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Öğretmen, geometri konularını detaylı şekilde anlatırken Gökhan Hoca ile etkileşim halindedir.","Video, geometride \"hayat kurtaran teoremler\" olarak adlandırılan çeşitli teoremleri ele almaktadır. Stewart teoremi, kesen doğrular teoremi, ağırlık merkezi, Seba teoremi, Kar teoremi, Pisagor teoremi, sinüs teoremi ve kosinüs teoremi gibi temel geometri teoremleri detaylı olarak açıklanmaktadır. Her teorem önce teorik olarak anlatıldıktan sonra çeşitli örnek sorular üzerinden uygulamalı olarak gösterilmektedir.","Videoda ayrıca oran-orantı problemlerinin çözümünde kullanılan \"mela\" ve \"şalvar\" gibi özel yöntemler de anlatılmaktadır. Öğretmen, geometri problemlerini çözerken bu teoremlerin ve yöntemlerin nasıl kullanılabileceğini, farklı geometrik şekillerde (üçgenler, dörtgenler, çemberler) bu teoremlerin uygulamalarını örneklerle göstermektedir. Video boyunca interaktif bir öğrenme ortamı oluşturulmakta ve öğrencilerin kendileri de çözümlerini yapabilecekleri sorular sunulmaktadır."]},"endTime":3160,"title":"Geometri Teoremleri ve Çözüm Teknikleri Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Geometride Halka Kurtaran Teoremler","list":{"type":"unordered","items":["Videoda geometride üçgenler konusunun devamı olan kesen teoremleri ele alınacak.","Kesen teoremleri müfredatta olmayan ancak işimizi ve hayatımızı kolaylaştıran önemli bir kısım teoremlerdir.","Bu teoremler sadece üçgenlerde değil, dörtgende, çemberde, katı cisimde ve analitikte de kullanılabilir."]},"beginTime":0,"endTime":65,"href":"/video/preview/328436375355464995?parent-reqid=1765296973926528-3381655333883168211-balancer-l7leveler-kubr-yp-vla-125-BAL&text=geometri+tamircisi+%28g%C3%B6khan+%C3%B6zdo%C4%9Fan%29&t=0&ask_summarization=1"},{"index":1,"title":"Stewart Teoremi","list":{"type":"unordered","items":["İlk teorem Stewart teoremi olarak adlandırılır ve her türlü doğruyu çözebilen iddialı bir teoremdir.","Stewart teoremi, üçgende doğruyu dik, açıortay, kenarortay olmasına, üçgenin eşkenar veya ikizkenar olmasına gerek kalmadan çözer.","Teoremin formülü: e² = b²·c + a²·c / (a+b) - a·b'dir."]},"beginTime":65,"endTime":142,"href":"/video/preview/328436375355464995?parent-reqid=1765296973926528-3381655333883168211-balancer-l7leveler-kubr-yp-vla-125-BAL&text=geometri+tamircisi+%28g%C3%B6khan+%C3%B6zdo%C4%9Fan%29&t=65&ask_summarization=1"},{"index":2,"title":"Stewart Teoreminin Uygulamaları","list":{"type":"unordered","items":["İlk soruda BD doğruyu bulmak için Stewart teoremi kullanılır ve x² = 25 eşitliği çözülür.","İkinci soruda DC doğruyu bulmak için tekrar Stewart teoremi uygulanır ve x² = 16 bulunur.","Üçüncü soruda Stewart teoremi ile kenarortay probleminin çözümü gösterilir ve x² = 24 bulunur."]},"beginTime":142,"endTime":569,"href":"/video/preview/328436375355464995?parent-reqid=1765296973926528-3381655333883168211-balancer-l7leveler-kubr-yp-vla-125-BAL&text=geometri+tamircisi+%28g%C3%B6khan+%C3%B6zdo%C4%9Fan%29&t=142&ask_summarization=1"},{"index":3,"title":"Stewart Teoreminin Avantajları","list":{"type":"unordered","items":["Stewart teoremi, kenarortay, açıortay ve dış açıortay problemlerini de çözebilen çok yönlü bir teoremdir.","Diğer teoremler gibi özel durumları çözerken, Stewart teoremi her türlü doğruyu genel bir formülle çözebilir."]},"beginTime":569,"endTime":647,"href":"/video/preview/328436375355464995?parent-reqid=1765296973926528-3381655333883168211-balancer-l7leveler-kubr-yp-vla-125-BAL&text=geometri+tamircisi+%28g%C3%B6khan+%C3%B6zdo%C4%9Fan%29&t=569&ask_summarization=1"},{"index":4,"title":"Stewart Teoremi ve Benzerlik","list":{"type":"unordered","items":["Stewart teoremi, benzerlik ilişkilerini kullanarak üçgenlerde uzunlukları hesaplamak için kullanılır.","Küçük üçgen ile büyük üçgen arasında açı-açı-açı benzerliği vardır ve bu benzerlik ilişkisi Stewart teoreminin temelini oluşturur.","Stewart teoremi, üçgenlerde uzunlukları hesaplamak için alternatif bir yöntem sunar ve bazı soruları daha kolay çözmeyi sağlar."]},"beginTime":650,"endTime":689,"href":"/video/preview/328436375355464995?parent-reqid=1765296973926528-3381655333883168211-balancer-l7leveler-kubr-yp-vla-125-BAL&text=geometri+tamircisi+%28g%C3%B6khan+%C3%B6zdo%C4%9Fan%29&t=650&ask_summarization=1"},{"index":5,"title":"Stewart Teoreminin Uygulamaları","list":{"type":"unordered","items":["Stewart teoremi, dikme çizmek yerine daha kolay ve hızlı çözümler sunabilir.","Çemberde kuvvet teoremi (x² = m(m+n)) Stewart teoremine benzer şekilde kullanılabilecek bir formüldür.","Stewart teoremi, üçgenlerde dikme çizmek yerine daha pratik çözümler sunar ve matematik problemlerini çözmeyi hızlandırır."]},"beginTime":689,"endTime":801,"href":"/video/preview/328436375355464995?parent-reqid=1765296973926528-3381655333883168211-balancer-l7leveler-kubr-yp-vla-125-BAL&text=geometri+tamircisi+%28g%C3%B6khan+%C3%B6zdo%C4%9Fan%29&t=689&ask_summarization=1"},{"index":6,"title":"Küçük Stewart Teoremi","list":{"type":"unordered","items":["Küçük Stewart teoremi, Stewart teoreminin bir varyasyonu olup özellikle ikizkenar üçgenlerde kullanılır.","Küçük Stewart teoremi, Stewart teoremine göre daha basit bir formüldür ve açıortay teoremine benzer şekilde kullanılır.","Bu teorem, ikizkenar üçgenlerde uzunlukları hesaplamak için kullanılabilecek ve çember problemlerinde de uygulanabilir bir formüldür."]},"beginTime":801,"endTime":945,"href":"/video/preview/328436375355464995?parent-reqid=1765296973926528-3381655333883168211-balancer-l7leveler-kubr-yp-vla-125-BAL&text=geometri+tamircisi+%28g%C3%B6khan+%C3%B6zdo%C4%9Fan%29&t=801&ask_summarization=1"},{"index":7,"title":"Şalvar Şekli ve 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çözülebilir."]},"beginTime":1036,"endTime":1147,"href":"/video/preview/328436375355464995?parent-reqid=1765296973926528-3381655333883168211-balancer-l7leveler-kubr-yp-vla-125-BAL&text=geometri+tamircisi+%28g%C3%B6khan+%C3%B6zdo%C4%9Fan%29&t=1036&ask_summarization=1"},{"index":9,"title":"Meal Şekli ve Çözüm Yöntemi","list":{"type":"unordered","items":["Meal şekli de şalvar şekli gibi çözülebilir, ancak önce gerekli oranlar bulunmalıdır.","Meal şekli de paralel çizerek çözülebilir, ancak hangi noktadan paralel çizileceğine karar vermek zor olabilir.","Şekil bodoslama dönüştürüldüğünde, hangi noktadan paralel çizileceğine karar verme zorluğu ortadan kalkar."]},"beginTime":1147,"endTime":1311,"href":"/video/preview/328436375355464995?parent-reqid=1765296973926528-3381655333883168211-balancer-l7leveler-kubr-yp-vla-125-BAL&text=geometri+tamircisi+%28g%C3%B6khan+%C3%B6zdo%C4%9Fan%29&t=1147&ask_summarization=1"},{"index":10,"title":"Açıortay Problemi","list":{"type":"unordered","items":["Açıortay dikildiğinde ikizkenar üçgen oluşur ve bu durumda şalvar şekli görülebilir.","Şalvar şekli kullanılarak problem çözülebilir.","Müfredatta olup olmaması önemli değil, soruyu çözmek için en kolay yöntem kullanılmalıdır."]},"beginTime":1311,"endTime":1421,"href":"/video/preview/328436375355464995?parent-reqid=1765296973926528-3381655333883168211-balancer-l7leveler-kubr-yp-vla-125-BAL&text=geometri+tamircisi+%28g%C3%B6khan+%C3%B6zdo%C4%9Fan%29&t=1311&ask_summarization=1"},{"index":11,"title":"Geometri Sorularının Çözümü","list":{"type":"unordered","items":["Eğitmen, geometri sorularında şekil incelemesinin önemini vurguluyor ve soruyu çözmek için şekil üzerinde değişiklikler yapmanın faydalı olduğunu gösteriyor.","Eğitmen, \"şalvar\" olarak adlandırdığı geometrik yapıyı kullanarak soruyu çözmeyi gösteriyor ve püf noktaları belirliyor.","Ağırlık merkezi kavramını kullanarak soruyu çözmeyi gösteriyor ve geometrik oranlarla ilgili hesaplamalar yapıyor."]},"beginTime":1423,"endTime":1622,"href":"/video/preview/328436375355464995?parent-reqid=1765296973926528-3381655333883168211-balancer-l7leveler-kubr-yp-vla-125-BAL&text=geometri+tamircisi+%28g%C3%B6khan+%C3%B6zdo%C4%9Fan%29&t=1423&ask_summarization=1"},{"index":12,"title":"Ceva Teoremi","list":{"type":"unordered","items":["Ceva teoremi, üçgende üç doğru bir noktada kesiştiğinde uygulanabilecek bir teorem olarak tanımlanıyor.","Teorem, herhangi bir köşeden başlayarak çiçek yaparak oranların çarpımının bir olduğunu belirtiyor.","Teoremi farklı şekillerde ifade eden farklı yöntemler gösteriliyor, örneğin \"tut-bırak\" yöntemi kullanılarak çözüm yapılıyor."]},"beginTime":1622,"endTime":1752,"href":"/video/preview/328436375355464995?parent-reqid=1765296973926528-3381655333883168211-balancer-l7leveler-kubr-yp-vla-125-BAL&text=geometri+tamircisi+%28g%C3%B6khan+%C3%B6zdo%C4%9Fan%29&t=1622&ask_summarization=1"},{"index":13,"title":"Kar Teoremi","list":{"type":"unordered","items":["Kar teoremi, üçgende diklerin bir noktada kesiştiğinde uygulanabilecek bir teorem olarak tanımlanıyor.","Teorem, tuttuklarının kareleri toplamının tutmadıklarının kareleri toplamına eşit olduğunu belirtiyor.","İkizkenar üçgen örneği kullanılarak teorem uygulanıyor ve Pisagor teoremiyle ilişkisi gösteriliyor."]},"beginTime":1752,"endTime":1893,"href":"/video/preview/328436375355464995?parent-reqid=1765296973926528-3381655333883168211-balancer-l7leveler-kubr-yp-vla-125-BAL&text=geometri+tamircisi+%28g%C3%B6khan+%C3%B6zdo%C4%9Fan%29&t=1752&ask_summarization=1"},{"index":14,"title":"Teoremin Uygulama Alanları","list":{"type":"unordered","items":["Teorem sadece belirli bir formatta değil, farklı şekillerde de uygulanabilir.","Diklerin kesiştiği veya uzantılarının kesiştiği noktada uygulama yapılabilir.","Teorem, dışarıdaki bir noktadan dikler atıldığında da aynı mantıkla çalışabilir."]},"beginTime":1896,"endTime":2090,"href":"/video/preview/328436375355464995?parent-reqid=1765296973926528-3381655333883168211-balancer-l7leveler-kubr-yp-vla-125-BAL&text=geometri+tamircisi+%28g%C3%B6khan+%C3%B6zdo%C4%9Fan%29&t=1896&ask_summarization=1"},{"index":15,"title":"Sinüs Teoremi","list":{"type":"unordered","items":["Sinüs teoremine göre her kenar, gördüğü açının sinüsü ile orantılıdır.","Teoremdeki \"r\" değeri, üçgenin çevrel çemberinin yarıçapıdır.","Sinüs teoremi, trigonometrik bilgiler gerektirir ve toplamları 90 ve 180 yapan açılar hakkında bilgi sahibi olmak önemlidir."]},"beginTime":2090,"endTime":2188,"href":"/video/preview/328436375355464995?parent-reqid=1765296973926528-3381655333883168211-balancer-l7leveler-kubr-yp-vla-125-BAL&text=geometri+tamircisi+%28g%C3%B6khan+%C3%B6zdo%C4%9Fan%29&t=2090&ask_summarization=1"},{"index":16,"title":"Sinüs Teoreminin Uygulamaları","list":{"type":"unordered","items":["Sinüs teoremi, kenar ve açı değerlerini hesaplamak 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