Category: Theorems about quadrilaterals

Anne's theorem
Anne's theorem, named after the French mathematician (1806–1850), is a statement from Euclidean geometry, which describes an equality of certain areas within a convex quadrilateral. Specifically, it s
Finsler–Hadwiger theorem
The Finsler–Hadwiger theorem is statement in Euclidean plane geometry that describes a third square derived from any two squares that share a vertex. The theorem is named after Paul Finsler and Hugo H
Theorem of the gnomon
The theorem of the gnomon states that certain parallelograms occurring in a gnomon have areas of equal size.
Parallelogram law
In mathematics, the simplest form of the parallelogram law (also called the parallelogram identity) belongs to elementary geometry. It states that the sum of the squares of the lengths of the four sid
Van Aubel's theorem
In plane geometry, Van Aubel's theorem describes a relationship between squares constructed on the sides of a quadrilateral. Starting with a given convex quadrilateral, construct a square, external to
British flag theorem
In Euclidean geometry, the British flag theorem says that if a point P is chosen inside a rectangle ABCD then the sum of the squares of the Euclidean distances from P to two opposite corners of the re
Varignon's theorem
Varignon's theorem is a statement in Euclidean geometry, that deals with the construction of a particular parallelogram, the Varignon parallelogram, from an arbitrary quadrilateral (quadrangle). It is
Bretschneider's formula
In geometry, Bretschneider's formula is the following expression for the area of a general quadrilateral: Here, a, b, c, d are the sides of the quadrilateral, s is the semiperimeter, and α and γ are a
Thébault's theorem
Thébault's theorem is the name given variously to one of the geometry problems proposed by the French mathematician Victor Thébault, individually known as Thébault's problem I, II, and III.
Petr–Douglas–Neumann theorem
In geometry, the Petr–Douglas–Neumann theorem (or the PDN-theorem) is a result concerning arbitrary planar polygons. The theorem asserts that a certain procedure when applied to an arbitrary polygon a
Euler's quadrilateral theorem
Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex quadrilateral and its diagonals. It is a gene