//
// Clear all Instantiation Theorems / Axioms / Definitions
//
public static void Clear()
{
//
// Algebra
//
RelationTransitiveSubstitution.Clear();
TransitiveSubstitution.Clear();
Point.Clear();
Angle.Clear();
Segment.Clear();
Arc.Clear();
Triangle.Clear();
Quadrilateral.Clear();
Circle.Clear();
TransitiveCongruentTriangles.Clear();
//
// Axioms
//
AASimilarity.Clear();
AngleAdditionAxiom.Clear();
ASA.Clear();
CongruentCorrespondingAnglesImplyParallel.Clear();
CorrespondingAnglesOfParallelLines.Clear();
SASCongruence.Clear();
SSS.Clear();
AnglesOfEqualMeasureAreCongruent.Clear();
//
// Definitions
//
AltitudeDefinition.Clear();
AngleBisectorDefinition.Clear();
ComplementaryDefinition.Clear();
CongruentSegmentsImplySegmentRatioDefinition.Clear();
CoordinateRightIsoscelesTriangles.Clear();
EquilateralTriangleDefinition.Clear();
IsoscelesTriangleDefinition.Clear();
MedianDefinition.Clear();
MidpointDefinition.Clear();
PerpendicularDefinition.Clear();
RightAngleDefinition.Clear();
RightTriangleDefinition.Clear();
SegmentBisectorDefinition.Clear();
//
// Theorems
//
AAS.Clear();
AdjacentAnglesPerpendicularImplyComplementary.Clear();
AltIntCongruentAnglesImplyParallel.Clear();
AltitudeOfRightTrianglesImpliesSimilar.Clear();
AngleBisectorIsPerpendicularBisectorInIsosceles.Clear();
CongruentAdjacentAnglesImplyPerpendicular.Clear();
CongruentAnglesInTriangleImplyCongruentSides.Clear();
CongruentSidesInTriangleImplyCongruentAngles.Clear();
ExteriorAngleEqualSumRemoteAngles.Clear();
HypotenuseLeg.Clear();
ParallelImplyAltIntCongruentAngles.Clear();
ParallelImplySameSideInteriorSupplementary.Clear();
PerpendicularImplyCongruentAdjacentAngles.Clear();
RelationsOfCongruentAnglesAreCongruent.Clear();
SameSideSuppleAnglesImplyParallel.Clear();
SASSimilarity.Clear();
SSSSimilarity.Clear();
TransversalPerpendicularToParallelImplyBothPerpendicular.Clear();
TriangleProportionality.Clear();
TwoPairsCongruentAnglesImplyThirdPairCongruent.Clear();
SupplementaryAndCongruentImplyRightAngles.Clear();
// Quadrilaterals
ParallelogramDefinition.Clear();
KiteDefinition.Clear();
RhombusDefinition.Clear();
RectangleDefinition.Clear();
SquareDefinition.Clear();
TrapezoidDefinition.Clear();
IsoscelesTrapezoidDefinition.Clear();
// Quadrilateral Theorems
BothPairsOppAnglesCongruentImpliesParallelogram.Clear();
BothPairsOppSidesCongruentImpliesParallelogram.Clear();
DiagonalsBisectEachOtherImplyParallelogram.Clear();
OnePairOppSidesCongruentParallelImpliesParallelogram.Clear();
// Circles
AngleInscribedSemiCircleIsRight.Clear();
CentralAngleEqualInterceptedArc.Clear();
ChordTangentAngleHalfInterceptedArc.Clear();
CongruentArcsHaveCongruentChords.Clear();
DiameterPerpendicularToChordBisectsChordAndArc.Clear();
ExteriorAngleHalfDifferenceInterceptedArcs.Clear();
InscribedAngleHalfInterceptedArc.Clear();
MinorArcsCongruentIfCentralAnglesCongruent.Clear();
PerpendicularToRadiusIsTangent.Clear();
TangentPerpendicularToRadius.Clear();
TangentsToCircleFromPointAreCongruent.Clear();
TwoChordsAnglesHalfSumInterceptedArc.Clear();
//TwoInterceptedArcsHaveCongruentAngles.Clear();
}
//
// Main instantiation function for all figures stated in the given list; worklist technique to construct the graph
//
public Hypergraph <GroundedClause, Hypergraph.EdgeAnnotation> Instantiate(List <ConcreteAST.GroundedClause> figure, List <ConcreteAST.GroundedClause> givens)
{
// The worklist initialized to initial set of ground clauses from the figure
List <GroundedClause> worklist = new List <GroundedClause>(figure);
worklist.AddRange(givens);
// Add all initial elements to the graph
figure.ForEach(g => { graph.AddNode(g); g.SetID(graph.Size()); });
givens.ForEach(g => { graph.AddNode(g); g.SetID(graph.Size()); });
// Indicate all figure-based information is intrinsic; this needs to verified with the UI
figure.ForEach(f => f.MakeIntrinsic());
// For problem generation, indicate that all given information is intrinsic
givens.ForEach(g => g.MakeGiven());
// Calculates Coverage of the figure
//HandleAllFigureIntrinsicFacts(figure);
HandleAllGivens(figure, givens);
//
// Process all new clauses until the worklist is empty
//
int numSequentialEquations = 0;
while (worklist.Any())
{
// Acquire the first element from the list for processing
GroundedClause clause = worklist[0];
worklist.RemoveAt(0);
if (Utilities.DEBUG)
{
Debug.WriteLine("Working on: " + clause.clauseId + " " + clause.ToString());
}
//
// Cutoff counter; seek a bunch of equations in sequence.
//
int NUMEQUATIONS_FOR_CUTOFF = 50;
if (clause is Equation || clause.IsAlgebraic() || clause is Supplementary)
{
numSequentialEquations++;
}
else
{
numSequentialEquations = 0;
}
if (numSequentialEquations >= NUMEQUATIONS_FOR_CUTOFF)
{
return(graph);
}
if (graph.Size() > 800)
{
return(graph);
}
//
// Apply the clause to all applicable instantiators
//
if (clause is Point)
{
Point.Record(clause);
}
else if (clause is Angle)
{
// A list of all problem angles
Angle.Record(clause);
if (clause is RightAngle)
{
HandleDeducedClauses(worklist, RightAngleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, ComplementaryDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RightTriangleDefinition.Instantiate(clause));
}
HandleDeducedClauses(worklist, ExteriorAngleEqualSumRemoteAngles.Instantiate(clause));
// HandleDeducedClauses(worklist, AngleAdditionAxiom.Instantiate(clause));
//HandleDeducedClauses(worklist, ConcreteAngle.Instantiate(null, clause));
//HandleDeducedClauses(worklist, AngleBisector.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularImplyCongruentAdjacentAngles.Instantiate(clause));
HandleDeducedClauses(worklist, AdjacentAnglesPerpendicularImplyComplementary.Instantiate(clause));
// Circle
HandleDeducedClauses(worklist, AngleInscribedSemiCircleIsRight.Instantiate(clause));
HandleDeducedClauses(worklist, InscribedAngleHalfInterceptedArc.Instantiate(clause));
HandleDeducedClauses(worklist, CentralAngleEqualInterceptedArc.Instantiate(clause));
HandleDeducedClauses(worklist, ChordTangentAngleHalfInterceptedArc.Instantiate(clause));
HandleDeducedClauses(worklist, TwoInterceptedArcsHaveCongruentAngles.Instantiate(clause));
}
else if (clause is Arc)
{
Arc.Record(clause);
if (clause is Semicircle)
{
HandleDeducedClauses(worklist, AngleInscribedSemiCircleIsRight.Instantiate(clause));
}
}
else if (clause is Segment)
{
HandleDeducedClauses(worklist, Segment.Instantiate(clause));
HandleDeducedClauses(worklist, AngleBisectorDefinition.Instantiate(clause));
Segment.Record(clause);
}
else if (clause is InMiddle)
{
HandleDeducedClauses(worklist, SegmentAdditionAxiom.Instantiate(clause));
HandleDeducedClauses(worklist, MidpointDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, MedianDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, SegmentBisectorDefinition.Instantiate(clause));
}
else if (clause is ArcInMiddle)
{
// HandleDeducedClauses(worklist, ArcAdditionAxiom.Instantiate(clause));
}
else if (clause is Intersection)
{
HandleDeducedClauses(worklist, AltitudeDefinition.Instantiate(clause));
if (clause is PerpendicularBisector)
{
HandleDeducedClauses(worklist, PerpendicularBisectorDefinition.Instantiate(clause));
}
else if (clause is Perpendicular)
{
HandleDeducedClauses(worklist, PerpendicularImplyCongruentAdjacentAngles.Instantiate(clause));
HandleDeducedClauses(worklist, AdjacentAnglesPerpendicularImplyComplementary.Instantiate(clause));
HandleDeducedClauses(worklist, TransversalPerpendicularToParallelImplyBothPerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularToRadiusIsTangent.Instantiate(clause));
}
else
{
HandleDeducedClauses(worklist, VerticalAnglesTheorem.Instantiate(clause));
HandleDeducedClauses(worklist, AltIntCongruentAnglesImplyParallel.Instantiate(clause));
HandleDeducedClauses(worklist, SameSideSuppleAnglesImplyParallel.Instantiate(clause));
HandleDeducedClauses(worklist, TriangleProportionality.Instantiate(clause));
HandleDeducedClauses(worklist, SegmentBisectorDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, CorrespondingAnglesOfParallelLines.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentCorrespondingAnglesImplyParallel.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentAdjacentAnglesImplyPerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, AngleBisectorIsPerpendicularBisectorInIsosceles.Instantiate(clause));
HandleDeducedClauses(worklist, TransversalPerpendicularToParallelImplyBothPerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, ParallelImplyAltIntCongruentAngles.Instantiate(clause));
HandleDeducedClauses(worklist, ParallelImplySameSideInteriorSupplementary.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, MedianDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, SupplementaryDefinition.Instantiate(clause));
// Quad Theorems
HandleDeducedClauses(worklist, DiagonalsParallelogramBisectEachOther.Instantiate(clause));
// Circles
HandleDeducedClauses(worklist, ChordTangentAngleHalfInterceptedArc.Instantiate(clause));
HandleDeducedClauses(worklist, DiameterPerpendicularToChordBisectsChordAndArc.Instantiate(clause));
HandleDeducedClauses(worklist, ExteriorAngleHalfDifferenceInterceptedArcs.Instantiate(clause));
HandleDeducedClauses(worklist, TangentPerpendicularToRadius.Instantiate(clause));
HandleDeducedClauses(worklist, TangentsToCircleFromPointAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, TwoChordsAnglesHalfSumInterceptedArc.Instantiate(clause));
}
}
else if (clause is Complementary)
{
HandleDeducedClauses(worklist, RelationsOfCongruentAnglesAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, ComplementaryDefinition.Instantiate(clause));
}
else if (clause is Altitude)
{
HandleDeducedClauses(worklist, AltitudeDefinition.Instantiate(clause));
}
else if (clause is AngleBisector)
{
HandleDeducedClauses(worklist, AngleBisectorDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, AngleBisectorTheorem.Instantiate(clause));
HandleDeducedClauses(worklist, AngleBisectorIsPerpendicularBisectorInIsosceles.Instantiate(clause));
}
else if (clause is Supplementary)
{
HandleDeducedClauses(worklist, SameSideSuppleAnglesImplyParallel.Instantiate(clause));
HandleDeducedClauses(worklist, RelationsOfCongruentAnglesAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, SupplementaryAndCongruentImplyRightAngles.Instantiate(clause));
}
else if (clause is SegmentRatio)
{
HandleDeducedClauses(worklist, TransitiveSubstitution.Instantiate(clause)); // Simplifies as well
}
else if (clause is Equation)
{
HandleDeducedClauses(worklist, TransitiveSubstitution.Instantiate(clause)); // Simplifies as well
HandleDeducedClauses(worklist, SegmentRatio.InstantiateEquation(clause));
if (clause is AngleEquation)
{
HandleDeducedClauses(worklist, AnglesOfEqualMeasureAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, ComplementaryDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RightAngleDefinition.Instantiate(clause));
}
// If a geometric equation was constructed, it may not have been checked for proportionality
if ((clause as Equation).IsGeometric())
{
HandleDeducedClauses(worklist, ProportionalAngles.Instantiate(clause));
HandleDeducedClauses(worklist, SegmentRatio.InstantiateEquation(clause));
}
}
else if (clause is Midpoint)
{
HandleDeducedClauses(worklist, MidpointDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, MidpointTheorem.Instantiate(clause));
}
else if (clause is Collinear)
{
HandleDeducedClauses(worklist, StraightAngleDefinition.Instantiate(clause));
}
else if (clause is Median)
{
HandleDeducedClauses(worklist, MedianDefinition.Instantiate(clause));
}
else if (clause is SegmentBisector)
{
HandleDeducedClauses(worklist, SegmentBisectorDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, MedianDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsBisectEachOtherImplyParallelogram.Instantiate(clause));
}
else if (clause is Parallel)
{
HandleDeducedClauses(worklist, TriangleProportionality.Instantiate(clause));
HandleDeducedClauses(worklist, CorrespondingAnglesOfParallelLines.Instantiate(clause));
HandleDeducedClauses(worklist, TransversalPerpendicularToParallelImplyBothPerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, ParallelImplyAltIntCongruentAngles.Instantiate(clause));
HandleDeducedClauses(worklist, ParallelImplySameSideInteriorSupplementary.Instantiate(clause));
// Quadrilaterals
HandleDeducedClauses(worklist, ParallelogramDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, TrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, OnePairOppSidesCongruentParallelImpliesParallelogram.Instantiate(clause));
}
else if (clause is SegmentRatioEquation)
{
HandleDeducedClauses(worklist, SASSimilarity.Instantiate(clause));
HandleDeducedClauses(worklist, SSSSimilarity.Instantiate(clause));
// HandleDeducedClauses(worklist, SegmentRatio.InstantiateProportion(clause));
HandleDeducedClauses(worklist, TransitiveSubstitution.Instantiate(clause)); // Simplifies as well
}
else if (clause is ProportionalAngles)
{
HandleDeducedClauses(worklist, ProportionalAngles.InstantiateProportion(clause));
}
else if (clause is CongruentTriangles)
{
HandleDeducedClauses(worklist, CongruentTriangles.Instantiate(clause));
HandleDeducedClauses(worklist, TransitiveCongruentTriangles.Instantiate(clause));
}
else if (clause is CongruentAngles)
{
HandleDeducedClauses(worklist, SupplementaryAndCongruentImplyRightAngles.Instantiate(clause));
HandleDeducedClauses(worklist, TwoPairsCongruentAnglesImplyThirdPairCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, SASCongruence.Instantiate(clause));
HandleDeducedClauses(worklist, ASA.Instantiate(clause));
HandleDeducedClauses(worklist, AAS.Instantiate(clause));
HandleDeducedClauses(worklist, AngleAdditionAxiom.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentAnglesInTriangleImplyCongruentSides.Instantiate(clause));
HandleDeducedClauses(worklist, SASSimilarity.Instantiate(clause));
HandleDeducedClauses(worklist, AASimilarity.Instantiate(clause));
HandleDeducedClauses(worklist, AltIntCongruentAnglesImplyParallel.Instantiate(clause));
HandleDeducedClauses(worklist, TransitiveSubstitution.Instantiate(clause)); // Simplifies as well
HandleDeducedClauses(worklist, CongruentCorrespondingAnglesImplyParallel.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentAdjacentAnglesImplyPerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, RelationsOfCongruentAnglesAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, AngleBisectorDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RightAngleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, SupplementaryDefinition.Instantiate(clause));
// Quadrilaterals
HandleDeducedClauses(worklist, BothPairsOppAnglesCongruentImpliesParallelogram.Instantiate(clause));
// Circles
HandleDeducedClauses(worklist, MinorArcsCongruentIfCentralAnglesCongruent.Instantiate(clause));
}
else if (clause is CongruentSegments)
{
HandleDeducedClauses(worklist, SegmentBisectorDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, SSS.Instantiate(clause));
HandleDeducedClauses(worklist, SASCongruence.Instantiate(clause));
HandleDeducedClauses(worklist, ASA.Instantiate(clause));
HandleDeducedClauses(worklist, AAS.Instantiate(clause));
HandleDeducedClauses(worklist, HypotenuseLeg.Instantiate(clause));
HandleDeducedClauses(worklist, EquilateralTriangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, IsoscelesTriangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, MidpointDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, TransitiveSubstitution.Instantiate(clause)); // Simplifies as well
HandleDeducedClauses(worklist, CongruentSidesInTriangleImplyCongruentAngles.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentSegmentsImplySegmentRatioDefinition.Instantiate(clause));
// For quadrilaterals
HandleDeducedClauses(worklist, IsoscelesTrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, KiteDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RhombusDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, BothPairsOppSidesCongruentImpliesParallelogram.Instantiate(clause));
HandleDeducedClauses(worklist, OnePairOppSidesCongruentParallelImpliesParallelogram.Instantiate(clause));
// Circles
HandleDeducedClauses(worklist, CongruentCircleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentArcsHaveCongruentChords.Instantiate(clause));
}
else if (clause is Triangle)
{
Triangle.Record(clause);
//HandleDeducedClauses(worklist, SumAnglesInTriangle.Instantiate(clause));
HandleDeducedClauses(worklist, Angle.InstantiateReflexiveAngles(clause));
HandleDeducedClauses(worklist, Triangle.Instantiate(clause));
HandleDeducedClauses(worklist, SSS.Instantiate(clause));
HandleDeducedClauses(worklist, SASCongruence.Instantiate(clause));
HandleDeducedClauses(worklist, ASA.Instantiate(clause));
HandleDeducedClauses(worklist, AAS.Instantiate(clause));
HandleDeducedClauses(worklist, HypotenuseLeg.Instantiate(clause));
HandleDeducedClauses(worklist, EquilateralTriangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, IsoscelesTriangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, ExteriorAngleEqualSumRemoteAngles.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentAnglesInTriangleImplyCongruentSides.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentSidesInTriangleImplyCongruentAngles.Instantiate(clause));
HandleDeducedClauses(worklist, SASSimilarity.Instantiate(clause));
HandleDeducedClauses(worklist, SSSSimilarity.Instantiate(clause));
HandleDeducedClauses(worklist, AASimilarity.Instantiate(clause));
HandleDeducedClauses(worklist, TriangleProportionality.Instantiate(clause));
HandleDeducedClauses(worklist, AcuteAnglesInRightTriangleComplementary.Instantiate(clause));
HandleDeducedClauses(worklist, TwoPairsCongruentAnglesImplyThirdPairCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, AltitudeDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RightTriangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, MedianDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentSegmentsImplySegmentRatioDefinition.Instantiate(clause));
if (clause is IsoscelesTriangle)
{
HandleDeducedClauses(worklist, IsoscelesTriangleTheorem.Instantiate(clause));
// CTA: Needs to worl with Equilateral Triangles as well
HandleDeducedClauses(worklist, AngleBisectorIsPerpendicularBisectorInIsosceles.Instantiate(clause));
}
if (clause is EquilateralTriangle)
{
HandleDeducedClauses(worklist, EquilateralTriangleHasSixtyDegreeAngles.Instantiate(clause));
}
}
else if (clause is Quadrilateral)
{
Quadrilateral.Record(clause);
if (clause is Quadrilateral)
{
if ((clause as Quadrilateral).IsStrictQuadrilateral())
{
HandleDeducedClauses(worklist, ParallelogramDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RhombusDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, SquareDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, KiteDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, TrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, BothPairsOppSidesCongruentImpliesParallelogram.Instantiate(clause));
HandleDeducedClauses(worklist, OnePairOppSidesCongruentParallelImpliesParallelogram.Instantiate(clause));
HandleDeducedClauses(worklist, BothPairsOppAnglesCongruentImpliesParallelogram.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsBisectEachOtherImplyParallelogram.Instantiate(clause));
}
}
if (clause is Parallelogram)
{
HandleDeducedClauses(worklist, ParallelogramDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RectangleDefinition.Instantiate(clause));
// Quad Theorems
HandleDeducedClauses(worklist, OppositeSidesOfParallelogramAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, OppositeAnglesOfParallelogramAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsParallelogramBisectEachOther.Instantiate(clause));
}
if (clause is Trapezoid)
{
HandleDeducedClauses(worklist, TrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, IsoscelesTrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, MedianTrapezoidParallelToBases.Instantiate(clause));
HandleDeducedClauses(worklist, MedianTrapezoidHalfSumBases.Instantiate(clause));
}
if (clause is IsoscelesTrapezoid)
{
HandleDeducedClauses(worklist, TrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, IsoscelesTrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, BaseAnglesIsoscelesTrapezoidCongruent.Instantiate(clause));
}
if (clause is Rhombus)
{
HandleDeducedClauses(worklist, RhombusDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, SquareDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsOfRhombusArePerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsOfRhombusBisectRhombusAngles.Instantiate(clause));
}
if (clause is Square)
{
HandleDeducedClauses(worklist, SquareDefinition.Instantiate(clause));
}
if (clause is Rectangle)
{
HandleDeducedClauses(worklist, RectangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsOfRectangleAreCongruent.Instantiate(clause));
}
if (clause is Kite)
{
HandleDeducedClauses(worklist, KiteDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsOfKiteArePerpendicular.Instantiate(clause));
}
}
else if (clause is Strengthened)
{
HandleDeducedClauses(worklist, IsoscelesTriangleTheorem.Instantiate(clause));
HandleDeducedClauses(worklist, IsoscelesTriangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, EquilateralTriangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, AcuteAnglesInRightTriangleComplementary.Instantiate(clause));
HandleDeducedClauses(worklist, AngleBisectorIsPerpendicularBisectorInIsosceles.Instantiate(clause));
HandleDeducedClauses(worklist, EquilateralTriangleHasSixtyDegreeAngles.Instantiate(clause));
HandleDeducedClauses(worklist, SASCongruence.Instantiate(clause));
HandleDeducedClauses(worklist, HypotenuseLeg.Instantiate(clause));
// For strengthening an intersection to a perpendicular
HandleDeducedClauses(worklist, PerpendicularImplyCongruentAdjacentAngles.Instantiate(clause));
HandleDeducedClauses(worklist, AdjacentAnglesPerpendicularImplyComplementary.Instantiate(clause));
HandleDeducedClauses(worklist, AltitudeDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, TransversalPerpendicularToParallelImplyBothPerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, RightTriangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularBisectorDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, SegmentBisectorDefinition.Instantiate(clause));
// InMiddle Strengthened to Midpoint
HandleDeducedClauses(worklist, MidpointDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, MidpointTheorem.Instantiate(clause));
HandleDeducedClauses(worklist, MedianDefinition.Instantiate(clause));
// Right Angle
HandleDeducedClauses(worklist, RightAngleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, ComplementaryDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RightTriangleDefinition.Instantiate(clause));
// Correlating isoceles triangles with right triangles.
CoordinateRightIsoscelesTriangles.Instantiate(clause);
// For quadrilateral definitions
HandleDeducedClauses(worklist, TrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, IsoscelesTrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, SquareDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, KiteDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, ParallelogramDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RectangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RhombusDefinition.Instantiate(clause));
// Quad Theorems
HandleDeducedClauses(worklist, OppositeSidesOfParallelogramAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, OppositeAnglesOfParallelogramAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsParallelogramBisectEachOther.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsBisectEachOtherImplyParallelogram.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsOfRectangleAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsOfKiteArePerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsOfRhombusArePerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsOfRhombusBisectRhombusAngles.Instantiate(clause));
HandleDeducedClauses(worklist, BaseAnglesIsoscelesTrapezoidCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, MedianTrapezoidParallelToBases.Instantiate(clause));
HandleDeducedClauses(worklist, MedianTrapezoidHalfSumBases.Instantiate(clause));
// Circle
HandleDeducedClauses(worklist, AngleInscribedSemiCircleIsRight.Instantiate(clause));
HandleDeducedClauses(worklist, ChordTangentAngleHalfInterceptedArc.Instantiate(clause));
HandleDeducedClauses(worklist, DiameterPerpendicularToChordBisectsChordAndArc.Instantiate(clause));
HandleDeducedClauses(worklist, ExteriorAngleHalfDifferenceInterceptedArcs.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularToRadiusIsTangent.Instantiate(clause));
HandleDeducedClauses(worklist, TangentPerpendicularToRadius.Instantiate(clause));
HandleDeducedClauses(worklist, TangentsToCircleFromPointAreCongruent.Instantiate(clause));
}
else if (clause is CircleIntersection)
{
HandleDeducedClauses(worklist, DiameterPerpendicularToChordBisectsChordAndArc.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularToRadiusIsTangent.Instantiate(clause));
}
else if (clause is Tangent)
{
// HandleDeducedClauses(worklist, ChordTangentAngleHalfInterceptedArc.Instantiate(clause));
// HandleDeducedClauses(worklist, ExteriorAngleHalfDifferenceInterceptedArcs.Instantiate(clause));
HandleDeducedClauses(worklist, TangentPerpendicularToRadius.Instantiate(clause));
HandleDeducedClauses(worklist, TangentsToCircleFromPointAreCongruent.Instantiate(clause));
}
else if (clause is CongruentArcs)
{
HandleDeducedClauses(worklist, TransitiveSubstitution.Instantiate(clause)); // Simplifies as well
HandleDeducedClauses(worklist, CongruentArcsHaveCongruentChords.Instantiate(clause));
HandleDeducedClauses(worklist, MinorArcsCongruentIfCentralAnglesCongruent.Instantiate(clause));
}
else if (clause is Circle)
{
Circle.Record(clause);
HandleDeducedClauses(worklist, CircleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, CentralAngleEqualInterceptedArc.Instantiate(clause));
//HandleDeducedClauses(worklist, ExteriorAngleHalfDifferenceInterceptedArcs.Instantiate(clause));
HandleDeducedClauses(worklist, InscribedAngleHalfInterceptedArc.Instantiate(clause));
//HandleDeducedClauses(worklist, TwoChordsAnglesHalfSumInterceptedArc.Instantiate(clause));
HandleDeducedClauses(worklist, InscribedQuadrilateralOppositeSupplementary.Instantiate(clause));
HandleDeducedClauses(worklist, TwoInterceptedArcsHaveCongruentAngles.Instantiate(clause));
}
else if (clause is CongruentCircles)
{
HandleDeducedClauses(worklist, CongruentCircleDefinition.Instantiate(clause));
}
}
return(graph);
}