Search results

...cription|Given a triangle and a point, constructs a second triangle with a special point}} '''Maxwell's theorem''' is the following statement about triangles in the plane. ...

...circumcenter]] and <math>O_a,O_b,O_c</math> are the circumcenters of three triangles <math>OBC</math>, <math>OCA</math>, and <math>OAB</math> respectively. The ...tension from a circle to a conic having center: The creative method of new theorems], International Journal of Computer Discovered Mathematics, pp.21-32.</ref> ...

{{Short description|Theorem about right triangles}} ...le:Sehnensatz hoehensatz.svg|thumb|upright=1.2|geometric mean theorem as a special case of the [[intersecting chords theorem]]:<br/><math>|CD||DE|=|AD||DB| \L ...

...ry)#Congruence_of_triangles|SAS congruence theorem for triangles]] all six triangles are congruent, which yields |''IP_a''|=|''IQ_a''|=|''IP ...Side divider theorem2a.svg|thumb|upright=1.37|Conway's circle theorem as a special case of the generalisation, called "side divider theorem" (Villiers) or "wi ...

...y [[convex set]],{{r|emch|eggleston}} two special cases that both apply to triangles. | title = Squares inscribed in angles and triangles ...

{{for|the theorem about the moment of a force|Varignon's theorem (mechanics)}} ...etermine the area of the quadrilateral, and then to find areas of the four triangles divided by each side of the inner parallelogram. ...

== Special cases == [[Category:Theorems about triangles]] ...

[[Image:Pivot theorem.svg|thumb|right|300px|The Pivot Theorem for various triangles]] ...de|extensions]]). Draw three [[circumcircle]]s ('''Miquel's circles''') to triangles ''AB´C´'', ''A´BC´'', and ''A´B´C''. Miquel's theorem states that these cir ...

{{short description|Rational right triangles cannot have square area}} [[File:Fermat right triangles.svg|thumb|Two right triangles with the two legs of the top one equal to the leg and hypotenuse of the bot ...

...thumb|A triangulated polygon. The two vertices at the ends of the chain of triangles form ears. However, this polygon also has other ears that are not evident i ...on (a graph with one vertex per triangle and one edge per pair of adjacent triangles) will be a [[Tree (graph theory)|tree]] and each leaf of the tree will form ...

...{{cite book|last=Kimberling|first=Clark|title=Triangle Centers and Central Triangles|publisher=Utilitas Mathematica Publishing, Inc.|location=Winnipeg, Canada|u ...rspective and let {{mvar|DEF}} be the [[axis of perspectivity]] of the two triangles. The line {{mvar|DEF}} is the trilinear polar of the point {{mvar|Y}}. {{mv ...

* '''Routh's theorem''' - Many problems involving triangles with cevians will ask for areas, and mass points does not provide a method ...h special properties, like an [[angle bisector]] or an [[altitude]], other theorems may be used alongside mass point geometry that determine length ratios. On ...

...is used widely in [[Euclidean geometry]] to facilitate the proofs of many theorems and other results in geometry, especially in mathematical competitions and ...e.<ref name=":1">{{Cite journal|last=Baca|first=Jafet|date=2019|title=On a special center of spiral similarity|journal=Mathematical Reflections|volume=1|pages ...

...matics]], '''Marden's theorem''', named after [[Morris Marden]] but proved about 100 years earlier by Jörg Siebeck, gives a geometric relationship between t In the special case that the triangle is equilateral (as happens, for instance, for the po ...

The Droz-Farny line theorem is a special case of this result, when <math>P</math> is the orthocenter of triangle <ma [[Category:Theorems about triangles]] ...

...of hyperedges. It is a generalization of the [[graph removal lemma]]. The special case in which the graph is a tetrahedron is known as the [[tetrahedron remo [[Graph removal lemma]] is a special case with <math>r=2</math>. ...

...es of the prism relative to each other, breaking each square face into two triangles separated by a non-convex edge. Some twist angles produce a ''jumping polyh ...prism]], with two parallel equilateral triangles as its faces. One of the triangles is rotated ...

...>{{harvp|Anderson|2005}}; {{harvp|Reid|Szendröi|2005|loc= §3.10 Hyperbolic triangles and trig}}; {{harvp|Reiman|1999}}.</ref> It can also be related to the rela In comparison, the [[velocity addition formula]]s of [[special relativity]] for the x and y-directions as well as under an arbitrary angle ...

...clid's ''[[Euclid's Elements|Elements]]'' contains description of the four special points – [[centroid]], [[incenter]], [[circumcenter]] and [[orthocenter]] - In fact, the concurrency of the symmedians is a special case of a more general result: For any point P in the plane of triangle ABC ...

{{Short description|Property of all triangles on a Euclidean plane}} {{About|the trigonometric identity|the cosine law of optics|Lambert's cosine law}} ...