USE 2022 Mathematics. Profile level. Supporting tasks in geometry. Planimetry. Stereometry

The manual contains solutions to the supporting tasks of planimetry and stereometry, their use in solving substantial geometric problems for the construction, evidence and calculation.
Finding distances and angles in space is the most important part of the stereometry section, on which all its metric issues are based, based, including the location of the areas and volumes of geometric shapes and bodies. In this regard, this manual proposes methodological recommendations for developing the ability to calculate distances, angles between straight and planes. These skills are proposed to develop through the implementation of thematic tasks, which are composed of tasks selected according to the principle of "simple to complex" using images of the correct tetrahedron, cube, correct pyramids and prisms. Along with the geometric method of solving stereometric problems to find distances and angles in this manual, a vector-coordinate method of solving them is considered. The supporting tasks for geometric transformations of space, combinations of correct polyhedra and spheres are also offered.
The thematic set of tasks of each task is preceded by solving similar problems. The answers are indicated to all tasks.
The manual presents the main theorems and formulas of planimetry and stereometry.
The textbook is addressed to students and teachers of mathematics of schools, lyceums, gymnasiums, colleges.
By order No. 699 of the Ministry of Education and Science of the Russian Federation, the textbooks of the publishing house "Examination" were allowed for use in general educational organizations