A quadrilateral in which a pair of opposite sides have the same length and are inclined at 
to each other (or equivalently, satisfy 
). Some interesting theorems
hold for such quadrilaterals. Let 
be an equilic quadrilateral with 
and 
. Then
1. The midpoints 
, 
, and 
of the diagonals and the side 
always determine an equilateral
triangle.
2. If equilateral triangle 
is drawn outwardly on 
, then 
is also an equilateral
triangle.
3. If equilateral triangles are drawn on 
,
,
and 
away from 
,
then the three new graph vertices 
, 
, and 
are collinear.
See Honsberger (1985) for additional theorems.
