\[\boxed{\mathbf{560.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано}:\ \]
\[\mathrm{\Delta}\text{ABC\ }и\ \mathrm{\Delta}A_{1}B_{1}C_{1}.\]
\[Доказать:\]
\[\mathrm{\Delta}ABC\sim\mathrm{\Delta}A_{1}B_{1}C_{1}.\]
\[Доказательство.\]
\[\textbf{а)}\ AB = 3\ см;BC = 5\ см;\]
\[CA = 7\ см;A_{1}B_{1} = 4,5\ см;\ \]
\[B_{1}C_{1} = 7,5\ см:\]
\[C_{1}A_{1} = 10,5\ см;\]
\[\frac{\text{AB}}{A_{1}B_{1}} = \frac{3}{4,5} = \frac{2}{3};\]
\[\frac{\text{BC}}{B_{1}C_{1}} = \frac{5}{7,5} = \frac{2}{3};\]
\[\frac{\text{AC}}{A_{1}C_{1}} = \frac{7}{10,5} = \frac{2}{3};\]
\[\frac{\text{AB}}{A_{1}B_{1}} = \frac{\text{BC}}{B_{1}C_{1}} = \frac{\text{AC}}{A_{1}C_{1}} = \frac{2}{3} \Longrightarrow\]
\[\Longrightarrow \mathrm{\Delta}ABC\sim\mathrm{\Delta}A_{1}B_{1}C_{1}\ \]
\[(по\ трем\ сторонам).\]
\[Что\ и\ требовалось\ доказать.\]
\[\textbf{б)}\ AB = 1,7\ см;BC = 3\ см;\]
\[CA = 4,2\ см;A_{1}B_{1} = 34\ дм;\]
\[B_{1}C_{1} = 60\ дм;\]
\[C_{1}A_{1} = 84\ дм:\]
\[\frac{\text{AB}}{A_{1}B_{1}} = \frac{1,7}{340} = \frac{1}{200};\]
\[\frac{\text{BC}}{B_{1}C_{1}} = \frac{3}{600} = \frac{1}{200};\]
\[\frac{\text{AC}}{A_{1}C_{1}} = \frac{4,2}{840} = \frac{1}{200};\]
\[\frac{\text{AB}}{A_{1}B_{1}} = \frac{\text{BC}}{B_{1}C_{1}} = \frac{\text{AC}}{A_{1}C_{1}} = \frac{1}{200} \Longrightarrow\]
\[\Longrightarrow \mathrm{\Delta}ABC\sim\mathrm{\Delta}A_{1}B_{1}C_{1}\ \]
\[(по\ трем\ сторонам)\mathbf{.}\]
\[\mathbf{Что\ и\ требовалось\ доказать}\mathbf{.}\]
\[\boxed{\mathbf{560.еуроки - ответы\ на\ пятёрку}}\]
\[Рисунок\ по\ условию\ задачи:\]
\[S_{параллелограмма} = a \bullet h_{1} = b \bullet h_{2}.\]
\[\mathbf{а)\ }a = 18\ см;\ b = 30\ см;\ \]
\[h_{1} = 6\ см;\ h_{2} > h_{1}.\]
\[S_{\text{ABCD}}:\ \ \ \]
\[6 \bullet 30 = h_{2} \bullet 18\]
\[h_{2} = \frac{6 \bullet 30}{18} = 10\ см.\]
\[\mathbf{б)\ }a = 10\ см;\ b = 15\ см;\]
\[\text{\ h}_{2} = 6\ см;\ h_{2} > h_{1}.\]
\[S_{\text{ABCD}}:\ \ \ \]
\[10 \bullet 6 = 15 \bullet h_{1}\]
\[h_{1} = \frac{10 \bullet 6}{15} = 4\ см.\]
\[\mathbf{в)\ }a = 4,5\ см;b = 6\ см;\]
\[S = 54\ см^{2}.\]
\[S_{\text{ABCD}}:\ \ \ \]
\[54\ см^{2} = h_{1} \bullet 4,5 = h_{2} \bullet 6\]
\[h_{1} = \frac{54}{4,5} = 12\ см\]
\[h_{2} = \frac{54}{6} = 9\ см.\]
\[\mathbf{Дано:}\]
\[\mathbf{Найти:}\]
\[\mathbf{Решение.}\]
\[Ответ:а)\ h_{2} = 10\ см;\]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ б)\ h_{1} = 4\ см;\]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ в)\ h_{1} = 12см;\text{\ h}_{2} = 9\ см.\]