Plane Geometry

Positional Problems

A:

  • 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)

B:

  • Mutual position of line and circle
  • Mutual position of two circles

C:

  • Sets of points with a given property 
  • Thales' circle

Triangles

A:

  • 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 

B:

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

C:

  • Law of sines and law of cosines
  • More complex application problems

Polygons

A:

Computational problems on angles, lengths and areas
  • Square
  • Rectangle
  • Rhombus

B:

Computational problems on angles, lengths and areas
  • Trapezoid
  • Parallelogram
  • Regular polygons

C:

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

Circles

A:

  • Inscribed and central angle

B:

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

C:

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

Transformations

A:

  • Point symmetry
  • Line symmetry (reflection symmetry)

B:

  • Translation
  • Rotation

C:

  • Dilation