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sınıf matematik alan, 10 sınıf üçgende alan, Değerli 10. sınıf öğrencilerim maarif modeli, yeni müfredat 10. sınıf matematik konu anlatımlarımıza hoş geldiniz. açıortay, kenarortay, yükseklik...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/4613253/1b87e902c1fb1d2625009ff12281deff/564x318_1"},"target":"_self","position":"3","reqid":"1765274132018437-8301958655174908337-balancer-l7leveler-kubr-yp-sas-128-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1765274132018437-8301958655174908337-balancer-l7leveler-kubr-yp-sas-128-BAL&text=videoid:3611667998137082801","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin 10. sınıf öğrencilerine yönelik hazırladığı kapsamlı bir eğitim içeriğidir. Öğretmen, üçgenlerde alan hesaplamaları ve benzerlik konularını detaylı şekilde anlatmaktadır.","Video, üçgende alan formülleri ile başlayıp, sinüs alan formülü, üçgenlerde alan parçalamaları, açıortay ve kenarortay teoremleri, benzerlik oranı ile alan arasındaki ilişki gibi konuları içermektedir. Öğretmen, her konuyu örnek sorular üzerinden pekiştirmekte ve farklı çözüm yöntemlerini göstermektedir.","Videoda ayrıca klaket döndürme problemi, dik üçgenlerde alan hesaplamaları, üçgenleri böldüğünde oluşan alanların oranlarını hesaplama, kenarortayların kesim noktasının ağırlık merkezi olduğu, kenarortayların oluşturduğu üçgenlerin alanlarının eşit olduğu ve 3-1-2 kuralı gibi konular da ele alınmaktadır. Video yaklaşık iki saat sürmekte ve öğretmen, konuyu yüzeysel değil, detaylı bir şekilde anlattığını vurgulamaktadır."]},"endTime":3503,"title":"10. 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Kullanımı","list":{"type":"unordered","items":["ABC üçgeninin alanı için sinüslü alan formülü kullanılarak 1/2 × 30 × x × sin(alfa) hesaplanmış.","Diğer üçgenin alanı için de sinüslü alan formülü kullanılarak 1/2 × 12 × (x+15) × sin(alfa) hesaplanmış.","İki alan ifadesinin eşit olduğu denklemi çözülerek x değeri 10 olarak bulunmuş."]},"beginTime":729,"endTime":832,"href":"/video/preview/3611667998137082801?parent-reqid=1765274132018437-8301958655174908337-balancer-l7leveler-kubr-yp-sas-128-BAL&text=Alan+Dzhamankulov&t=729&ask_summarization=1"},{"index":5,"title":"Sinüslü Alan Formülü ile Alan Parçalama","list":{"type":"unordered","items":["Sinüslü alan formülü biliniyorsa alan parçalamada kolay bir yöntem kullanılabilir, ancak sinüslü alan formülü bilinmese de önceki derste sinüs kullanmadan alan parçalamaları yapılmıştır.","Üçgenler ortak bir köşeye sahip olduğunda, sinüslü alan formülü kullanılarak üçgenlerin alanları hesaplanabilir.","Sinüslü alan formülü: Alan = 1/2 × kenar1 × kenar2 × sin(aralarındaki açı) şeklindedir."]},"beginTime":836,"endTime":1005,"href":"/video/preview/3611667998137082801?parent-reqid=1765274132018437-8301958655174908337-balancer-l7leveler-kubr-yp-sas-128-BAL&text=Alan+Dzhamankulov&t=836&ask_summarization=1"},{"index":6,"title":"Alan Parçalama Yöntemi","list":{"type":"unordered","items":["Alan parçalamada, küçük üçgenin alanı kenarlarının çarpımının yarısı olarak hesaplanabilir.","Büyük üçgenin alanı, tüm kenarların çarpımının yarısı olarak hesaplanabilir.","İki üçgenin alanları arasındaki oran, kenarların çarpımlarının oranına eşittir."]},"beginTime":1005,"endTime":1243,"href":"/video/preview/3611667998137082801?parent-reqid=1765274132018437-8301958655174908337-balancer-l7leveler-kubr-yp-sas-128-BAL&text=Alan+Dzhamankulov&t=1005&ask_summarization=1"},{"index":7,"title":"Örnek Problemler","list":{"type":"unordered","items":["ABC üçgeninin tüm alanının 24 olduğu bilindiğinde, sinüslü alan formülü kullanılarak üçgenlerin alanları hesaplanabilir.","Sinüslü alan formülü bilinmese de, önceki derste anlatılan yöntemle üçgenler bölünerek alanlar hesaplanabilir.","Alan parçalama problemlerinde, sinüslü alan formülü yazılı sınavlarda karşınıza gelebilir."]},"beginTime":1243,"endTime":1512,"href":"/video/preview/3611667998137082801?parent-reqid=1765274132018437-8301958655174908337-balancer-l7leveler-kubr-yp-sas-128-BAL&text=Alan+Dzhamankulov&t=1243&ask_summarization=1"},{"index":8,"title":"Üçgen Alan Hesaplama","list":{"type":"unordered","items":["Sinüslü alan hesaplaması için önce en küçük üçgenin alanı (2ab/2 = 2s) bulunur.","İkinci üçgenin alanı (4b×4a/2 = 16s) hesaplanır ve toplam alan 16s+14s = 36s olarak bulunur.","En büyük üçgenin alanı 36s olarak hesaplanır ve istenen alan 14s/36s = 7/18 olarak bulunur."]},"beginTime":1515,"endTime":1607,"href":"/video/preview/3611667998137082801?parent-reqid=1765274132018437-8301958655174908337-balancer-l7leveler-kubr-yp-sas-128-BAL&text=Alan+Dzhamankulov&t=1515&ask_summarization=1"},{"index":9,"title":"Açıortay Bağıntıları","list":{"type":"unordered","items":["Açıortay bağıntısında kolların bacaklara oranları eşittir.","Üçgenin alanı 42 ise, kenarların oranları 6/8 = 3/4 olduğundan alanlar 18s ve 24s olur.","Açıortayların kesim noktası içte çemberin merkezidir ve kollara çizilen dikmeler birbirine eşittir."]},"beginTime":1607,"endTime":1817,"href":"/video/preview/3611667998137082801?parent-reqid=1765274132018437-8301958655174908337-balancer-l7leveler-kubr-yp-sas-128-BAL&text=Alan+Dzhamankulov&t=1607&ask_summarization=1"},{"index":10,"title":"Kenarortay Özellikleri","list":{"type":"unordered","items":["Tek başına bir kenarortay çizildiğinde üçgeni eşit iki parçaya ayırır.","Kenarortayların kesim noktası ağırlık merkezidir ve ağırlık merkezine çizilen doğrular üçgeni eşit üç parçaya ayırır.","Kenarortayların kesim noktasından kenar orta noktalarını birleştiren doğru, üç yüz on iki kuralını oluşturur."]},"beginTime":1817,"endTime":1999,"href":"/video/preview/3611667998137082801?parent-reqid=1765274132018437-8301958655174908337-balancer-l7leveler-kubr-yp-sas-128-BAL&text=Alan+Dzhamankulov&t=1817&ask_summarization=1"},{"index":11,"title":"Örnek Sorular","list":{"type":"unordered","items":["Dik üçgende açıortay çizildiğinde, kenarlarla orantılı bölme yapılır ve alan hesaplaması yapılır.","Açıortay bağıntısında, bir bölgenin alanı bir bölgenin alanının üç katıysa, aynı köşeden çizilen kenar da üç katıdır.","Dik üçgende açıortay ve dik açı kullanılarak alan hesaplamaları yapılabilir."]},"beginTime":1999,"endTime":2129,"href":"/video/preview/3611667998137082801?parent-reqid=1765274132018437-8301958655174908337-balancer-l7leveler-kubr-yp-sas-128-BAL&text=Alan+Dzhamankulov&t=1999&ask_summarization=1"},{"index":12,"title":"Dış Açıortay Problemi","list":{"type":"unordered","items":["Dış açıortay teoremine göre, bir üçgende bir iç açıortayla bir dış açıortay çizilirse onların arası 90 derece olur.","Dış açıortay teoremi kullanılarak, x/x+4a = k/3k oranı kurularak x = 2a bulunur.","a = 8 olduğunda, x = 16 olarak hesaplanır."]},"beginTime":2133,"endTime":2235,"href":"/video/preview/3611667998137082801?parent-reqid=1765274132018437-8301958655174908337-balancer-l7leveler-kubr-yp-sas-128-BAL&text=Alan+Dzhamankulov&t=2133&ask_summarization=1"},{"index":13,"title":"Dik Üçgen Alanı Hesaplama","list":{"type":"unordered","items":["Dik üçgende dik kolların çarpımlarının yarısı formülü kullanılarak alan hesaplanır.","Benzerlik kuralı kullanılarak x² = 180 bulunur ve x = 6√5 olarak hesaplanır.","Pisagor bağıntısı kullanılarak diğer kenar uzunlukları bulunur ve dörtgenin alanı 81 birim kare olarak hesaplanır."]},"beginTime":2235,"endTime":2430,"href":"/video/preview/3611667998137082801?parent-reqid=1765274132018437-8301958655174908337-balancer-l7leveler-kubr-yp-sas-128-BAL&text=Alan+Dzhamankulov&t=2235&ask_summarization=1"},{"index":14,"title":"Açıortay Özellikleri","list":{"type":"unordered","items":["Açıortay çizildiğinde, açıortayın bir kenara olan uzaklıkları birbirine eşittir.","Dik açılar atıldığında oluşan diklikler birbirine eşittir.","Öklit bağıntısı kullanılarak kenar uzunlukları bulunur ve alan hesaplanır."]},"beginTime":2430,"endTime":2503,"href":"/video/preview/3611667998137082801?parent-reqid=1765274132018437-8301958655174908337-balancer-l7leveler-kubr-yp-sas-128-BAL&text=Alan+Dzhamankulov&t=2430&ask_summarization=1"},{"index":15,"title":"Kenarortay ve Ağırlık Merkezi","list":{"type":"unordered","items":["Üçgenin ağırlık merkezi G 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