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...m]] and a square version of the [[Napoleon's theorem]]. All three of these theorems are just a special case of [[Petr–Douglas–Neumann theorem]]. ...e vertex of the square distant from both triangles and the vertices of the triangles distant from the square is equilateral.<ref>http://www.cut-the-knot.org/Cur ...

{{Short description|Geometry theorem relating to triangles}} [[File:Hinge theorem.svg|400px|right]] ...

...mula]]'' can be thought as a special case of the Brahmagupta's formula for triangles. ...roaches zero, a cyclic quadrilateral converges into a cyclic triangle (all triangles are cyclic), and Brahmagupta's formula simplifies to Heron's formula. ...

[[Image:Carnot theorem2.svg|345px|right|thumb|<math>\begin{align} & DG + DH + DF \\ = {} & |DG| + |DH| + |DF| \\ = [[Category:Theorems about triangles and circles]] ...

...nt on [[inellipse]]s of triangles. From a projective point of view the two triangles <math>P_1P_3P_5</math> and <math>P_2P_4P_6</math> lie perspectively with ce [[Category:Theorems in projective geometry]] ...

[[File:Euler theorem2.svg|thumb|right|upright=1.0|Euler's theorem:<br/><math>d=|IO| =\sqrt{R (R-2r)}</math>]] ...+\frac{c}{a}-1 \geq \frac{2}{3} \left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a} \right) \geq 2,</math> ...

| align = right ...ter how one triangulates a cyclic ''quadrilateral'', the sum of inradii of triangles is constant. ...

...oint ''F'' the triangles ''FPX'', ''FQY'', and ''FRZ'' are similar to the triangles ''AOI, BOI, COI'' respectively.<ref name=Kiss/>{{rp|Propos. 4}} Its [[barycentric coordinate system#Barycentric coordinates on triangles|barycentric coordinates]] are<ref name=Kiss/> ...

[[Image:Triangle ABC with bisector AD.svg|thumb|240px|right|The theorem states for any triangle {{math|∠ ''DAB''}} and {{math|∠ ''DAC ===Proof using similar triangles=== ...

[[File:Congruent_non-congruent_triangles.svg|thumb|upright=1.2|The two triangles on the left are congruent. The third is [[Similarity (geometry)|similar]] t *Third, ''rotate'' the translated figure about the matched vertex until one pair of [[corresponding sides]] matches. ...

{{short description|Two triangles are in perspective axially if and only if they are in perspective centrally ...f perspectivity. The lines which run through corresponding vertices on the triangles meet at a point called the center of perspectivity. Desargues's theorem sta ...

...orem in 1746.<ref>{{citation|first=Matthew|last=Stewart|title=Some General Theorems of Considerable Use in the Higher Parts of Mathematics|year=1746|publisher= ...be positive or negative according to whether {{mvar|A}} is to the left or right of {{mvar|B}} in some fixed orientation of the line. In this formulation, t ...

[[File:Triangledissection.svg|thumb|right|By the Wallace–Bolyai–Gerwien theorem, a [[square]] can be cut into parts a ...gon into triangles and [[trapezoids]], which in turn can be converted into triangles. ...

[[File:Triangle with notations 2.svg|thumb|198px|right|Figure 1 – A triangle. The angles {{math|''α''}}, {{math|''β''}}, and {{mat ...ric Delights'', [[Princeton University Press]], 2002.</ref> is a statement about the relationship between the tangents of two angles of a [[triangle]] and t ...

In a [[right triangle]], the altitude drawn to the [[hypotenuse]] {{mvar|c}} divides the ...cides with a leg and intersects the opposite side at (has its foot at) the right-angled vertex, which is the orthocenter.]] ...

...st=Andrew P.|last=Guinand|title=Euler lines, tritangent centers, and their triangles|journal=[[American Mathematical Monthly]]|volume=91|issue=5|jstor=2322671|y ...oncurrent lines|concurrent]] at the nine-point center common to all of the triangles.<ref name="ac">Altshiller-Court, Nathan, ''College Geometry'', Dover Public ...

[[File:Menelaus' theorem 1.svg|right|thumb|Menelaus's theorem, case 1: line {{mvar|DEF}} passes inside triangle ...elaus's theorem''', named for [[Menelaus of Alexandria]], is a proposition about [[triangle]]s in [[plane geometry]]. Suppose we have a triangle {{math|△''A ...

==Theorems on books== ...

...riosity with regards to [[geometry]] and [[trigonometry]] – particularly [[triangles]] and [[rectangles]]. These were the shapes which provided the most questio Proof as we know it came about with one specific question: “what is a proof?” Traditionally, a proof is a ...

[[File:Morley triangle.svg|right|frame|If each vertex angle of the outer triangle is trisected, Morley's tri ...if all the trisectors are intersected, one obtains four other equilateral triangles. ...