ГДЗ по геометрии 8 класс Атанасян Задание 800

\[\boxed{\mathbf{800.}\mathbf{ОК\ ГДЗ - домашка\ на}\ 5}\]

\[\mathbf{Дано:}\]

\[\textbf{а)}\ \overrightarrow{m} \nearrow \nearrow \overrightarrow{n};\ \]

\[\textbf{б)}\ \overrightarrow{m} \nearrow \nearrow \overrightarrow{n}\ и\ \ \left| \overrightarrow{m} \right| \geq \overrightarrow{n}.\]

\[\mathbf{Доказать:}\]

\[\textbf{а)}\ \left| \overrightarrow{m} + \overrightarrow{n} \right| = \left| \overrightarrow{m} \right| + \left| \overrightarrow{n} \right|;\]

\[\textbf{б)}\ \left| \overrightarrow{m} + \overrightarrow{n} \right| = \left| \overrightarrow{m} \right| - \left| \overrightarrow{n} \right|.\]

\[\mathbf{Доказательство.}\]

\[\textbf{а)}\ \left| \overrightarrow{\text{AB}} \right| + \left| \overrightarrow{\text{BC}} \right| = \left| \overrightarrow{\text{AC}} \right|:\]

\[\ \left| \overrightarrow{m} + \overrightarrow{n} \right| = \left| \overrightarrow{m} \right| + \left| \overrightarrow{n} \right|.\]

\[\textbf{б)}\ AB = AC + BC:\]

\[\overrightarrow{\text{AC}} = \left| \overrightarrow{m} \right| + \left| \overrightarrow{n} \right|\ \]

\[\left| \overrightarrow{\text{AC}} \right| = \left| \overrightarrow{\text{AB}} \right| - \left| \overrightarrow{\text{BC}} \right|.\]

\[Следовательно:\]

\[\left| \overrightarrow{m} \right| + \left| \overrightarrow{n} \right| = \left| \overrightarrow{m} \right| - \left| \overrightarrow{n} \right|\]