Syllabus
Triangles. Quadrilaterals.
Cyclic and tangential quadrilaterals. Circle.
Circle power. Radical line.
Euclidan constructions. Constructions using other tools.
Sets of points of given properties. Definition and basic properties of geometric congruences in plane.
Composition of geometric congruences. Classification of geometric congruences in plane.
Direct and indirect geometric congruences. Group of geometric congruences.
Definition and basic properties of homothecy. Similitude ration and its properties.
Composition of homothecies. Monge's theorem.
Circle in homothecy. Group of homothecies.
Definition and basic properties of similarity. Decomposition of direct and indirect similarity (processes of construction).
Similarity invariants (processes of construction). Classification of similarities in plane.
Menelaos' and Ceva's theorem. Pappus's theorem.
Double similitude ratio and its properties. Circle inversion (basic properties Apollonius' problems).
Principles of axiomatic system conception of geometry.
Annotation
Basic notions and problems of plane geometry are introduced. The course consolidates and deepens secondary school knowledge.