Search results

{{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: ...

[[File:GeneralisationOfNapoleonPoint.svg|300px|right|thumb|Adjacent colored angles are equal in measure. The point {{mvar|N}} is ...4 }}</ref><ref name=Vickers2016>Glenn T. Vickers, "The 19 Congruent Jacobi Triangles", ''[[Forum Geometricorum]]'' 16, 2016, 339–344. http://forumgeom.fau.edu/F ...

[[File:Kosnita points.svg|300px|right|thumb|X(54) is the Kosnita point of the triangle ABC]] ...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 ...

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}} [[File:Bottema's_theorem.png| thumb | right | 350px | Bottema's theorem construction; changing the location of vertex < ...

[[File:Herontriangle1greek.svg|thumb|270px|right|A triangle, showing the "incircle" and the partitioning of the sides. The [[File:Herontriangle2greek.svg|thumb|270px|right|By the above reasoning, all six parts are as shown.]] ...

{{Short description|Theorem about right triangles}} ...between the [[Altitude (triangle)|altitude]] on the [[hypotenuse]] in a [[right triangle]] and the two line segments it creates on the hypotenuse. It state ...

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

...or a right-angled triangle, two parallelograms attached to the legs of the right angle yield a rectangle of equal area on the third side and again if the tw [[Category:Theorems about triangles]] ...

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

...y [[convex set]],{{r|emch|eggleston}} two special cases that both apply to triangles. ...In a [[right triangle]] there are two inscribed squares, one touching the right angle of the triangle and the other lying on the opposite side. An [[obtuse ...

...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]] ...