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Консультация № 194859
04.03.2019, 01:19
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Дана теорема:в любом прямоугольнике диагонали равны.
1. Выделите структурные элементы.
2. Сформулируйте данную теорему с помощью слов "следует".
3.Сформулируйте обратное,противоположное и обратное противоположному утверждения.
Дана теорема:в любом прямоугольнике диагонали равны.
1. Выделите структурные элементы.
2. Сформулируйте данную теорему с помощью слов "следует".
3.Сформулируйте обратное,противоположное и обратное противоположному утверждения.
Обсуждение
05.03.2019, 09:41
общий
это ответ
Здравствуйте, Екатерина!
При указанной категорической формулировке условием теоремы является высказывание "в любом прямоугольнике", а заключением -- высказывание "диагонали равны".
С помощью слова "следует" теорему можно сформулировать так: "Из того, что четырёхугольник является прямоугольником, следует, что его диагонали равны".
Приняв заданную теорему за прямую, получим следующие утверждения в импликативной формулировке:
- обратное: если диагонали четырёхугольника равны, то он является прямоугольником;
- противоположное: если четырёхугольник не является прямоугольником, то его диагонали не равны;
- обратное противоположному: если диагонали четырёхугольника не равны, то он не является прямоугольником.
При указанной категорической формулировке условием теоремы является высказывание "в любом прямоугольнике", а заключением -- высказывание "диагонали равны".
С помощью слова "следует" теорему можно сформулировать так: "Из того, что четырёхугольник является прямоугольником, следует, что его диагонали равны".
Приняв заданную теорему за прямую, получим следующие утверждения в импликативной формулировке:
- обратное: если диагонали четырёхугольника равны, то он является прямоугольником;
- противоположное: если четырёхугольник не является прямоугольником, то его диагонали не равны;
- обратное противоположному: если диагонали четырёхугольника не равны, то он не является прямоугольником.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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