This lecture covers the construction of the mediatrice, which is the locus of points equidistant from two distinct points A and B. Through reflections and geometric axioms, the mediatrice is shown to be the line that intersects the segment [AB] at a single point, serving as an axis of symmetry. The process involves drawing circles centered at A and B, finding the intersection points, and justifying the properties of the mediatrice through isometries and geometric axioms.