This lecture discusses the concept of symmetry in parallelograms, demonstrating that every parallelogram has a unique center of symmetry at the intersection point of its diagonals. Through a step-by-step proof, the instructor shows how the symmetry operation transforms the vertices of the parallelogram, leading to the conclusion that the center of symmetry cannot be a vertex. The lecture also covers the properties of midpoints and the relationships between the diagonals and sides of the parallelogram.