Category
page 1Theorems about triangles
Heron's formula
formula for calculating the area of a triangle
law of sines
property of all triangles on a Euclidean plane
law of cosines
property of all triangles on a Euclidean plane
Menelaus' theorem
theorem
Ceva's theorem
theorem in planar Euclidean geometry
law of tangents
theorem
Stewart's theorem
theorem describing a relation between the lengths of the sides and the length of a cevian in a triangle
Apollonius' theorem
theorem
Napoleon's theorem
theorem that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the lines connecting the centres of those equilateral triangles themselves form an equilateral triangle
Desargues' theorem
theorem that two triangles are in perspective axially if and only if they are in perspective centrally
Morley's trisector theorem
theorem
angle bisector theorem
two segments that divide a triangle
Mollweide's formula
two equations relating the side lengths and angles of a triangle
law of cotangents
theorem
exterior angle theorem
mathematical theorem, valid in absolute geometry, that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles
Routh's theorem
geometrical theorem of triangles
Pappus' area theorem
Relates areas of three parallelograms attached to three sides of an arbitrary triangle
midpoint theorem
geometric theorem involving midpoints on a triangle
Carnot's theorem (perpendiculars)
Condition for 3 lines with common point to be perpendicular to the sides of triangle
Marden's theorem
Geometric relationship between the zeros of a cubic polynomial and of its derivative
Jacobi's theorem
plane geometry theorem by Karl Friedrich Andreas Jacobi
Maxwell's theorem
Given a triangle and a point, constructs a second triangle with a special point
Bottema's theorem
theorem that, if one is given a triangle ABC and constructs squares on AC and BC, the midpoint of the line segment connecting the vertices of the squares opposite C is independent of the location of C
hinge theorem
geometry theorem relating to triangles
Droz-Farny line theorem
theorem in Euclidean geometry
Legendre's theorem on spherical triangles
theorem in geometry
Carnot's theorem (conics)
relation between conic sections and triangles
Thomsen's theorem
Sylvester's triangle problem
solved problem in mathematics