In a theory, a proposition that is obvious on its own and is not subject to any demonstration.


All mathematical theories are based on a set of definitions of mathematical objects and axioms that set the elementary properties of these objects.

Traditional Euclidean geometry is based on these elements:

  • basic objects:
    • a point is an elementary object that does not have any dimension;
    • the geometric plane is an unlimited set of points;
    • the lines of the plane are subsets of the points aligned in the plane
  • the axioms:
    • any two distinct points determine one single line;
    • a line segment can be indefinitely extended in a straight line;
    • given any line segment, a circle can be drawn by taking this segment as the radius and one of its end points as the centre;
    • all right angles are congruent;
    • in a plane, there is only one single line parallel to a given line through a point that is outside the line.

Try Buzzmath activities for free

and see how the platform can help you.