Complete quadrilateral
A configuration of four lines in general position, their six pairwise intersections, and the three pairs of opposite vertices and sides.
Projective plane: A geometric plane in which any two distinct lines meet at exactly one point. The configuration’s incidence relations hold naturally in projective geometry.
Diagonal triangle: The triangle formed by the three diagonal points of a complete quadrilateral. It captures the three intersections of opposite sides, central to the configuration.
Pappus's theorem: A projective geometry theorem asserting collinearity of three intersections formed from two triples of points on a line. Classical treatments relate its incidence structure to complete quadrilaterals.
Complete quadrangle: A configuration of four points, their six joining lines, and the associated opposite pairs. It is the point-line dual of the complete quadrilateral, often distinguished by terminology.
Complete polygon: A polygonal configuration formed by a finite set of points or lines and their connecting incidences. The quadrilateral is a four-line instance of the broader complete-polygon idea.
Incidence geometry: The study of points, lines, and other objects connected by incidence relations. The quadrilateral is defined by which lines meet at which points.
Diagonal points theorem: The theorem that the three diagonal points of a complete quadrangle are noncollinear in a projective plane. It states the basic incidence constraint on the quadrilateral’s three opposite-vertex intersections.
Jakob Steiner: A Swiss mathematician known for foundational work in geometry, especially projective and synthetic geometry. Steiner developed influential synthetic geometry around configurations including quadrilaterals.
Brianchon's theorem: A theorem stating that the three diagonals of a hexagon circumscribed about a conic are concurrent. Degenerate conic configurations connect its concurrency statement to quadrilateral geometry.
Affine geometry: The geometry of points, lines, and parallelism, without treating points at infinity as ordinary points. In an affine plane, parallel defining lines lack finite intersections, unlike in projective completion.