represents the assertion that the geometric object obj satisfies prop.


represents the assertion that the obji satisfy prop.


represents the assertion that objs satisfies each of the propi.


  • GeometricAssertion can be used in stating hypotheses in GeometricScene.
  • The propi can either be predicates that apply to individual geometric objects or relations that hold between geometric objects.
  • The following predicates for polygons can be used:
  • "Clockwise"the vertices are in clockwise order
    "Convex"the polygon is convex
    "Counterclockwise"the vertices are in counterclockwise order
    "Cyclic"the vertices lie on a circle
    "Equiangular"the interior angles are all equal
    "Equilateral"the side lengths are all equal
    "Regular"the polygon is regular
  • The following relations between points can be used:
  • "Clockwise"the points are in clockwise order if successively joined
    "Collinear"the points lie on a line
    "Counterclockwise"the points are in counterclockwise order if successively joined
    "CyclicallyOrdered"the points are in either clockwise or counterclockwise order
    "Distinct"the points are distinct
    {"EqualAngles",pt}successive angles subtended at pt are equal
  • The following relations between lines can be used:
  • "Antiparallel"the lines are parallel but in opposite directions
    "Concurrent"the lines intersect at a common point
    {"Concurrent",pt}the lines intersect at the point pt
    "MatchingParallel"the lines are parallel and in the same direction
    "Parallel"the lines are parallel (with any relative orientation)
    "Perpendicular"the lines are perpendicular
  • The following relations between geometric objects can be used:
  • "Congruent"the objects are congruent
    "PairwiseTangent"the objects are tangent to each other, in pairs
    "Similar"the objects are similar
    "Tangent"the objects are all tangent to each other at a common point
    {"Tangent",pt}the objects are all tangent at the point pt
  • If prop is a predicate, then GeometricAssertion[{obj1,obj2,},prop] is equivalent to GeometricAssertion[obj1,prop]&&GeometricAssertion[obj2,prop]&&.
  • GeometricAssertion[objs,prop1,prop2,] is equivalent to GeometricAssertion[objs,prop1]&&GeometricAssertion[objs,prop2]&&.


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Basic Examples  (1)

Use GeometricAssertion in a GeometricScene:

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Scope  (24)

Introduced in 2019