Plane geometry

The topic is divided into the following subtopics:

Positional problems
Triangles
Polygons
Circles
Geometric mappings

Positional problems

Part I:

Point, line, half-line, and line segment
Half-plane
Angle, pair of angles (corresponding, alternate, adjacent, vertical)
Relative position of two lines (parallel, intersecting, perpendicular)

Part II:

Mutual position of line and circle
Mutual position of two circles

Part III:

Sets of points with a given property
Thales' circle

Triangles

Part I:

Computation of angle measures in a triangle where the angles satisfy the given condition
Relationships between sides and angles of a triangle
Properties of triangles, computational problems
Medians, altitudes, midlines
Circle circumscribed and inscribed in a triangle

Part II:

Trigonometric functions in a right triangle
Application problems solved using trigonometric functions
Area of a triangle

Part III:

Law of sines and law of cosines
More complex application problems

Polygons

Part I:

Computational problems on angles, lengths and areas

Square
Rectangle
Rhombus

Part II:

Computational problems on angles, lengths and areas

Trapezoid
Parallelogram
Regular polygons

Part III:

Computational problems on angles, lengths and areas

Deltoid (Kite)
Complex computational problems on angles, lengths and areas

Circles

Part I:

Inscribed and central angle

Part II:

Angles between tangents
Polygons inscribed to a circle
Disc, annulus
Circular sector and circular segment

Part III:

Disc, circular sector and circular segment – complex problems
Segment angle

Geometric mappings

Part I:

Point symmetry
Line symmetry (reflection symmetry)

Part II:

Translation
Rotation

Part III:

Dilation