Предмет: Математика, автор: 6yxapb4

Реши самостоятельно

В прямоугольной трапеции ABCD проведена диагональ BD. Найти ВС, если = 90°, ZABC = 135°, ZCDB = 45°, AD =30 см.

Дескрипторы:
- применяет свойство прямоугольной трапеции;
- применяет свойство углов и сторон равнобедренного треугольника;
- использует свойство высоты, проведенной в равнобедренном
треугольнике из вершины к основанию;
- находит меньшее основание трапеции ВС.

Приложения:

Ответы

Автор ответа: ViMan89

Ответ:трапеция АВСД, уголА=180-уголВ=180-135=45, уголС=90, уголД=180-уголС=180-90=90, АВСД прямоугольная трапеция, ВД-диагональ, треугольник ВСД, уголВДС=45. уголДВС=90-45=45, треугольник ВСД равнобедренный, ВС=СД, проводим высоту ВН на АД, уголНВД=уголНВС-уголДВС=90-45=45, угол НДВ=90-45=45, треугольник НВД равнобедренный, ВН=НД, треугольник АВН прямоугольный, угол АВН=90-уголА=90-45=45, треугольник АВН равнобедренный, АН=ВН=НД=1/2АД=30/2=15, НВСД прямоугольник ВС=НД=15

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