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...] to the same [[inscribed circle]]. Pitot's theorem states that, for these quadrilaterals, the two sums of lengths of opposite sides are the same. Both sums of lengt ...edu/FG2011volume11/FG201108.pdf|title=More characterizations of tangential quadrilaterals|journal=Forum Geometricorum|volume=11|year=2011|pages=65–82|mr=2877281|acce ...

...n easily be derived from [[Anne's theorem]] considering that in tangential quadrilaterals the combined lengths of opposite sides are equal ([[Pitot theorem]]: ''a''& ...iculum/Geometry/NewtonTheorem.shtml#explanation ''Newton’s and Léon Anne’s Theorems''] at cut-the-knot.org ...

| title = A Cornucopia of Quadrilaterals ...iculum/Geometry/NewtonTheorem.shtml#explanation ''Newton's and Léon Anne's Theorems''] at cut-the-knot.org ...

...cause of the latter the restatement of the Pythagorean theorem in terms of quadrilaterals is occasionally called the '''Euler–Pythagoras theorem'''. ...[cycle graph]].<ref>Geoffrey A. Kandall: ''Euler's Theorem for Generalized Quadrilaterals''. The College Mathematics Journal, Vol. 33, No. 5 (Nov., 2002), pp. 403–40 ...

The '''eyeball theorem''' is a statement in elementary geometry about a property of a pair of disjoined circles. ...ow that this theorem is a consequence of the [[Japanese theorem for cyclic quadrilaterals]].<ref>[https://www.cut-the-knot.org/Curriculum/Geometry/Eyeball.shtml ''Th ...

[[Category:Theorems about triangles and circles]] [[Category:Theorems about equilateral triangles]] ...

== Complete quadrilaterals == == Applications to cyclic quadrilaterals== ...

{{for|the theorem about the moment of a force|Varignon's theorem (mechanics)}} ...for [[Polygon|''n''-gons]], then this area equality also holds for complex quadrilaterals.<ref name=Coxeter>[[Coxeter|Coxeter, H. S. M.]] and Greitzer, S. L. "Quadra ...

...hedron|convex polyhedra]]. It states that, for given numbers of triangles, quadrilaterals, pentagons, heptagons, and other polygons other than hexagons, ...other types that obeys this equation it is possible to choose a number of quadrilaterals that allows a 4-regular polyhedron to be realized.{{r|cp}} ...

*[[Japanese theorem for cyclic quadrilaterals]] [[Category:Theorems about triangles and circles]] ...

== General theorem about nested parallelograms == The theorem of gnomon is special case of a more general statement about nested parallelograms with a common diagonal. For a given parallelogram <ma ...

| title = A Cornucopia of Quadrilaterals | title = Some surprising theorems about rectangles in triangles ...

* [[Clifford's circle theorems]] [[Category:Theorems about triangles and circles]] ...

...points of tangency. The other faces of this arrangement are either bounded quadrilaterals, or unbounded. As the <math>n</math> lines have <math>n-2</math> consecuti [[Category:Eponymous theorems of geometry]] ...

...proofs that there are precisely two {{math|S{{sub|4}}}} that are actually "theorems": the Möbius configuration and one other. The latter (which corresponds to ...tion, the [[Möbius–Kantor configuration]] formed by two mutually inscribed quadrilaterals, has the [[Möbius–Kantor graph]], a subgraph of {{math|''Q''₄}}, ...

...is used widely in [[Euclidean geometry]] to facilitate the proofs of many theorems and other results in geometry, especially in mathematical competitions and ...rotation of the [[Cartesian coordinate system|plane]] followed a dilation about a center <math>O</math> with coordinates <math>c</math> in the plane.<ref n ...

...Book&nbsp;I of the ''Almagest'' presents [[Euclidean geometry|geometric]] theorems used for computing chords. Ptolemy used geometric reasoning based on Propo He used [[Ptolemy's theorem]] on quadrilaterals inscribed in a circle to derive formulas for the chord of a half-arc, the c ...

The [[theorem]] is named for [[Anders Johan Lexell]], who presented a paper about it {{c.|1777}} (published 1784) including both a [[spherical trigonometry|t ...5, using [[#Spherical parallelogram|spherical parallelogram]]s – spherical quadrilaterals with congruent opposite sides, which have parallel small circles passing th ...

...tional symmetry''. If the isometry is the reflection of a [[plane figure]] about a line, then the figure is said to have [[reflectional symmetry]] or [[line In one dimension, there is a point of symmetry about which reflection takes place; in two dimensions, there is an axis of symmet ...

...essentially the same as the minimum number of [[convex polygon|convex]] [[quadrilaterals]] determined by a set of {{mvar|n}} points in general position. The problem ...realized that this inequality yielded very simple proofs of some important theorems in [[Incidence (geometry)|incidence geometry]], such as [[Beck's theorem (g ...