{"id":3090,"date":"2011-10-05T10:46:13","date_gmt":"2011-10-05T07:46:13","guid":{"rendered":"http:\/\/www.islamidavet.com\/kutuphane\/\/?p=3090"},"modified":"2011-10-05T10:46:13","modified_gmt":"2011-10-05T07:46:13","slug":"aci-kenar-bagintilari","status":"publish","type":"post","link":"https:\/\/www.islamidavet.com\/kutuphane\/aci-kenar-bagintilari\/","title":{"rendered":"A\u00e7\u0131-Kenar Ba\u011f\u0131nt\u0131lar\u0131"},"content":{"rendered":"<p>1. Bir \u00fc\u00e7gende \u00f6l\u00e7\u00fcs\u00fc b\u00fcy\u00fck olan a\u00e7\u0131n\u0131n kar\u015f\u0131s\u0131ndaki kenar uzunlu\u011fu, \u00f6l\u00e7\u00fcs\u00fc k\u00fc\u00e7\u00fck olan a\u00e7\u0131n\u0131n kar\u015f\u0131s\u0131ndaki kenar uzunlu\u011fundan daha b\u00fcy\u00fckt\u00fcr.ABC \u00fc\u00e7geninde m(A) > m(B) > m(C)<br \/>\na > b > c<br \/>\nTerside ge\u00e7erlidir. Uzun kenar\u0131 g\u00f6ren a\u00e7\u0131 k\u0131sa kenar\u0131 g\u00f6ren a\u00e7\u0131dan daha b\u00fcy\u00fckt\u00fcr.<br \/>\n\u0130kizkenar \u00fc\u00e7genden de bildi\u011fimiz gibi e\u015fit a\u00e7\u0131lar\u0131n kar\u015f\u0131lar\u0131ndaki kenarlar e\u015fittir.<br \/>\nm(B) = m(C) => |AB| = |AC|<br \/>\nm(A) < m(B) = m(C) ise\n|BC| < |AB| = |AC| olur.\n\nBir \u00fc\u00e7gende bir tane geni\u015f a\u00e7\u0131 olabilece\u011finden geni\u015f a\u00e7\u0131n\u0131n kar\u015f\u0131s\u0131ndaki kenar daima en b\u00fcy\u00fck kenar olur.\n2. Bir \u00fc\u00e7gende herhangi bir kenar\u0131n uzunlu\u011fu di\u011fer iki kenar\u0131n uzunluklar\u0131 toplam\u0131ndan k\u00fc\u00e7\u00fck fark\u0131n\u0131n mutlak de\u011ferinden b\u00fcy\u00fckt\u00fcr. ABC \u00fc\u00e7geninde \nlb - c l <a < (b + c)Di\u011fer kenarlar i\u00e7in de ayn\u0131 durum ge\u00e7erlidir.\n|a \u2013 c| < b < (a + c) ve |a \u2013 b| < c < (a + b) olur.\n3. Dik, dar ve geni\u015f a\u00e7\u0131l\u0131 \u00fc\u00e7genlerde kenarlar aras\u0131ndaki ili\u015fkiler. a. Bir dik \u00fc\u00e7gende\nkenarlar aras\u0131nda\na2 = b2 + c2 ba\u011f\u0131nt\u0131s\u0131 vard\u0131r.\nb. Dar a\u00e7\u0131l\u0131 \u00fc\u00e7gen b ve c sabit tutulup A a\u00e7\u0131s\u0131 k\u00fc\u00e7\u00fclt\u00fcl\u00fcrse a da k\u00fc\u00e7\u00fcl\u00fcr.\nm(A) < 90\u00b0 \u00db a2 < b2 + c3c. Geni\u015f a\u00e7\u0131l\u0131 \u00fc\u00e7gen b ve c sabit tutulup A a\u00e7\u0131s\u0131 b\u00fcy\u00fct\u00fcl\u00fcrse a da b\u00fcy\u00fcr.\nm(A) < 90\u00b0 \u00db a2 > b2 + c34. \u00c7e\u015fitkenar bir \u00fc\u00e7gende ayn\u0131 k\u00f6\u015feden \u00e7izilen y\u00fckseklik, a\u00e7\u0131ortay ve kenarortay uzunluklar\u0131n\u0131n s\u0131ralanmas\u0131,|AH| = ha ; y\u00fckseklik<br \/>\n|AN| = nA ; a\u00e7\u0131ortay<br \/>\n|AD| = Va ; kenarortay<\/p>\n<p>ha< nA <Va\n5. \u00c7e\u015fitkenar bir \u00fc\u00e7gende, a\u00e7\u0131, a\u00e7\u0131ortay, kenarortay ve y\u00fckseklik aras\u0131ndaki s\u0131ralama;\nABC \u00fc\u00e7geninde a, b, c kenar uzunluklar\u0131d\u0131r. \nm(A) > m(B) > m(C) oldu\u011funa varsayal\u0131m.<br \/>\nBu durumda \u00fc\u00e7gende<br \/>\nkenarlar : a > b > c<br \/>\ny\u00fckseklikler : ha < hb < hc\nA\u00e7\u0131ortaylar : nA < nB < nC\nKenarortaylar : Va < Vb < Vc\n\u015feklinde s\u0131ralan\u0131rlar. Yani \u00fc\u00e7genin yard\u0131mc\u0131 elemanlar\u0131 kenarlar\u0131n\u0131n s\u0131ras\u0131na ters olarak s\u0131ralan\u0131r.\nE\u015fkenar ve ikizkenar \u00fc\u00e7gen i\u00e7in bu s\u0131ralamalar ge\u00e7erli de\u011fildir.\n6. Bir kenarlar\u0131 ortak olan i\u00e7i\u00e7e iki \u00fc\u00e7genden i\u00e7tekinin \u00e7evresi daha k\u00fc\u00e7\u00fck olur. \n|BD| + |DC| < |AB| + |AC|\nABCD bir d\u00f6rtgen, a, b, c, d kenar uzunluklar\u0131 [AC] ve [BD] k\u00f6\u015fegenlerdir.\nABCD d\u00f6rtgeninde kar\u015f\u0131l\u0131kl\u0131 kenarlar\u0131n uzunluklar\u0131 toplam\u0131, k\u00f6\u015fegenlerin uzunluklar\u0131 toplam\u0131ndan k\u00fc\u00e7\u00fckt\u00fcr.\na + c < |AC| + |BD| ve b + d < |AC| + |BD|\nk\u00f6\u015fegen uzunluklar\u0131 toplam\u0131 \u00e7evreden daha b\u00fcy\u00fck ve \u00e7evrenin yar\u0131s\u0131ndan daha k\u00fc\u00e7\u00fck olamaz.\n\u0130\u00e7 i\u00e7e \u015fekillerde i\u00e7teki \u015feklin \u00e7evresi daha k\u00fc\u00e7\u00fck olaca\u011f\u0131ndan\n|DA| + |AB| + |BC|\ntoplam\u0131 |DE| + |EF| + |FC|\ntoplam\u0131ndan daha b\u00fcy\u00fckt\u00fcr. \n \n7. ABC \u00fc\u00e7geninin i\u00e7indeki herhangi bir P noktas\u0131 i\u00e7in; |AP| + |BP| + |CP|\ntoplam\u0131 ABC \u00fc\u00e7geninin \u00e7evresinden b\u00fcy\u00fck, \u00e7evresinin yar\u0131s\u0131ndan k\u00fc\u00e7\u00fck olamaz.\n \nBurada ve \u00c7evre de\u011ferleri s\u0131n\u0131r de\u011fer de\u011fildir.\n<\/p>\n","protected":false},"excerpt":{"rendered":"<p>1. Bir \u00fc\u00e7gende \u00f6l\u00e7\u00fcs\u00fc b\u00fcy\u00fck olan a\u00e7\u0131n\u0131n kar\u015f\u0131s\u0131ndaki kenar uzunlu\u011fu, \u00f6l\u00e7\u00fcs\u00fc k\u00fc\u00e7\u00fck olan a\u00e7\u0131n\u0131n kar\u015f\u0131s\u0131ndaki kenar uzunlu\u011fundan daha b\u00fcy\u00fckt\u00fcr.ABC \u00fc\u00e7geninde m(A) > m(B) > m(C) a > b > c Terside ge\u00e7erlidir. Uzun kenar\u0131 g\u00f6ren a\u00e7\u0131 k\u0131sa kenar\u0131 g\u00f6ren a\u00e7\u0131dan daha b\u00fcy\u00fckt\u00fcr. \u0130kizkenar \u00fc\u00e7genden de bildi\u011fimiz gibi e\u015fit a\u00e7\u0131lar\u0131n kar\u015f\u0131lar\u0131ndaki kenarlar e\u015fittir. m(B) = m(C) &hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1404,1403],"tags":[7288,7224,7223],"class_list":["post-3090","post","type-post","status-publish","format-standard","hentry","category-matematik-odevleri","category-odevler","tag-aci-kenar-bagintilari","tag-aciortay","tag-kenarortay"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3090","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/comments?post=3090"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3090\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=3090"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=3090"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=3090"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}