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A line segment joining the midpoints of opposite sides of a quadrilateral or tetrahedron. Varignon's theorem states that the bimedians of a quadrilateral bisect each other ...

Given a quadrilateral ABCD, the three diagonal points P, Q, and R defined as the pairwise intersections of the lines determined by the sides AB intersection CD, AC ...

If two pairs of opposite polygon vertices of a complete quadrilateral are pairs of harmonic conjugate points, then the third pair of opposite polygon vertices is likewise a ...

For a quadrilateral which is not cyclic, Ptolemy's theorem becomes an inequality: AB×CD+BC×DA>AC×BD. The Ptolemy inequality is still valid when ABCD is a triangular pyramid ...

A parallelogram in which angles are oblique and adjacent sides are of unequal length.

Divide the sides of a quadrilateral into three equal parts. The figure formed by connecting and extending adjacent points on either side of a polygon vertex is a ...

A quadrilateral whose consecutive sides have the lengths a_1b_3, a_3b_2, a_2b_3, a_3b_1, where a_1^2+a_2^2=a_3^2 (1) and b_1^2+b_2^2=b_3^2. (2) Brahmagupta's trapezium is a ...

The orthopoles of a line l with respect to the four triangles formed by three out of four vertices of any quadrilateral ABCD lie on a straight line L known as the orthopolar ...

An natural equation which expresses a curve in terms of its arc length s and tangential angle phi.

The three diagonal points of a complete quadrilateral are never collinear.