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Консультация № 143410
08.09.2008, 20:18
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В параллелограмме биссектриса угла делит противоположную сторону на отрезки, равные 3 и 5 см. Найти его периметр.
Обсуждение
Неизвестный
08.09.2008, 21:13
общий
это ответ
Здравствуйте, Belmont!
Пусть АBCD-параллелограмм, угол А-острый, АЕ-биссектриса (точка Е на CD), CE=3, ED=5. CD=8, следовательно противоположная ей сторона АВ тоже равна 8. При параллельных прямых АВ и CD секущая АЕ, значит, равны накрест лежащие углы EAB и AED. Углы DAE и DEA равны, следовательно треугольник DAE-равнобедренный, DE=5=AD. AD=BC=5 (противоположные стороны в параллелограмме). Итак, периметр
2*5+2*8=26.
Ответ: 26.
Пусть АBCD-параллелограмм, угол А-острый, АЕ-биссектриса (точка Е на CD), CE=3, ED=5. CD=8, следовательно противоположная ей сторона АВ тоже равна 8. При параллельных прямых АВ и CD секущая АЕ, значит, равны накрест лежащие углы EAB и AED. Углы DAE и DEA равны, следовательно треугольник DAE-равнобедренный, DE=5=AD. AD=BC=5 (противоположные стороны в параллелограмме). Итак, периметр
2*5+2*8=26.
Ответ: 26.
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