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Консультация № 190002
09.11.2016, 22:07
0.00 руб.
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Здравствуйте! У меня возникли сложности с таким вопросом:
Дан ромб ABCD. N - середина стороны ВС, К - середина стороны DC, M - середина стороны AB. Найти угол MNK.
Дан ромб ABCD. N - середина стороны ВС, К - середина стороны DC, M - середина стороны AB. Найти угол MNK.
Обсуждение
10.11.2016, 05:54
общий
это ответ
Здравствуйте, svrvsvrv!
Так как точки M и N - середины сторон AB и BC, то отрезок MN является средней линией треугольника ABC и параллелен его стороне AC. Аналогично, отрезок NK параллелен BD (как средняя линия треугольника BCD). Так как ABCD - ромб, то его диагонали AC и BD перпендикулярны. Следовательно, отрезки MN и NK, параллельные диагоналям, также перпендикулярны, то есть угол между ними (а это и есть искомый угол MNK) равен 90[$186$].
Так как точки M и N - середины сторон AB и BC, то отрезок MN является средней линией треугольника ABC и параллелен его стороне AC. Аналогично, отрезок NK параллелен BD (как средняя линия треугольника BCD). Так как ABCD - ромб, то его диагонали AC и BD перпендикулярны. Следовательно, отрезки MN и NK, параллельные диагоналям, также перпендикулярны, то есть угол между ними (а это и есть искомый угол MNK) равен 90[$186$].
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