Решебник по геометрии 8 класс Мерзляк Задание 495

\[\text{ABC\ }и\ A_{1}B_{1}C_{1} - треугольники:\]

\[A_{1}B_{1} = 9\ см;B_{1}C_{1} = 24\ см;\ \]

\[A_{1}C_{1} = 27\ см;\]

\[AB\ :BC\ :AC = 3\ :8\ :9.\]

\[Решение.\]

\[\mathrm{\Delta}ABC\sim\mathrm{\Delta}A_{1}B_{1}C_{1} - третий\ \]

\[признак:\]

\[\frac{A_{1}B_{1}}{B_{1}C_{1}} = \frac{9}{24} = \frac{3}{8};\ \]

\[\frac{B_{1}C_{1}}{A_{1}C_{1}} = \frac{24}{27} = \frac{8}{9};\]

\[A_{1}B_{1}\ :B_{1}C_{1}\ :A_{1}C_{1} = 3\ :8\ :9;\]

\[A_{1}B_{1}\ :B_{1}C_{1}\ :A_{1}C_{1} = AB\ :BC\ :AC;\]

\[AB\ :A_{1}B_{1} = BC\ :B_{1}C_{1} = AC\ :A_{1}C_{1}.\]

\[Ответ:\ \ да.\]