This list of triangle topics includes things related to the geometric shape, either abstractly, as in idealizations studied by geometers, or in triangular arrays such as Pascal's triangle or triangular matrices, or concretely in physical space. It does not include metaphors like love triangle in which the word has no reference to the geometric shape.
Geometry
Triangle
Acute and obtuse triangles
Altern base
Altitude (triangle) Area bisector of a triangle Angle bisector of a triangle Angle bisector theorem Apollonius point Apollonius' theorem Automedian triangle Barrow's inequality Barycentric coordinates (mathematics) Bernoulli's quadrisection problem Brocard circle Brocard points Brocard triangle Carnot's theorem (conics) Carnot's theorem (inradius, circumradius) Carnot's theorem (perpendiculars) Catalogue of Triangle Cubics Centroid Ceva's theorem Cevian Circumconic and inconic Circumscribed circle Clawson point Cleaver (geometry) Congruence (geometry) Congruent isoscelizers point Contact triangle Conway triangle notation CPCTC Delaunay triangulation de Longchamps point Desargues' theorem Droz-Farny line theorem Encyclopedia of Triangle Centers Equal incircles theorem Equal parallelians point Equidissection Equilateral triangle Euler's line Euler's theorem in geometry Erdős–Mordell inequality Exeter point Exterior angle theorem Fagnano's problem Fermat point Fermat's right triangle theorem Fuhrmann circle Fuhrmann triangle Geometric mean theorem GEOS circle Gergonne point Golden triangle (mathematics) Gossard perspector Hadley's theorem Hadwiger–Finsler inequality Heilbronn triangle problem Heptagonal triangle Heronian triangle Heron's formula Hofstadter points Hyperbolic triangle (non-Euclidean geometry) Hypotenuse Incircle and excircles of a triangle Inellipse Integer triangle Isodynamic point Isogonal conjugate Isoperimetric point Isosceles triangle Isosceles triangle theorem Isotomic conjugate Isotomic lines Jacobi point Japanese theorem for concyclic polygons Johnson circles Kepler triangle Kobon triangle problem Kosnita's theorem Leg (geometry) Lemoine's problem Lester's theorem List of triangle inequalities Mandart inellipse Maxwell's theorem (geometry) Medial triangle Median (geometry) Menelaus' theorem Miquel's theorem Mittenpunkt Modern triangle geometry Monsky's theorem Morley centers Morley triangle Morley's trisector theorem Musselman's theorem Nagel point Napoleon points Napoleon's theorem Nine-point circle Nine-point hyperbola One-seventh area triangle Orthocenter Orthocentric system Orthocentroidal circle Orthopole Pappus' area theorem Parry point Pedal triangle Perimeter bisector of a triangle Perpendicular bisectors of triangle sides Polar circle (geometry) Pompeiu's theorem Pons asinorum Pythagorean theorem Inverse Pythagorean theorem Reuleaux triangle Regiomontanus Regiomontanus' angle maximization problem Reuschle's theorem Right triangle Routh's theorem Scalene triangle Schwarz triangle Schiffler's theorem Sierpinski triangle (fractal geometry) Similarity (geometry) Similarity system of triangles Simson line Special right triangles Spieker center Spieker circle Spiral of Theodorus Splitter (geometry) Steiner circumellipse Steiner inellipse Steiner–Lehmus theorem Stewart's theorem Steiner point Symmedian Tangential triangle Tarry point Ternary plot Thales' theorem Thomson cubic Triangle center Triangle conic Triangle group Triangle inequality Triangular bipyramid Triangular prism Triangular pyramid Triangular tiling Triangulation Trilinear coordinates Trilinear polarity Trisected perimeter point Viviani's theorem Wernau points Yff center of congruence