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Консультация № 189996
09.11.2016, 21:53
0.00 руб.
10.11.2016, 06:56
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1
1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Дан равносторонний треугольник АВС , точка D принадлежит АВ, точка Е принадлежит ВС, точка F принадлежит АС, ADEF - параллелограмм, его периметр равен 16 см. Найти АВ.
Дан равносторонний треугольник АВС , точка D принадлежит АВ, точка Е принадлежит ВС, точка F принадлежит АС, ADEF - параллелограмм, его периметр равен 16 см. Найти АВ.
Обсуждение
10.11.2016, 06:35
общий
это ответ
Здравствуйте, svrvsvrv!
Так как ADEF - параллелограмм, то DE||AC и EF||AB. Так как DE параллельна AC, то треугольники DBE и ABC подобны, следовательно, треугольник DBE является равносторонним (как и ABC), и DB = DE. Аналогично, треугольник ECF подобен треугольнику BCA, то есть является равносторонним, и EF = CF. Тогда периметр параллелограмма равен AD+DE+EF+FA=AD+DB+CF+FA=AB+CA=16 см, откуда AB = CA = 8 см.
Так как ADEF - параллелограмм, то DE||AC и EF||AB. Так как DE параллельна AC, то треугольники DBE и ABC подобны, следовательно, треугольник DBE является равносторонним (как и ABC), и DB = DE. Аналогично, треугольник ECF подобен треугольнику BCA, то есть является равносторонним, и EF = CF. Тогда периметр параллелограмма равен AD+DE+EF+FA=AD+DB+CF+FA=AB+CA=16 см, откуда AB = CA = 8 см.
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