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.