ГДЗ по геометрии 8 класс Атанасян ФГОС Задание 1369

\[\boxed{\mathbf{1369.еуроки - ответы\ на\ пятёрку}}\]

\[\mathbf{Дано:}\]

\[MNPQ - четырехугольник;\]

\[\overrightarrow{\text{ON}} - \overrightarrow{\text{OM}} = \overrightarrow{\text{OP}} - \overrightarrow{\text{OQ}}.\]

\[\mathbf{Найти:}\]

\[Вид\ MNPQ - ?\]

\[\mathbf{Решение.}\]

\[1)\ Найдем\ разности\ векторов:\]

\[\overrightarrow{\text{ON}} - \overrightarrow{\text{OM}} = \overrightarrow{\text{ON}} + \overrightarrow{\text{MO}} =\]

\[= \overrightarrow{\text{MO}} + \overrightarrow{\text{ON}} = \overrightarrow{\text{MN}};\]

\[\overrightarrow{\text{OP}} - \overrightarrow{\text{OQ}} = \overrightarrow{\text{OP}} + \overrightarrow{\text{QO}} =\]

\[= \overrightarrow{\text{QO}} + \overrightarrow{\text{OP}} = \overrightarrow{\text{QP}}.\]

\[2)\ \overrightarrow{\text{MN}} = \overrightarrow{\text{QP}} \Longrightarrow\]

\[\Longrightarrow MN \parallel QP\ и\ MN = QP:\]

\[\mathbf{Ответ:}MNPQ -\]

\[параллелограмм.\]