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Консультация № 192497
30.01.2018, 10:05
0.00 руб.
1
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1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Дано:пятиугольник ABCDE , BE и CE биссектрисы,площадь треугольника BCE равна 11, угол А=35град, угол D= 145 град.Найти площадь ABCDE .
Дано:пятиугольник ABCDE , BE и CE биссектрисы,площадь треугольника BCE равна 11, угол А=35град, угол D= 145 град.Найти площадь ABCDE .
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Обсуждение
01.02.2018, 12:06
общий
это ответ
Здравствуйте, Анатолий!
[$8736$]BEC > [$8736$]BEA, т.к. [$946$] < 35[$186$]. Отложим [$8736$]BEC слева от отрезка BE.
На пересечении продолжения AB со стороной отложенного угла получим точку C'.
[$916$]ВСЕ = [$916$]BC'E, следовательно, [$8736$]C' = [$946$], C'E = CE.
[$8736$]C'AE = 180 - 35 = 145[$186$], значит, [$916$]C'AE = [$916$]CDE.
Учитывая равенство [$916$]BEC=[$916$]BC'E, заключаем, что SABCDE = 2SBEC = 22.
[$8736$]BEC > [$8736$]BEA, т.к. [$946$] < 35[$186$]. Отложим [$8736$]BEC слева от отрезка BE.
На пересечении продолжения AB со стороной отложенного угла получим точку C'.
[$916$]ВСЕ = [$916$]BC'E, следовательно, [$8736$]C' = [$946$], C'E = CE.
[$8736$]C'AE = 180 - 35 = 145[$186$], значит, [$916$]C'AE = [$916$]CDE.
Учитывая равенство [$916$]BEC=[$916$]BC'E, заключаем, что SABCDE = 2SBEC = 22.
5
Большое Вам спасибо!Я уж думал,что никто не ответит.
02.02.2018, 13:26
общий
Адресаты:
ΔВСЕ = ΔBC'E, на каком основании они равны?Сторона BC' никак не равна ни одной стороне треугольника ΔВСЕ .Треугольники подобны по трём углам,но не равны.По рисунку видно,что стороны разные.Я не догоняю здесь... подробнее разъясните где?
02.02.2018, 13:37
общий
Адресаты:
BE - общая сторона, и углы при ней равны. [$8736$]С'BE = [$8736$]CBE, потому, что BE - биссектриса по условию, [$8736$]BEC' = [$8736$]BEC по построению.
02.02.2018, 13:46
общий
02.02.2018, 13:56
Адресаты:
Лангваген Сергей Евгеньевич BE - общая сторона, и углы при ней равны.
02.02.2018, 13:59
общий
Адресаты:
BC' не равна BC по рисунку..... построение выполнено схематично,а не точно,меня это и сбило. Прошу прощение.
02.02.2018, 14:14
общий
Адресаты:
У треугольников BCE и BC'E общая сторона BE. Даже чертеж не нужен, чтобы это заметить - две пары вершин совпадают.
И эти треугольники равны. На чертеже они немного разные, но «геометрия есть искусство правильно рассуждать на неправильном чертеже». Если будут вопросы еще, задавайте.
И эти треугольники равны. На чертеже они немного разные, но «геометрия есть искусство правильно рассуждать на неправильном чертеже». Если будут вопросы еще, задавайте.
02.02.2018, 14:38
общий
Адресаты:
Лангваген Сергей Евгеньевич На чертеже они немного разные
Лангваген Сергей Евгеньевич есть искусство правильно рассуждать на неправильном чертеже».
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