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{{short description|Relation between conic sections and triangles}} ...van Kempen: [http://forumgeom.fau.edu/FG2006volume6/FG200626.pdf ''On Some Theorems of Poncelet and Carnot'']. Forum Geometricorum, Volume 6 (2006), pp. 229–23 ...

...umgeom.fau.edu/FG2005volume5/FG200514.pdf ''On the Geometry of Equilateral Triangles'']. Forum Geometricorum, Volume 5 (2005), pp. 107–117 [[Category:Theorems about triangles and circles]] ...

...be the radius of the incircle, then ''r'' is also the altitude of all four triangles.{{r|alsina}} ...iculum/Geometry/NewtonTheorem.shtml#explanation ''Newton’s and Léon Anne’s Theorems''] at cut-the-knot.org ...

'''Maxwell's theorem''' is the following statement about triangles in the plane. ...-pp.12-20.pdf "Generalizations of some famous classical Euclidean geometry theorems."] ''International Journal of Computer Discovered Mathematics'', Vol. 1, No ...

...r|L}} lies on the [[Newton line]] if the two sums of the areas of opposing triangles are equal, according to Anne's theorem.]] ...e]]s with the edges of {{mvar|ABCD}}. If the two sums of areas of opposite triangles are equal: ...

...4 }}</ref><ref name=Vickers2016>Glenn T. Vickers, "The 19 Congruent Jacobi Triangles", ''[[Forum Geometricorum]]'' 16, 2016, 339–344. http://forumgeom.fau.edu/F ...N'' and triangles ''LMY'', ''NOZ'' and ''PKX'' are respectively similar to triangles ''OPD'', ''KLE'' and ''MNF'', then ''DY'', ''EZ'' and ''FX'' are concurrent ...

...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> ...

Therefore, the corresponding sides and angles of congruent triangles are equal ===Proof by similar triangles=== ...

...e [[Inscribed angle|inscribed-angle theorem]]). Consider the angles of the triangles {{math|△''ASD''}} and {{math|△''BSC''}}: This means the triangles {{math|△''ASD''}} and {{math|△''BSC''}} are similar and therefore ...

...from a given point to a given line such that the inscribed circles of the triangles formed by adjacent rays and the base line are equal. In the illustration th The theorem states that the incircles of the triangles formed (starting from any given ray) by every other ray, every third ray, e ...

{{Short description|On triangles in line arrangements}} ...le, four lines form at least two triangles, five lines form at least three triangles, etc. It is named after [[Samuel Roberts (mathematician)|Samuel Roberts]], ...

...theorem about two intersecting lines and a circle - the [[Power_of_a_point#Theorems|power of point theorem]]. [[Category:Theorems about circles]] ...

{{short description|Theorem about the midpoint of a line connecting squares on two sides of a triangle}} ...html GeoGebra Demonstrations Project - A Generalized Theorem - Equilateral Triangles] ...

...have an area of {{math|{{sfrac|1|2}}''r''(''s'' − ''a'')}}. So those two triangles together have an area of {{math|''r''(''s'' − ''a'')}}, and the area {{mvar ...Stefanov |first2=H. |last3=Velchev |first3=A. |title= Cosine and Cotangent Theorems for a Quadrilateral, two new Formulas for its Area and Their Applications | ...

{{Short description|Theorem about right triangles}} The triangles {{math|△''ADC'' , △'' BCD'' }} are [[Similar triangle#Similar triangles|similar]], since: ...

[[Category:Theorems about triangles]] ...

...eneralizes the Pythagorean theorem twofold. Firstly it works for arbitrary triangles rather than only for right angled ones and secondly it uses parallelograms [[Category:Theorems about triangles]] ...

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

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

...ry)#Congruence_of_triangles|SAS congruence theorem for triangles]] all six triangles are congruent, which yields |''IP_a''|=|''IQ_a''|=|''IP [[Category:Theorems about triangles and circles]] ...