{"id":3471,"date":"2023-09-23T07:26:38","date_gmt":"2023-09-23T07:26:38","guid":{"rendered":"https:\/\/www.sorumatix.com\/blog\/?p=3471"},"modified":"2023-09-23T07:26:38","modified_gmt":"2023-09-23T07:26:38","slug":"ayt-geometri-ucgende-aciortay-bagintilari-konu-anlatimi","status":"publish","type":"post","link":"https:\/\/www.sorumatix.com\/blog\/ayt-geometri-ucgende-aciortay-bagintilari-konu-anlatimi.html","title":{"rendered":"AYT &#8211; Geometri &#8211; \u00dc\u00e7gende A\u00e7\u0131ortay Ba\u011f\u0131nt\u0131lar\u0131 Konu Anlat\u0131m\u0131"},"content":{"rendered":"<p><center><iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/7lKnMSQl49Q\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/center><html><head><\/head><body><\/p>\n<p>\u00dc\u00e7gende A\u00e7\u0131ortay Ba\u011f\u0131nt\u0131lar\u0131: Geometrinin Sihirli D\u00fcnyas\u0131!<\/p>\n<p>Merhaba gen\u00e7ler! Bug\u00fcn sizlere geometri dersinde s\u0131kl\u0131kla kar\u015f\u0131la\u015faca\u011f\u0131n\u0131z ve AYT s\u0131nav\u0131nda da kar\u015f\u0131n\u0131za \u00e7\u0131kabilecek bir konudan bahsedece\u011fim: \u00dc\u00e7gende A\u00e7\u0131ortay Ba\u011f\u0131nt\u0131lar\u0131. Bu konu, \u00fc\u00e7genlerin i\u00e7 a\u00e7\u0131lar\u0131n\u0131n \u00f6zelliklerini inceleyerek, a\u00e7\u0131ortaylar\u0131n nas\u0131l ili\u015fkili oldu\u011funu ke\u015ffetmemizi sa\u011flar.<\/p>\n<p>Hadi ba\u015flayal\u0131m!<\/p>\n<p>1. A\u00e7\u0131ortay Nedir?<\/p>\n<p>A\u00e7\u0131ortay, bir \u00fc\u00e7genin i\u00e7 a\u00e7\u0131lar\u0131n\u0131 iki e\u015f par\u00e7aya b\u00f6len do\u011frudur. Bu do\u011fru, \u00fc\u00e7genin bir k\u00f6\u015fesinden kar\u015f\u0131 kenar\u0131na uzan\u0131r ve bu kenar\u0131 iki e\u015f par\u00e7aya b\u00f6ler. \u0130ki e\u015f par\u00e7an\u0131n bulu\u015ftu\u011fu nokta, \u00fc\u00e7genin i\u00e7 te\u011fet \u00e7emberinin merkezi olarak da adland\u0131r\u0131l\u0131r.<\/p>\n<p>2. A\u00e7\u0131ortay Ba\u011f\u0131nt\u0131lar\u0131<\/p>\n<p>\u00dc\u00e7gende A\u00e7\u0131ortay Ba\u011f\u0131nt\u0131lar\u0131, \u00fc\u00e7genin a\u00e7\u0131ortaylar\u0131 aras\u0131ndaki ili\u015fkileri inceler. \u015eimdi, bu ba\u011f\u0131nt\u0131lara bir g\u00f6z atal\u0131m:<\/p>\n<p>2.1. A\u00e7\u0131ortay Ba\u011f\u0131nt\u0131s\u0131 1<\/p>\n<p><center><img decoding=\"async\" src=\"https:\/\/www.sorumatix.com\/blog\/wp-content\/uploads\/2023\/09\/uploaded-image-ayt-geometri-ucgende-aciortay-bagintilari-konu-anlatimi-1694518049583.jpg\" title=\"AYT - Geometri - \u00dc\u00e7gende A\u00e7\u0131ortay Ba\u011f\u0131nt\u0131lar\u0131 Konu Anlat\u0131m\u0131 \" alt=\"AYT - Geometri - \u00dc\u00e7gende A\u00e7\u0131ortay Ba\u011f\u0131nt\u0131lar\u0131 Konu Anlat\u0131m\u0131 \"><\/center><\/p>\n<p>Bir \u00fc\u00e7gende, bir a\u00e7\u0131n\u0131n a\u00e7\u0131ortay\u0131 di\u011fer iki taraf\u0131 orant\u0131lar. Yani, bir \u00fc\u00e7genin bir a\u00e7\u0131s\u0131n\u0131n a\u00e7\u0131ortay\u0131 di\u011fer iki kenar\u0131 orant\u0131lar. Bu ba\u011f\u0131nt\u0131y\u0131 \u015fu \u015fekilde ifade edebiliriz:<\/p>\n<p>AC \/ AB = DC \/ DB<\/p>\n<p>Yukar\u0131daki ba\u011f\u0131nt\u0131da, A \u00fc\u00e7genin bir k\u00f6\u015fesi olup BC kenar\u0131n\u0131 ikiye b\u00f6len a\u00e7\u0131ortayd\u0131r. D noktas\u0131 ise bu a\u00e7\u0131ortay\u0131n BC kenar\u0131 ile kesi\u015fti\u011fi noktad\u0131r.<\/p>\n<p>2.2. A\u00e7\u0131ortay Ba\u011f\u0131nt\u0131s\u0131 2<\/p>\n<p>Bir \u00fc\u00e7gende, bir a\u00e7\u0131n\u0131n a\u00e7\u0131ortay\u0131 di\u011fer iki kar\u015f\u0131 kenar\u0131n uzunluklar\u0131n\u0131n oran\u0131yla ters orant\u0131l\u0131d\u0131r. Yani, bir \u00fc\u00e7genin bir a\u00e7\u0131s\u0131n\u0131n a\u00e7\u0131ortay\u0131, kar\u015f\u0131 kenarlar\u0131n uzunluklar\u0131na ters orant\u0131l\u0131d\u0131r. Bu ba\u011f\u0131nt\u0131y\u0131 \u015fu \u015fekilde ifade edebiliriz:<\/p>\n<p>AD \/ DB = AC \/ CB<\/p>\n<p>Yukar\u0131daki ba\u011f\u0131nt\u0131da, D noktas\u0131 \u00fc\u00e7genin bir k\u00f6\u015fesini ve BC kenar\u0131n\u0131 ikiye b\u00f6len a\u00e7\u0131ortayd\u0131r. Ayr\u0131ca, AC ve CB, s\u0131ras\u0131yla, D noktas\u0131ndan \u00f6nceki ve sonraki a\u00e7\u0131ortay\u0131n kenarlar\u0131d\u0131r.<\/p>\n<p>3. \u00d6rneklerle Anlama<\/p>\n<p>Geometriyi daha iyi anlamak i\u00e7in birka\u00e7 \u00f6rnek yapal\u0131m:<\/p>\n<p>\u00d6rnek 1:<\/p>\n<p>ABCD d\u00fczg\u00fcn d\u00f6rtgeninde, AD do\u011frusu DC do\u011frusunu yar\u0131ya b\u00f6lmektedir. Bu durumda, \u2220CAB a\u00e7\u0131s\u0131n\u0131n \u00f6l\u00e7\u00fcs\u00fc ka\u00e7 derecedir?<\/p>\n<p>\u00c7\u00f6z\u00fcm:<\/p>\n<p>AD, DC do\u011frusunu yar\u0131ya b\u00f6ld\u00fc\u011f\u00fcne g\u00f6re, ACD a\u00e7\u0131s\u0131n\u0131n \u00f6l\u00e7\u00fcs\u00fc 90\u00b0 olur. D\u00fczg\u00fcn d\u00f6rtgen oldu\u011fu i\u00e7in \u2220ADB a\u00e7\u0131s\u0131n\u0131n da \u00f6l\u00e7\u00fcs\u00fc 90\u00b0&#8217;dir. Ayr\u0131ca, a\u00e7\u0131ortay ba\u011f\u0131nt\u0131s\u0131 1&#8217;e g\u00f6re:<\/p>\n<p>AC \/ AB = CD \/ DB<\/p>\n<p>Yar\u0131ya b\u00f6l\u00fcnme durumu g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda,<\/p>\n<p>AC \/ AB = 1 \/ 2<\/p>\n<p>Yukar\u0131daki e\u015fitlikten dolay\u0131, AC = (1\/2)AB olur. Bu durumda, ABC \u00fc\u00e7geni acil \u00fc\u00e7gendir ve ABD a\u00e7\u0131s\u0131 da bir dik a\u00e7\u0131d\u0131r. ABD a\u00e7\u0131s\u0131n\u0131n \u00f6l\u00e7\u00fcs\u00fc 90\u00b0 oldu\u011fu i\u00e7in \u2220CAB a\u00e7\u0131s\u0131n\u0131n \u00f6l\u00e7\u00fcs\u00fc de 90\u00b0 olacakt\u0131r.<\/p>\n<p>\u00d6rnek 2:<\/p>\n<p>B<\/p>\n<p><\/body><\/html><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00dc\u00e7gende A\u00e7\u0131ortay Ba\u011f\u0131nt\u0131lar\u0131: Geometrinin Sihirli D\u00fcnyas\u0131! Merhaba gen\u00e7ler! Bug\u00fcn sizlere geometri dersinde s\u0131kl\u0131kla kar\u015f\u0131la\u015faca\u011f\u0131n\u0131z ve AYT s\u0131nav\u0131nda da kar\u015f\u0131n\u0131za \u00e7\u0131kabilecek<\/p>\n","protected":false},"author":1,"featured_media":3468,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"colormag_page_container_layout":"default_layout","colormag_page_sidebar_layout":"default_layout","footnotes":""},"categories":[3],"tags":[],"class_list":["post-3471","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematik-dersleri"],"_links":{"self":[{"href":"https:\/\/www.sorumatix.com\/blog\/wp-json\/wp\/v2\/posts\/3471","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sorumatix.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sorumatix.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sorumatix.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sorumatix.com\/blog\/wp-json\/wp\/v2\/comments?post=3471"}],"version-history":[{"count":0,"href":"https:\/\/www.sorumatix.com\/blog\/wp-json\/wp\/v2\/posts\/3471\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.sorumatix.com\/blog\/wp-json\/wp\/v2\/media\/3468"}],"wp:attachment":[{"href":"https:\/\/www.sorumatix.com\/blog\/wp-json\/wp\/v2\/media?parent=3471"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sorumatix.com\/blog\/wp-json\/wp\/v2\/categories?post=3471"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sorumatix.com\/blog\/wp-json\/wp\/v2\/tags?post=3471"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}