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The Wolfram Language provides not only extensive support for analytic geometry, but also support for the symbolic representation of synthetic geometry scenes in a form suitable for automated coordinate-independent reasoning, as well as automated visualization.
GeometricScene — symbolic representation of a geometric scene defined by constraints
RandomInstance — find and display a random instance of a geometric scene
GeometricSolveValues — solve for values in a geometric scene
GeometricTest — get conditions for a geometric assertion outside of a geometric scene
FindGeometricConjectures — find conjectures about a geometric scene
GeometricScene — entities representing notable theorems and constructions
Assertions in Geometric ScenesGeometricAssertion — assert geometric properties or relations (convex, parallel, congruent, ...)
Equal ( ) — assert equality of geometric objects or quantities
Element ( ∈ ), RegionMember — assert that a point is in a geometric region
UnconstrainedParameters — option defining unconstrained points or quantities in a scene
GeometricStep — group hypotheses into a step in the construction of a geometric scene
Basic Geometric ObjectsLine — straight line through symbolically specified points
HalfLine, InfiniteLine — half-infinite and doubly infinite lines through pairs of points
Triangle, Polygon — triangle, polygon defined by corners
Circle, Disk — circle, disk defined by center and radius
RegularPolygon — regular polygon with sides, defined by center, etc.
Triangle FunctionsTriangleCenter — orthocenter, circumcenter, incenter, ... of triangles
TriangleConstruct — incircle, circumcircle, altitude, ... of triangles
TriangleMeasurement — circumradius, height, ... of triangles
Objects Created by Geometric ConstructionsCircleThrough — circle through specified points
Midpoint — midpoint of a line
PerpendicularBisector — infinite perpendicular at the midpoint of a line
AngleBisector — infinite line bisecting an angle
RegionCentroid — centroid of any region
RegionBoundary — boundary of any region
RegionNearest — point in a region nearest to a given point
Measurements on Geometric ObjectsEuclideanDistance — Euclidean distance between points
PlanarAngle — planar angle defined by three points
PolygonAngle — vertex angle of a polygon
Area — area of a geometric region
Perimeter — perimeter of a geometric region
ArcLength — arc lengths of circles, etc.
RegionMeasure — measure of a 1D, 2D, etc. region
RegionDistance — shortest distance from a point to a geometric region
SignedRegionDistance — distance positive/negative for points outside/inside
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