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Консультация № 192043
08.12.2017, 16:36
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Уважаемые эксперты! Пожалуйста, помогите решить задачу:
Диагонали трапеции ABCD пересекаются в точке O, S(BC0)=2,S(COD)=5.Чему равна площадь трапеции?
Диагонали трапеции ABCD пересекаются в точке O, S(BC0)=2,S(COD)=5.Чему равна площадь трапеции?
Обсуждение
08.12.2017, 22:36
общий
это ответ
Здравствуйте, borisova.sw2012!
Предположим, что отрезки
и 
-- большее и меньшее основания трапеции соответственно.
Треугольники
и 
имеют основание и одинаковые высоты, проведённые к этому основанию. Поэтому
(ед. площади) -- площадь треугольника 
Треугольники
и 
имеют одинаковые высоты, проведённые из вершины 
Поэтому
Треугольники и 
подобны по двум углам (углы 
и 
равны как вертикальные, углы 
и 
равны как внутренние накрест лежащие при пересечении параллельных прямых и 
секущей 
). Поэтому
(ед. площади) -- площадь треугольника 
Значит, площадь трапеции
составляет
(ед. площади).
Рисунок к решению задачи выполните сами.
Предположим, что отрезки
и -- большее и меньшее основания трапеции соответственно.Треугольники
и имеют основание и одинаковые высоты, проведённые к этому основанию. Поэтому (ед. площади) -- площадь треугольника Треугольники
и имеют одинаковые высоты, проведённые из вершины ПоэтомуТреугольники
и подобны по двум углам (углы и равны как вертикальные, углы и равны как внутренние накрест лежащие при пересечении параллельных прямых и секущей ). Поэтому (ед. площади) -- площадь треугольника Значит, площадь трапеции
составляет (ед. площади).Рисунок к решению задачи выполните сами.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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