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Консультация № 188952
16.03.2016, 16:20
0.00 руб.
0
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Внутри квадрата АВСД отмечена точка К, не лежащая на диагонали ВД, а на стороне СД - точка М, так, что МК=КД и ВК перпендикулярен КМ. Найдите величину угла КВМ.
Внутри квадрата АВСД отмечена точка К, не лежащая на диагонали ВД, а на стороне СД - точка М, так, что МК=КД и ВК перпендикулярен КМ. Найдите величину угла КВМ.
Обсуждение
16.03.2016, 18:58
общий
это ответ
Здравствуйте, svrvsvrv!
пусть угол [$8736$]KMD=[$945$] и [$946$]=90[$176$]-[$945$]
через точку K проведём LN||AD
Нетрудно установить, что
[$8736$]MKN=90[$176$]-[$945$]=[$946$]
[$8736$]LKB=180[$176$]-[$946$]-90[$176$]=[$945$]
[$8736$]ABK=90[$176$]-[$945$]=[$946$]
с другой стороны,
[$8736$]KDC=[$8736$]KMD=[$945$]
[$8736$]ADK=90[$176$]-[$945$]=[$946$]
из равенства углов [$8736$]ABK=[$8736$]ADK делаем вывод, что BK и DK взаимно симметричны относительно диагонали AC, на которой и располагается точка K.
Но отсюда следует также BK=DK=MK,
то есть [$8895$]KBM не только прямоугольный, но и равнобедренный!
Отсюда делаем вывод [$8736$]KBM=45[$176$]
пусть угол [$8736$]KMD=[$945$] и [$946$]=90[$176$]-[$945$]
через точку K проведём LN||AD
Нетрудно установить, что
[$8736$]MKN=90[$176$]-[$945$]=[$946$]
[$8736$]LKB=180[$176$]-[$946$]-90[$176$]=[$945$]
[$8736$]ABK=90[$176$]-[$945$]=[$946$]
с другой стороны,
[$8736$]KDC=[$8736$]KMD=[$945$]
[$8736$]ADK=90[$176$]-[$945$]=[$946$]
из равенства углов [$8736$]ABK=[$8736$]ADK делаем вывод, что BK и DK взаимно симметричны относительно диагонали AC, на которой и располагается точка K.
Но отсюда следует также BK=DK=MK,
то есть [$8895$]KBM не только прямоугольный, но и равнобедренный!
Отсюда делаем вывод [$8736$]KBM=45[$176$]
5
Спасибо!
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