What is a complete quadrilateral?

Complete Quadrilateral. CompleteQuadrilateral. The figure determined by four lines, no three of which are concurrent, and their six points of intersection (Johnson 1929, pp. 61-62). Note that this figure is different from a complete quadrangle. read more

The complete quadrilateral is nothing but a 4-line in Morley's terminology. In a 1903 paper he showed that the perpendiculars from the 9-point centers. of the four triangles to the respective lines omitted from the 4-line in order to obtain the triangles, meet in a point. read more

A complete quadrilateral has three diagonals (compared to two for an ordinary quadrilateral). The midpoints of the diagonals of a complete quadrilateral are collinear on a line. A theorem due to Steiner states that in a complete quadrilateral, the bisectors of angles are concurrent at 16 points which are the incenters and excentres of the four triangles. read more

Theorem of Complete Quadrilateral. Four lines in general position (no two are parallel, no three pass through a point) define six points. The configuration of the six points and the connecting line segments that belong to the given lines is known as complete quadrilateral. read more

Note that this figure is different from a complete quadrangle. A complete quadrilateral has three diagonals (compared to two for an ordinary quadrilateral). read more