015ftir? A) |KM| > |KL| > |LM| B) |KM| > |LM| > |KL| C) |KL| > |KM| > |LM| D) |KL| > |LM| > |KM| 2. A\u015fa\u011f\u0131daki bir k\u0131sm\u0131 k\u0131r\u0131lan ayd\u0131nlatma dire\u011finin g\u00f6- r\u00fcn\u00fcm\u00fc verilmi\u015ftir. 5. D 8m 16 cm 6m Buna g\u00f6re dire\u011fin k\u0131r\u0131lmadan \u00f6nceki uzunlu\u011fu 45\u00b0 ka\u00e7 metredir? E G 14 cm F A) 12 B) 14 C) 16 D) 18 \u015eekilde verilenlere g\u00f6re |DF| ka\u00e7 santimetredir? A) 30 B) 32 C) 34 D) 36 3. Uzun kenar\u0131 24 cm, k\u00f6\u015fegenlerinden birinin 6. Koordinat sisteminde K(5,2) ve L(\u20131,\u20134) noktala- uzunlu\u011fu 25 cm olan dikd\u00f6rtgen \u015feklindeki kar- r\u0131n\u0131n\u0131n aras\u0131ndaki uzakl\u0131k ka\u00e7 santimetredir? tonun bir y\u00fcz\u00fcn\u00fcn alan\u0131 ka\u00e7 santimetrekaredir? A) 168 B) 175 C) 192 D) 225 A) 10 B) 3\u00e610 C) 6\u00a72 D) 8 8. S\u0131n\u0131f 339","Uyguluyorum Pisagor Ba\u011f\u0131nt\u0131s\u0131 Test 78 7. 10. A\u015fa\u011f\u0131daki kareli zeminde verilen |KL| = 2\u00a75 cm\u2019dir. 3 cm x cm 3 cm z cm K D A C y cm 14 cm L 4 cm B 6 cm 12 cm \u015eekilde verilenlere g\u00f6re x + y \u2013 z ifadesinin de\u011feri ka\u00e7t\u0131r? A) 1 B) 2 C) 3 D) 4 Buna g\u00f6re ABCD dikd\u00f6rtgeninin alan\u0131 ka\u00e7 santi- metrekaredir? A) 40 B) 60 C) 80 D) 100 8. D 11. A\u015fa\u011f\u0131da daire bi\u00e7imindeki \u00f6zde\u015f \u00fc\u00e7 karton birbirine A 8 cm bir noktada temas edecek bi\u00e7imde ayn\u0131 do\u011frultuda E 30 cm yan yana yerle\u015ftirilmi\u015ftir. L B 20 cm C O O \u015eekilde verilenlere g\u00f6re |DE| ka\u00e7 santimetredir? K A) 12\u00a75 B) 10\u00a75 C) 20 D) 15 Kartonlardan birinin yar\u0131\u00e7ap\u0131 2\u00a73 cm oldu\u011funa g\u00f6re, K ve L noktalar\u0131 aras\u0131 uzakl\u0131k ka\u00e7 santimet- redir? A) 10\u00e615 B) 8\u00e615 C) 6\u00e615 D) 4\u00e615 9. A 12. 8\u00a73 cm 220 dm BDC 100 dm \u015eekildeki ABC \u00fc\u00e7geninin alan\u0131 64\u00a73 cm2 oldu\u011fu- na g\u00f6re \u00e7evresi ka\u00e7 santimetredir? 160 dm A) 16 B) 24 C) 36 D) 48 \u015eekilde zemine dik duran iki dire\u011fin u\u00e7 noktalar\u0131 aras\u0131ndaki uzakl\u0131k en az ka\u00e7 desimetredir? A) 280 B) 240 C) 200 D) 160 340 8. S\u0131n\u0131f","Test Pisagor Ba\u011f\u0131nt\u0131s\u0131 Ba\u015far\u0131yorum 79 1. \u015eekil 1\u2019de verilen basit makara d\u00fczene\u011finde, bir ucu C noktas\u0131na ba\u011fl\u0131 ve uzunlu\u011fu sabit olan ipin di\u011fer ucunda G cismi bulunmaktad\u0131r. B 12 m A B 12 m A 9m D GD G 7m CC \u015eekil I \u015eekil II Bu ip \u015eekil 2\u2019deki gibi D noktas\u0131na ba\u011fland\u0131\u011f\u0131nda G cismi ka\u00e7 metre a\u015fa\u011f\u0131ya iner? A) 4 B) 5 C) 6 D) 7 2. \u015eekil 1\u2019de gerilerek 30 cm h\u00e2line getirilmi\u015f bir lastik g\u00f6sterilmi\u015ftir. Bu lastik zemine paralel bi\u00e7imde sabit durumdad\u0131r. 30 cm CA 8 cm C A B \u015eekil 1 \u015eekil 2 Bu lasti\u011fin ortas\u0131na \u015eekil 2\u2019deki gibi bir cisim as\u0131ld\u0131\u011f\u0131nda lasti\u011fin orta noktas\u0131 ilk h\u00e2line g\u00f6re 8 cm a\u015fa\u011f\u0131 kay\u0131yor. Buna g\u00f6re lasti\u011fin son h\u00e2lindeki uzunlu\u011fu ka\u00e7 santimetredir? A) 30 B) 32 C) 34 D) 36 8. S\u0131n\u0131f 341","Ba\u015far\u0131yorum Pisagor Ba\u011f\u0131nt\u0131s\u0131 Test 79 3. A\u015fa\u011f\u0131da verilen a\u00e7\u0131k durumdaki bariyerde, bariyerin ba\u011fl\u0131 oldu\u011fu ve yere dik konumdaki mekanizman\u0131n y\u00fcksekli\u011fi 4 m\u2019dir. Bariyerin sa\u011f ucunun yere uzakl\u0131\u011f\u0131 12 m ve bu ucun zemine dik izd\u00fc\u015f\u00fcm\u00fc olan noktan\u0131n mekanizmaya uzakl\u0131\u011f\u0131 6 m\u2019dir. ? 12 m 4m 6m C) 15 \u015eekil 2 \u015eekil 1 D) 20 Buna g\u00f6re bariyerin uzunlu\u011fu ka\u00e7 metredir? A) 8 B) 10 4. \u015eekil 1\u2019de 170 cm y\u00fcksekli\u011findeki bir sandalye, y\u00fcksekli\u011fi 200 cm olan yere dik konumdaki duvara paralel olarak durmaktad\u0131r. 170 cm 200 cm 50 cm \u015eekil 1 x cm \u015eekil 2 Sandalye \u015eekil 2\u2019deki gibi duvara yasland\u0131\u011f\u0131nda sandalyenin duvara temas etti\u011fi nokta ile duvar\u0131n \u00fcst k\u0131sm\u0131 ara- s\u0131ndaki uzakl\u0131k 50 cm olmaktad\u0131r. Buna g\u00f6re sandalyenin yere temas eden aya\u011f\u0131n\u0131n duvara uzakl\u0131\u011f\u0131 ka\u00e7 santimetredir? A) 60 B) 70 C) 80 D) 90 342 8. S\u0131n\u0131f","Test Pisagor Ba\u011f\u0131nt\u0131s\u0131 Ba\u015far\u0131yorum 80 1. \u015eekil 1\u2019de verilen arac\u0131n kapal\u0131 durumdaki bagaj kapa\u011f\u0131n\u0131n alt noktas\u0131n\u0131n yere uzakl\u0131\u011f\u0131 80 cm\u2019dir. Bagaj kapa\u011f\u0131 \u015eekil 2\u2019deki gibi a\u00e7\u0131ld\u0131\u011f\u0131nda kapa\u011f\u0131n yere ve arabaya uzakl\u0131\u011f\u0131 160\u2019\u015far cm olmaktad\u0131r. ? 160 cm 160 cm 80 cm \u015eekil 1 \u015eekil 2 Buna g\u00f6re bagaj kapa\u011f\u0131n\u0131n uzunlu\u011fu (?) ka\u00e7 santimetredir? A) 100 B) 150 C) 200 D) 250 2. Yar\u0131\u00e7ap\u0131 r olan \u00e7emberin \u00e7evresi 2\u220fr\u2019dir. A\u015fa\u011f\u0131da \u015eekil 1\u2019de bir telin b\u00fck\u00fclmesiyle olu\u015fturulmu\u015f ve yar\u0131\u00e7ap uzunlu\u011fu verilen \u00e7ember \u015feklindeki b\u00f6lge g\u00f6ste- rilmi\u015ftir. 2 dm \u015eekil 1 \u015eekil 2 Bu tel a\u00e7\u0131larak uzunlu\u011funu kaybetmeden tekrar b\u00fck\u00fcl\u00fcyor ve \u015eekil 2\u2019deki gibi desimetre cinsinden kenar uzunluklar\u0131 tam say\u0131 olan \u00fc\u00e7gensel b\u00f6lge elde ediliyor. Buna g\u00f6re bu \u00fc\u00e7gensel b\u00f6lge i\u00e7in; I. E\u015fkenard\u0131r. II. Dar a\u00e7\u0131l\u0131d\u0131r. III. Dik a\u00e7\u0131l\u0131d\u0131r. yukar\u0131dakilerden hangileri s\u00f6ylenebilir? A) I ve II. B) I ve III. C) II ve III. D) I, II ve III. 8. S\u0131n\u0131f 343","Ba\u015far\u0131yorum Pisagor Ba\u011f\u0131nt\u0131s\u0131 Test 80 3. \u015eekilde A noktas\u0131ndaki bir u\u00e7ak B ve C rotalar\u0131n\u0131 takip ederek D noktas\u0131na ula\u015f\u0131yor. D A 100 br 260 br 60 br BC 160 br 100 br 100 br 340 br Buna g\u00f6re A ile D noktalar\u0131 aras\u0131ndaki en k\u0131sa uzakl\u0131k ka\u00e7 birimdir? A) 400 B) 360 C) 300 D) 240 4. Ferda\u2019n\u0131n dikd\u00f6rtgen bi\u00e7imindeki odas\u0131n\u0131n \u00fcstten g\u00f6r\u00fcn\u00fcm\u00fc, odas\u0131ndaki baz\u0131 uzunluklar\u0131n santimetre cinsinden de\u011feri ve odas\u0131n\u0131n kap\u0131s\u0131 kapal\u0131yken ayn\u0131 hizada olan kap\u0131 ve duvar\u0131n g\u00f6r\u00fcn\u00fcm\u00fc \u015eekil 1\u2019de verilmi\u015ftir. C 48 100 A B AB 36 100 \u015eekil 1 \u015eekil 2 Ferda, odas\u0131n\u0131n kap\u0131s\u0131n\u0131 bir miktar a\u00e7t\u0131\u011f\u0131nda, kap\u0131 dikd\u00f6rtgen bi\u00e7imindeki yata\u011f\u0131n k\u00f6\u015fesi olan C noktas\u0131na \u015eekil 2\u2019deki gibi de\u011fmektedir. Ferda kap\u0131s\u0131n\u0131n kapanmamas\u0131 i\u00e7in belirli bir uzunluktaki tahta par\u00e7as\u0131n\u0131 kap\u0131ya dik olacak bi\u00e7imde B noktas\u0131ndan C noktas\u0131na \u015eekil 2\u2019deki gibi yerle\u015ftirmi\u015ftir. Buna g\u00f6re tahta par\u00e7as\u0131n\u0131n uzunlu\u011fu ka\u00e7 santimetredir? A) 65 B) 60 C) 54 D) 45 344 8. S\u0131n\u0131f","E\u015flik ve Benzerlik E\u015f \u00c7okgenler \u0130ki veya daha fazla \u00e7okgenin kar\u015f\u0131l\u0131kl\u0131 kenarlar\u0131 ve a\u00e7\u0131lar\u0131n\u0131n \u00f6l\u00e7\u00fcleri e\u015fit ise bu \u00e7okgenlere e\u015f \u00e7okgenler denir ve \u201c\u2248\u201d sembol\u00fc ile g\u00f6sterilir. \u00d6rnek: A DK N ABCD\u2248KLMN Harflerin yaz\u0131l\u0131\u015f s\u0131ras\u0131 \u00f6nemlidir. CM BL m(A\uf8ff) = m(K)\uf8ff , m(B)\uf8ff = m(L)\uf8ff , m(C)\uf8ff = m(M)\uf8ff , m(D\uf8ff) = m(N\uf8ff) |AB| = |KL|, |BC| = |LM|, |CD| = |MN|, |DA| = |NK| 80 1. A\u015fa\u011f\u0131daki kareli zeminde numaraland\u0131r\u0131lm\u0131\u015f \u00e7okgenlerden e\u015f olan ikilileri bulunuz. 1 2 45 3 67 11 12 8 9 10 13 14 E\u015f \u00e7okgenler: 8. S\u0131n\u0131f 345","E\u015flik ve Benzerlik 2. A\u015fa\u011f\u0131da noktal\u0131 zeminde verilen \u00e7okgenlerin e\u015f- 4. A\u015fa\u011f\u0131daki \u015feklide ABCD \u2248 EFGH\u2019dir. lik durumlar\u0131n\u0131 yaz\u0131n\u0131z. Buna g\u00f6re x - y de\u011ferini bulunuz. D a) A A E (2x+3) cm H 15 cm D F BC B (3y) cm C F 12 cm G E b) K N T P S LM 5. A\u015fa\u011f\u0131daki \u015feklide MK\u2206L \u2248 MN\u2206P\u2019dir. R Buna g\u00f6re |MN|\u2019nu bulunuz. E\u015f olan a\u00e7\u0131lar: K 10 cm M 8 cm P E\u015f olan kenarlar: E\u015flik durumu: 3. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerin e\u015flik durumlar\u0131n\u0131 yaz\u0131n\u0131z. 11 cm a) A L 35\u00b0 N 25\u00b0 D B 8 cm C 25\u00b0 E 8 cm 6. E\u015flik Durumu: 120\u00b0 Uzun kenar\u0131n\u0131n uzunlu\u011fu 21 cm olan e\u015f dikd\u00f6rt- F genlerle olu\u015fturulmu\u015f yukar\u0131daki \u015feklin \u00e7evresini bulunuz. b) K M 70\u00b0 D 15 cm F 60\u00b0 13 cm 50\u00b0 60\u00b0 L E E\u015flik Durumu: 346 8. S\u0131n\u0131f","Benzer \u00c7okgenler \u0130ki veya daha fazla \u00e7okgende birbirine kar\u015f\u0131l\u0131k gelen a\u00e7\u0131 \u00f6l\u00e7\u00fcleri e\u015fit, kenar uzunluklar\u0131 orant\u0131l\u0131 ise bu \u00e7okgenlere benzer \u00e7okgenler denir. Benzerlik \u201c \u223c \u201d sembol\u00fc ile g\u00f6sterilir. \u00d6rnek: A \u2022 m(A)\uf8ff = m(D\uf8ff), m(B)\uf8ff = m(E\uf8ff), m(C\uf8ff) = m(F)\uf8ff D \u2022 Kar\u015f\u0131l\u0131kl\u0131 kenarlar\u0131n\u0131n oran\u0131 sabittir. 8 cm 6 cm 4 cm 3 cm 10 8 6 5 4 3 = = =2 (Benzerlik oran\u0131) B 10 cm CE 5 cm F AB\u2206C \u223c DE\u2206F \u2022 Benzer \u00e7okgenlerde orant\u0131l\u0131 kenarlar\u0131n oran\u0131na benzerlik oran\u0131 denir ve \u201ck\u201d ile g\u00f6sterilir. \u2022 E\u015f \u015fekiller ayn\u0131 zamanda benzerdir. Ancak benzer olan her \u015fekil e\u015f de\u011fildir. 81 3. A\u015fa\u011f\u0131daki kareli zeminde verilen \u00e7okgenlerin benzerlik oranlar\u0131n\u0131 bulunuz. 1. A\u015fa\u011f\u0131daki \u00e7okgen ile benzerlik oran\u0131 2 olacak bi- \u00e7imde daha b\u00fcy\u00fck bir \u00e7okgen \u00e7iziniz. a) 3 cm 3 cm 7 cm 6 cm b) 2. A\u015fa\u011f\u0131daki \u00fc\u00e7gen ile benzerlik oran\u0131 3 olacak bi- c) \u00e7imde daha k\u00fc\u00e7\u00fck bir \u00e7okgen \u00e7iziniz. 18 cm 36 cm 24 cm 8. S\u0131n\u0131f 347","Benzer \u00c7okgenler 4. A\u015fa\u011f\u0131da kareli zeminde verilen \u00e7okgenlerden benzer olanlar\u0131 bulunuz. D EF A BC 5. A\u015fa\u011f\u0131daki \u00e7okgenlerden ABCD \u223c EFGH\u2019dir. 7. A\u015fa\u011f\u0131daki benzer \u00e7okgenlerin \u00e7evrelerini bulu- nuz. Buna g\u00f6re verilmeyen kenarlar\u0131n uzunluklar\u0131n\u0131 bulunuz. a) E 9 cm H 25 cm AD 15 cm 15 cm 12 cm 8 cm 20 cm B 10 cm C F 15 cm G 6. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerin benzerlik oran\u0131 1 oldu\u011fu- b) 3 20 cm 16 cm na g\u00f6re PRS \u00fc\u00e7geninin \u00e7evresini bulunuz. 12 cm P 28 cm K 35 cm 7 cm 6 cm L 8 cm M R S NOT: Benzer iki \u00e7okgenin \u00e7evreleri oran\u0131, ben- NOT: Benzer iki \u00e7okgenin alanlar\u0131 oran\u0131, ben- zerlik oran\u0131na e\u015fittir. zerlik oran\u0131n\u0131n karesine e\u015fittir. 348 8. S\u0131n\u0131f","Benzer \u00c7okgenler 8. A\u015fa\u011f\u0131da verilen \u015fekillerin benzerlik oran\u0131 ve alanlar\u0131 oran\u0131n\u0131 bulunuz. a) 8 cm b) 6 cm 4 cm 4 cm 4 cm 8 cm 21 cm 14 cm Benzerlik oran\u0131: Alanlar\u0131 oran\u0131: Benzerlik oran\u0131: Alanlar\u0131 oran\u0131: 9. A\u015fa\u011f\u0131da verilen dikd\u00f6rtgenler benzer oldu\u011funa 11. A\u015fa\u011f\u0131daki \u015fekilde [DE] \/\/ [BC]\u2019dir. g\u00f6re x\u2019i bulunuz. A 8 cm (4x-2) cm 6 cm 8 cm 9 cm D 12 cm E 9 cm (3x+1) cm x cm B y cm C Buna g\u00f6re x ve y de\u011ferlerini bulunuz. 12. K 20 cm N 4 cm 10. PR\u2206S \u223c TVZ\u2206 , \u00c7evre_P&RSi = 3 ve |VZ| = 36 cm M \u00c7evre_T&VZi 4 5 cm LP oldu\u011funa g\u00f6re |RS| ka\u00e7 cm\u2019dir? \u015eekilde [KL] \/\/ [NP] oldu\u011funa g\u00f6re |LM| ka\u00e7t\u0131r? NOT: E\u015f \u00e7okgenlerin benzerlik oran\u0131 1\u2019dir. 8. S\u0131n\u0131f 349"]