Geometry is the mathematical study of shapes, sizes, positions, and spatial relationships in two and three dimensions. It forms the foundation for understanding our physical world — from architecture and engineering to computer graphics and navigation. At its core, geometry involves points, lines, angles, and figures that combine to create everything from simple triangles to complex polyhedra. The field divides into plane geometry (2D shapes on flat surfaces), solid geometry (3D objects in space), and analytic geometry (coordinates and algebraic methods). A key mental model: every geometric relationship can be proven using logic — unlike arithmetic where you calculate, in geometry you construct, measure, and demonstrate why things must be true.