Syllabus
Structure and classification of constructive geometric tasks
Collinear transformation, incidence, cross-ratio, Pappus' theorem, Desargues's theorem
Affine transformation, parallelism, affine ratio, Menelaus' and Ceva's theorem
Similarity transformation, angle, trigonometry
Isometric transformation, distance, area, classification of isometries, theorems on triangles
Circle and its properties
Polygons
Loci given by certain conditions, conics
Circle inversion
Apollonius' problems
Annotation
The students will be with the use of synthetic approach introduced to the development and methods of solving constructive geometric tasks, geometric transformations in a plane, properties of planar shapes, and proofs of elementary theorems. The content's structure is focused on the consecutive systematic description of fundamental terms and orientation in geometry.