View source for Quadrangle, complete

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A collection of four points $A,B,C,D$ (lying in a plane), no three of which lie on the same line, and the six lines connecting these points (cf. Fig.).

<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/q076010a.gif" />

Figure: q076010a

The points $A,B,C,D$ are called the vertices, and the lines $AB,CD,AC,BD,BC,AD$ are called the edges of the complete quadrangle. Edges that have no common vertex are called opposite; the points $P,Q,R$ of intersection of the opposite edges are called diagonal points.

If $S$ and $T$ are the points of intersection of the line $PQ$ with the lines $AD$ and $BC$, then the four points $P,Q,S,T$ form a [[Harmonic quadruple|harmonic quadruple]] of points. The dual figure to a quadrangle is called a quadrilateral — a collection of four lines (in a plane), no three of which contain a common point.

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  H.S.M. Coxeter,   "Projective geometry" , Springer  (1987)  pp. 7; 95</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  H.S.M. Coxeter,   "Introduction to geometry" , Wiley  (1963)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  M. Berger,   "Geometry" , '''1–2''' , Springer  (1987)  (Translated from French)</TD></TR></table>

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