Решебник по геометрии 8 класс Мерзляк Задание 427

\[Схематический\ рисунок.\]

\[Дано:\]

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

\[\frac{\text{AB}}{A_{1}B_{1}} = \frac{\text{BC}}{B_{1}C_{1}};\]

\[\angle A = 25{^\circ};\]

\[\angle B = 70{^\circ}.\]

\[Найти:\]

\[\angle A_{1};\ \angle B_{1};\ \angle C_{1}.\]

\[Решение.\]

\[1)\ \frac{\text{AB}}{A_{1}B_{1}} = \frac{\text{BC}}{B_{1}C_{1}} = \frac{\text{AC}}{A_{1}C_{1}};\]

\[\angle A_{1} = \angle A = 25{^\circ};\]

\[\angle B_{1} = \angle B = 70{^\circ}.\]

\[2)\ В\ \mathrm{\Delta}B_{1}C_{1}:\]

\[\angle A_{1} + \angle B_{1} + \angle C_{1} = 180{^\circ}\]

\[25{^\circ} + 70{^\circ} + \angle C_{1} = 180{^\circ}\]

\[\angle C_{1} = 85{^\circ}.\]

\[Ответ:\ \ \angle A_{1} = 25{^\circ};\ \angle B_{1} = 70{^\circ};\ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \angle C_{1} = 85{^\circ}.\]