Предмет: Геометрия, автор: crash57

Пожалуйста, помогите
Нужно доказать, что CC1 и DD1 параллельны и равны.
Известно, что параллелограммы ABCD и ABC1D1 лежат в разных плоскостях

Приложения:

Ответы

Автор ответа: KuOV
0

Доказательство:

Свойство параллелограмма:

  • противоположные стороны параллелограмма равны.

Признак параллелограмма:

  • если в четырехугольнике две противоположные стороны параллельны и равны, то это параллелограмм.

Так как ABCD параллелограмм, то CD║АВ и CD = АВ.

Так как ABC₁D₁ параллелограмм, то C₁D₁║AB и C₁D₁ = АВ.

Тогда CD║C₁D₁ и CD = C₁D₁, значит CC₁D₁D - параллелограмм по признаку.

СС₁║DD₁ как стороны параллелограмма.

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