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Eğitmen, geometri ve trigonometri konularındaki önemli teoremleri detaylı şekilde anlatmaktadır.","Videoda Stewart, Ceva, Carnot, Menelaus, sinüs ve kosinüs teoremleri açıklanmakta ve her biri için sayısal örnekler çözülmektedir. Eğitmen, bu teoremlerin özellikle ÖSS ve TÜBİTAK sınavlarında önemli olduğunu vurgulamakta ve teorik bilgilerin yanı sıra pratik çözümlerle desteklenmektedir.","Video, özel açıların sinüs ve kosinüs değerlerinin hatırlatılmasıyla devam etmekte ve 1998 yılı sınav soruları üzerinden örnekler verilmektedir. Özellikle sinüs ve kosinüs teoremleri için özel açıların (30°, 45°, 60°, 120°, 135°, 150°) değerlerinin ezberlenmesi gerektiği vurgulanmaktadır."]},"endTime":3768,"title":"Geometri ve Trigonometri Teoremleri Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Geometriye Özel Teoremler","list":{"type":"unordered","items":["Bu derste geometrinin en önemli ve teknik konularından özel teoremler anlatılacaktır.","Son yıllarda zorlaşan geometri sorularında bu konuyu iyi özümsemek gerekmektedir.","Stewart teoremi, özel teoremlerden en önemlilerinden biridir."]},"beginTime":1,"endTime":48,"href":"/video/preview/11530514730157355730?parent-reqid=1776620502751935-2578710650756820149-balancer-l7leveler-kubr-yp-vla-256-BAL&text=T3+Akademi&t=1&ask_summarization=1"},{"index":1,"title":"Stewart Teoremi","list":{"type":"unordered","items":["Stewart teoremi, bir üçgende köşeden çıkan doğru karşısındaki kenarı farklı iki bölgeye ayırırken kullanılır.","Formülü: x² = (b²·m + c²·n) / (m+n) - m·n'dir.","Stewart teoremi ile bir üçgende verilen beş uzunluktan biri istenirse, aranan uzunluk bulunabilir."]},"beginTime":48,"endTime":148,"href":"/video/preview/11530514730157355730?parent-reqid=1776620502751935-2578710650756820149-balancer-l7leveler-kubr-yp-vla-256-BAL&text=T3+Akademi&t=48&ask_summarization=1"},{"index":2,"title":"Stewart Teoremi Örneği","list":{"type":"unordered","items":["Örnek problemde x uzunluğu, Stewart teoremi veya daha sonra öğrenecekleriz kosinüs teoremi ile bulunabilir.","Formül uygulandığında x² = 20 olarak hesaplanır ve x = 2√5 birim olarak bulunur.","Stewart teoremi, herhangi bir üçgende karşısındaki kenarı iki parçaya bölen doğru parçasının uzunluğunu bulmak için kullanılır."]},"beginTime":148,"endTime":352,"href":"/video/preview/11530514730157355730?parent-reqid=1776620502751935-2578710650756820149-balancer-l7leveler-kubr-yp-vla-256-BAL&text=T3+Akademi&t=148&ask_summarization=1"},{"index":3,"title":"Ceva Teoremi","list":{"type":"unordered","items":["Ceva teoremi, üçgenin içinde kesişen üç doğru parçası ve tabanlarda ayırdıkları parçaların uzunlukları arasındaki ilişkiyi gösterir.","Formülü: (a/b) · (c/b) · (f/b) = 1'dir.","Son 15 yıldan beri üniversite seçme sınavlarında sorulmamış olsa da, her zaman için aklımızda bulundurulması gereken önemli bir teoremdir."]},"beginTime":352,"endTime":497,"href":"/video/preview/11530514730157355730?parent-reqid=1776620502751935-2578710650756820149-balancer-l7leveler-kubr-yp-vla-256-BAL&text=T3+Akademi&t=352&ask_summarization=1"},{"index":4,"title":"Ceva Teoremi Örneği","list":{"type":"unordered","items":["Örnek problemde ABC üçgeninde A köşesinden çıkan doğru BC'yi K'da, B köşesinden çıkan doğru AC'yi M'de, C köşesinden çıkan doğru AB'yi N'de kesiyor.","BK = 2, KC = 3, MC = 5, MA = 2, AN = 8 birim ise, AN uzunluğu Ceva teoremi ile bulunur.","Hesaplamalar sonucunda AN = 3 birim olarak bulunur."]},"beginTime":497,"endTime":693,"href":"/video/preview/11530514730157355730?parent-reqid=1776620502751935-2578710650756820149-balancer-l7leveler-kubr-yp-vla-256-BAL&text=T3+Akademi&t=497&ask_summarization=1"},{"index":5,"title":"Carnot Teoremi","list":{"type":"unordered","items":["Carnot teoremi, üçgenin içindeki herhangi bir noktadan kenarlarına indirilen dikmelerin ayakları arasındaki ilişkileri gösterir.","Formülü: h₁² + h₃² = m² + p² = k² + t²'dir.","Bu teorem, TÜBİTAK sınavlarında dikkat edilmesi gereken temel formül olarak karşımıza çıkmaktadır."]},"beginTime":693,"endTime":865,"href":"/video/preview/11530514730157355730?parent-reqid=1776620502751935-2578710650756820149-balancer-l7leveler-kubr-yp-vla-256-BAL&text=T3+Akademi&t=693&ask_summarization=1"},{"index":6,"title":"Üçgende Nokta ve Kenar Uzunlukları","list":{"type":"unordered","items":["ABC üçgenindeki herhangi bir nokta P'den tabanlara dikler indirilerek, P noktasının kenarlara olan uzaklıkları (x, 2, 3, 4, 7, 5, 12, 4 birim) kullanılarak bir formül uygulanmaktadır.","Formül uygulaması sonucunda x² = 28 bulunur ve x değeri 2√7 olarak hesaplanır."]},"beginTime":876,"endTime":1021,"href":"/video/preview/11530514730157355730?parent-reqid=1776620502751935-2578710650756820149-balancer-l7leveler-kubr-yp-vla-256-BAL&text=T3+Akademi&t=876&ask_summarization=1"},{"index":7,"title":"Menelaus Teoremi","list":{"type":"unordered","items":["Menelaus teoremi, üçgende önemli bir teorem olup, bir doğru üçgenin kenarlarını keserse oluşan kesim noktaları arasındaki oranların çarpımı 1'e eşit olduğunu belirtir.","Menelaus teoremi, benzerlik uygulaması değerlendirmesi yapılarak bulunabilir ve geometri problemlerinde çözüm için kullanılır.","Menelaus teoremi, bir doğru üçgenin kenarlarını keserken (birinci kesim, ikinci kesim ve uzantıda üçüncü kesim) oluşan kesim noktaları arasındaki oranların çarpımı 1'e eşit olduğunu gösterir."]},"beginTime":1021,"endTime":1326,"href":"/video/preview/11530514730157355730?parent-reqid=1776620502751935-2578710650756820149-balancer-l7leveler-kubr-yp-vla-256-BAL&text=T3+Akademi&t=1021&ask_summarization=1"},{"index":8,"title":"Menelaus Teoreminin Uygulaması","list":{"type":"unordered","items":["Menelaus teoremi, üçgenin farklı kenarları üzerindeki kesim noktaları için de geçerlidir ve her iki yönünde uygulanabilir.","Menelaus teoremi, üçgenin kenarlarını kesen bir doğru için kesim noktaları arasındaki oranların çarpımı 1'e eşit olduğunu gösterir.","Menelaus teoremi, geometri problemlerinde kesim noktalarını bulmak için kullanılır ve orantı kurarak çözümler yapılabilir."]},"beginTime":1326,"endTime":1624,"href":"/video/preview/11530514730157355730?parent-reqid=1776620502751935-2578710650756820149-balancer-l7leveler-kubr-yp-vla-256-BAL&text=T3+Akademi&t=1326&ask_summarization=1"},{"index":9,"title":"Sinüs Teoremi","list":{"type":"unordered","items":["Sinüs teoremi, özel 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(kök2/2)."]},"beginTime":1808,"endTime":1899,"href":"/video/preview/11530514730157355730?parent-reqid=1776620502751935-2578710650756820149-balancer-l7leveler-kubr-yp-vla-256-BAL&text=T3+Akademi&t=1808&ask_summarization=1"},{"index":11,"title":"Sinüs Teoremi Uygulaması","list":{"type":"unordered","items":["Sinüs teoremi uygulamak için üçgenin iki açısı ve karşılık gelen iki kenar bilinmelidir.","İlk örnekte, 75 derece, 60 derece ve kök2 uzunluğuna sahip üçgende x kenarının değeri 2/3 olarak bulunmuştur.","Sinüs teoremi orantı kurarak çapraz çarpımların birbirine eşit olduğu prensibiyle uygulanır."]},"beginTime":1899,"endTime":2139,"href":"/video/preview/11530514730157355730?parent-reqid=1776620502751935-2578710650756820149-balancer-l7leveler-kubr-yp-vla-256-BAL&text=T3+Akademi&t=1899&ask_summarization=1"},{"index":12,"title":"İkinci Sinüs Teoremi Örneği","list":{"type":"unordered","items":["Bir üçgende bir köşeden çıkan doğru karşısını iki eşit parçaya bölerken, sinüs teoremi uygulanabilir.","İki üçgen için ayrı ayrı sinüs teoremi yazılabilir ve sonuçlar birleştirilebilir.","Sonuç olarak, teta açısının sinüsü 1/2 olarak bulunmuş ve teta açısının 30 derece olduğu belirlenmiştir."]},"beginTime":2139,"endTime":2484,"href":"/video/preview/11530514730157355730?parent-reqid=1776620502751935-2578710650756820149-balancer-l7leveler-kubr-yp-vla-256-BAL&text=T3+Akademi&t=2139&ask_summarization=1"},{"index":13,"title":"Kosinüs Teoremi","list":{"type":"unordered","items":["Kosinüs teoremi uygulamak için üçgenin üç kenarı ve bir açısı bilinmelidir.","Önemli açıların kosinüs değerleri: kos30= kök3/2, kos45= kök2/2, kos60= 1/2, kos150= -kök3/2, kos135= -kök2/2, kos120= -1/2'dir.","Kosinüs teoremi formülü: c² = a² + b² - 2ab·cos(alfa) 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Bir öğretmen, 8. sınıf öğrencilerine geometri konularını anlatmaktadır.","Video, üçgenin yardımcı elemanları (yükseklik, kenarortay, açıortay ve kenar orta dikme) ile üçgenlerin kenarları arasındaki bağıntıları (iki kenarın toplamının bir kenardan fazla olmaması, farkının ise bir kenardan küçük olmaması) detaylı şekilde açıklamaktadır. Ayrıca açılar arasındaki bağıntılar, üçgenlerin iç açıları toplamı, dikdörtgenlerin çevre ve alan hesaplamaları gibi konular ele alınmaktadır.","Video, teorik bilgilerin ardından örnek sorularla devam etmekte ve öğrencilerin geometri sorularını çözebilmeleri için pratik çözümler sunmaktadır. Üçgen türlerinin (dar açılı, dik açılı, geniş açılı) yardımcı elemanların konumları ve ikizkenar üçgenlerle ilgili bağıntılar da videoda işlenen konular arasındadır."]},"endTime":1356,"title":"8. 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Video, temel mantığı iyi öğrendiğimizde harfli ifadelerle de aynı kolaylıkla çözülebileceğini vurgulayarak sona ermektedir."]},"endTime":611,"title":"Yüzde Problemleri Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Yüzde Problemleri Giriş","list":{"type":"unordered","items":["Bu derste bir değer diğerinin yüzde kaçına eşit olduğu soruları çözülecek.","Sonlara doğru bilmeyen ifadelerle bu tür soruların nasıl karşımıza geldiği gösterilecek."]},"beginTime":19,"endTime":36,"href":"/video/preview/538227301314255384?parent-reqid=1776620502751935-2578710650756820149-balancer-l7leveler-kubr-yp-vla-256-BAL&text=T3+Akademi&t=19&ask_summarization=1"},{"index":1,"title":"İlk Örnek Soru","list":{"type":"unordered","items":["24 sayısı 40 sayısının yüzde kaçına eşittir sorusunda üç farklı çözüm yolu gösteriliyor.","İlk yol: 24/40 = 2/5 = 60/100 = %60 olarak hesaplanıyor.","İkinci yol: 24/40 = 12/20 = 60/100 = %60 olarak hesaplanıyor.","Üçüncü yol: 40/24 = 10/12 = 60/100 = %60 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bulunuyor ve hesap makinesinde sürekli 6 olarak devreden geçiyor."]},"beginTime":191,"endTime":290,"href":"/video/preview/538227301314255384?parent-reqid=1776620502751935-2578710650756820149-balancer-l7leveler-kubr-yp-vla-256-BAL&text=T3+Akademi&t=191&ask_summarization=1"},{"index":4,"title":"Dördüncü Örnek Soru","list":{"type":"unordered","items":["Ali 45, Veli ise 18 yaşındadır ve Velinin yaşı Ali'nin yaşının yüzde kaçını eşittir sorusunda çözüm yapılıyor.","İlk yol: 18/45 × 100 = 20/100 = %40 olarak hesaplanıyor.","İkinci yol: 18/45 = x/100 = 20/100 = %40 olarak hesaplanıyor."]},"beginTime":290,"endTime":345,"href":"/video/preview/538227301314255384?parent-reqid=1776620502751935-2578710650756820149-balancer-l7leveler-kubr-yp-vla-256-BAL&text=T3+Akademi&t=290&ask_summarization=1"},{"index":5,"title":"Beşinci Örnek Soru","list":{"type":"unordered","items":["Yüzde sekseni dolu olan bir havuza içindeki suyun yüzde kaçı kadar su eklenirse havuz dolar sorusunda çözüm yapılıyor.","Havuz 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