Lecture
This lecture introduces the concept of distance in the plane, defining it as a positive real number between two points. The distance axioms are presented, including symmetry, non-negativity, and the triangle inequality. The lecture also covers the construction of triangles from three segments and the existence of segments of a given length. Additionally, it discusses the property of triangle sides and the simplification brought by the distance axiom. The demonstration of the proposition regarding triangle side lengths concludes the lecture.