A Quadrilateral in which a pair of opposite sides have the same length and are inclined at 60° 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 Vertices , , and are Collinear.

See Honsberger (1985) for additional theorems.

References

Garfunkel, J. The Equilic Quadrilateral.'' Pi Mu Epsilon J. 7, 317-329, 1981.

Honsberger, R. Mathematical Gems III. Washington, DC: Math. Assoc. Amer., pp. 32-35, 1985.