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Консультация № 196642
10.10.2019, 18:45
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:Основания трапеции равны 4 см и 10 см. Боковая сторона разделена на три равные части. Через точки деления проведены прямые, параллельные основаниям. Найдите отрезки этих прямых, заключённые между боковыми сторонами трапеции. Заранее благодарен.
Обсуждение
10.10.2019, 22:47
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович!
abcd - трапеция. ab||dc; ab=A=4см; dc=B=10cм;
Проведём ae||bc;
В получившемся параллелограмме abcd ab=ec=A; Соответственно:
ab=e'c'=e"c"=A;
de=B-A;
Треугольники ade, ad'e', ad"e" подобны по двум углам;
так как ad'=d'd"=d"d то ad'=ad/3; и, следовательно (из подобия треугольников)
d'e'=de/3=(B-A)/3;
d'e'=de*2/3=(B-A)*2/3;
Из чего следует:
d'c'=A+(B-A)/3=4+(10-4)/3=6 см;
d"c"=A+(B-A)*2/3=4+(10-4)*2/3=8 см;
abcd - трапеция. ab||dc; ab=A=4см; dc=B=10cм;
Проведём ae||bc;
В получившемся параллелограмме abcd ab=ec=A; Соответственно:
ab=e'c'=e"c"=A;
de=B-A;
Треугольники ade, ad'e', ad"e" подобны по двум углам;
так как ad'=d'd"=d"d то ad'=ad/3; и, следовательно (из подобия треугольников)
d'e'=de/3=(B-A)/3;
d'e'=de*2/3=(B-A)*2/3;
Из чего следует:
d'c'=A+(B-A)/3=4+(10-4)/3=6 см;
d"c"=A+(B-A)*2/3=4+(10-4)*2/3=8 см;
5
Об авторе:
Понеже не словес красных бог слушает, но дел наших хощет
Понеже не словес красных бог слушает, но дел наших хощет
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