The Wolfram Language provides fully integrated support for plane geometry, including basic regions such as points, lines, triangles, and disks; functions for computing basic properties such as arc length and area; and nearest points to solvers to find the intersection of regions or integrals over regions.

Geometrical Objects »

Point  ▪  Line  ▪  HalfLine  ▪  InfiniteLine  ▪  HalfPlane  ▪  InfinitePlane

Rectangle  ▪  Parallelogram  ▪  RegularPolygon  ▪  Polygon

Circle  ▪  Disk

Geometric Constructions »

SSSTriangle — triangle specified by the length of its sides

SASTriangle  ▪  ASATriangle  ▪  AASTriangle  ▪  Triangle

Midpoint  ▪  AngleBisector  ▪  PerpendicularBisector  ▪  CircleThrough  ▪  ...

TriangleConstruct — incircle, circumcircle, altitude, ... of triangles

TriangleCenter — orthocenter, circumcenter, incenter, ... of triangles

Polygons »

Polygon — polygon or collections of polygons with or without holes

PolygonCoordinates  ▪  OuterPolygon  ▪  InnerPolygon  ▪  ...

Visualization

Graphics — visualize regions with different styles

Region — standard region visualization

Measures & Tests »

Area  ▪  Perimeter  ▪  ArcLength  ▪  PlanarAngle  ▪  PolygonAngle

TriangleMeasurement — circumradius, height, ... of triangles

RegionMember — test whether a point is in a region

RegionNearest — nearest point in a region to a given point

RegionQ  ▪  RegionDimension  ▪  RegionDistance  ▪  ...

CollinearPoints  ▪  PositivelyOrientedPoints  ▪  NegativelyOrientedPoints

Geometric Reasoning »

GeometricScene — symbolic representation of a geometric scene

RandomInstance — find and display a random instance of a geometric scene

FindGeometricConjectures — find conjectures about a geometric scene

GeometricAssertion — assert geometric properties or relations (convex, parallel, congruent, ...)

GeometricTest — test whether geometric objects satisfy given properties or relations

GeometricStep — representation of a step in the construction of a geometric scene

GeometricScene — entities representing notable theorems and constructions

Solving with Regions »

FindInstance — find examples of points in a region

Solve — find curve crossings etc.

NSolve  ▪  Reduce  ▪  Minimize  ▪  NMinimize  ▪  ...

Solid Geometry »

CSGRegion — constructive solid geometry region

Polygon  ▪  Polyhedron  ▪  Sphere  ▪  Ball  ▪  Cylinder  ▪  ...

General Geometry »

ImplicitRegion  ▪  MeshRegion  ▪  RegionUnion  ▪  ...

Geometric Data

PlaneCurve Lamina Polyhedron Solid