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Equilic Quadrilateral


A quadrilateral in which a pair of opposite sides have the same length and are inclined at 60 degrees to each other (or equivalently, satisfy <A>+<B>=120 degrees). Some interesting theorems hold for such quadrilaterals. Let ABCD be an equilic quadrilateral with AD=BC and <A>+<B>=120 degrees. Then

1. The midpoints P, Q, and R of the diagonals and the side CD always determine an equilateral triangle.

2. If equilateral triangle PCD is drawn outwardly on CD, then DeltaPAB is also an equilateral triangle.

3. If equilateral triangles are drawn on AC, DC, and DB away from AB, then the three new graph vertices P, Q, and R are collinear.

See Honsberger (1985) for additional theorems.


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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.

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Equilic Quadrilateral

Cite this as:

Weisstein, Eric W. "Equilic Quadrilateral." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EquilicQuadrilateral.html

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