Definition:Quadrangle/Complete

Definition

A complete quadrangle is a quadrangle whose $4$ points are joined by $6$ lines: one connecting each pair of points.

It is complete because every pair is connected.

Diagonal Points

Let $A$, $B$, $C$ and $D$ be the points of a complete quadrangle $ABCD$.

The diagonal points of $ABCD$ are the points of intersection of the lines:

$AB$ and $CD$

$AC$ and $BD$

$AD$ and $BC$.

In the above diagram, $ABCD$ are the initial $4$ points being connected.

The three diagonal points are $R$, $S$ and $T$.

Also see

• Definition:Simple Quadrangle

• Complete Quadrangle has Six Lines

• Definition:Complete Quadrilateral

• Results about complete quadrangles can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): complete quadrangle
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): quadrangle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): complete quadrangle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): quadrangle