predicates.md

Predicate Definitions

1. Geometric Shapes (20)

#	Predicates	Level	Logic form templates	Comments
1	Point	1	Point(A), Point($)
2	Line	1	Line(A,B), Line(m), Line($)
3	Angle	1	Angle(A,B,C), Angle(A), Angle(1), Angle($)
4	Triangle	1	Triangle(A,B,C), Triangle($), Triangle($1,$2,$3)
5	Quadrilateral	1	Quadrilateral(A,B,C,D), Quadrilateral($)
6	Parallelogram	1	Parallelogram(A,B,C,D), Parallelogram(1), Parallelogram($)
7	Square	1	Square(A,B,C,D), Square(1), Square($)
8	Rectangle	1	Rectangle(A,B,C,D), Rectangle(1), Rectangle($)
9	Rhombus	1	Rhombus(A,B,C,D), Rhombus(1), Rhombus($)
10	Trapezoid	1	Trapezoid(A,B,C,D), Trapezoid(1), Trapezoid($)
11	Kite	1	Kite(A,B,C,D), Kite(1), Kite($)
12	Polygon	1	Polygon($)
13	Pentagon	1	Pentagon(A,B,C,D,E), Pentagon($)
14	Hexagon	1	Hexagon(A,B,C,D,E,F), Hexagon($)
15	Heptagon	1	Heptagon(A,B,C,D,E,F,G), Heptagon($)
16	Octagon	1	Octagon(A,B,C,D,E,F,G,H), Octagon($)
17	Circle	1	Circle(A), Circle(1), Circle($)
18	Arc	1	Arc(A,B), Arc(A,B,C), Arc($)
19	Sector	1	Sector(O,A,B), Sector($)
20	Shape	1	Shape($)	Unknown shapes or regions

2. Unary Geometric Attributes (9)

#	Predicates	Level	Logic form templates	Comments
1	RightAngle	2	RightAngle(Angle($))
2	Right	2	Right(Triangle($))	Right triangle
3	Isosceles	2	Isosceles(Polygon($))	Isosceles polygon
4	Equilateral	2	Equilateral(Polygon($))	Equilateral polygon
5	Regular	2	Regular(Polygon($))
6	Red	2	Red(Shape($))
7	Blue	2	Blue(Shape($))
8	Green	2	Green(Shape($))
9	Shaded	2	Shaded(Shape($))

3. Geometric Attributes (17)

• Here [A-Z] stands for logic form of the prior level (e.g. level 1 logic forms - Shapes)

#	Predicates	Level	Logic form templates	Comments
1	AreaOf	2,3	AreaOf(A)
2	PerimeterOf	2,3	PerimeterOf(A)	Perimeter of the polygon A
3	RadiusOf	2,3	RadiusOf(A)
4	DiameterOf	2,3	DiameterOf(A)
5	CircumferenceOf	2,3	CircumferenceOf(A)	Perimeter of the circle A
6	AltitudeOf	2,3	AltitudeOf(A)	Altitude of the polygon A
7	HypotenuseOf	2,3	HypotenuseOf(A)	Hypotenuse of the triangle A
8	SideOf	2,3	SideOf(A)	Side of the square A
9	WidthOf	2,3	WidthOf(A)	Width of the quadrilateral A
10	HeightOf	2,3	HeightOf(A)	Height of the quadrilateral A
11	LegOf	2,3	LegOf(A)	Leg of the trapezoid A
12	BaseOf	2,3	BaseOf(A)	Base of the polygon A
13	MedianOf	2,3	MedianOf(A)	Median of the polygon A
14	IntersectionOf	2,3	IntersectionOf(A,B)	Intersection of shapes A and B
15	MeasureOf	2,3	MeasureOf(A)	Measure of the angle A
16	LengthOf	2,3	LengthOf(A)	Length of the line A
17	ScaleFactorOf	2,3	ScaleFactorOf(A,B)	Scale factor of the shape A to the shape B

4. Binary Geometric Relations (12)

#	Predicates	Level	Logic form templates	Comments
1	PointLiesOnLine	2,3	PointLiesOnLine(Point($),Line($1,$2)/LegOf(...))
2	PointLiesOnCircle	2,3	PointLiesOnCircle(Point($),Circle($))
3	Parallel	2,3	Parallel(Line($),Line($))
4	Perpendicular	2,3	Perpendicular(Line($),Line($))
5	IntersectAt	2,3	IntersectAt(Line($),Line($),Line($),Point($))
6	BisectsAngle	2,3	BisectsAngle(Line($),Angle($))
7	Congruent	2,3	Congruent(Polygon($),Polygon($))
8	Similar	2,3	Similar(Polygon($),Polygon($))
9	Tangent	2,3	Tangent(Line($),Circle($))
10	Secant	2,3	Secant(Line($),Circle($))
11	CircumscribedTo	2,3	CircumscribedTo(Shape($),Shape($))
12	InscribedIn	2,3	InscribedIn(Shape($),Shape($))

5. A-IsXOf-B Geometric Relations (15)

#	Predicates	Level	Logic form templates	Comments
1	IsMidpointOf	2,3	IsMidpointOf(Point($),Line($))	Point A is the midpoint of line B
2	IsCentroidOf	2,3	IsCentroidOf(Point($),Shape($))	Point A is the centroid of shape B
3	IsIncenterOf	2,3	IsIncenterOf(Point($),Shape($))	Point A is the incenter of shape B
4	IsRadiusOf	2,3	IsRadiusOf(Line($),Circle($))	Line A is the radius of circle B
5	IsDiameterOf	2,3	IsDiameterOf(Line($),Circle($))	Line A is the diameter of circle B
6	IsMidsegmentOf	2,3	IsMidsegmentOf(Line($),Triangle($))	Line A is the midsegment of triangle B
7	IsChordOf	2,3	IsChordOf(Line($),Circle($))	Line A is the chord of circle B
8	IsSideOf	2,3	IsSideOf(Line($),Polygon($))	Line A is the side of polygon B
9	IsHypotenuseOf	2,3	IsHypotenuseOf(Line($),Triangle($))	Line A is the hypotenuse of triangle B
10	IsPerpendicularBisectorOf	2,3	IsPerpendicularBisectorOf(Line($),Triangle($))	Line A is the perpendicular bisector of triangle B
11	IsAltitudeOf	2,3	IsAltitudeOf(Line($),Triangle($))	Line A is the altitude of triangle B
12	IsMedianOf	2,3	IsMedianOf(Line($),Quadrilateral($))	Line A is the median of quadrilateral B
13	IsBaseOf	2,3	IsBaseOf(Line($),Quadrilateral($))	Line A is the base of quadrilateral B
14	IsDiagonalOf	2,3	IsDiagonalOf(Line($),Quadrilateral($))	Line A is the diagonal of quadrilateral B
15	IsLegOf	2,3	IsLegOf(Line($),Trapezoid($))	Line A is the leg of trapezoid B

6. Numerical Attributes and Relations (18)

#	Predicates	Level	Logic form templates	Comments
1	SinOf	1,2	SinOf(Var)
2	CosOf	1,2	CosOf(Var)
3	TanOf	1,2	TanOf(Var)
4	CotOf	1,2	CotOf(Var)
5	HalfOf	1,2	HalfOf(Var)
6	SquareOf	1,2	SquareOf(Var)
7	SqrtOf	1,2	SqrtOf(Var)
8	RatioOf	2,3	RatioOf(Var), RatioOf(Var1,Var2)
9	SumOf	2,3	SumOf(Var1,Var2,...)
10	AverageOf	2,3	AverageOf(Var1,Var2,...)
11	Add	2,3	Add(Var1,Var2,...)
12	Mul	2,3	Mul(Var1,Var2,...)
13	Sub	2,3	Sub(Var1,Var2,...)
14	Div	2,3	Div(Var1,Var2,...)
15	Pow	2,3	Pow(Var1,Var2)
16	Equals	2,3	Equals(Var1,Var2)
17	Find	2,3	Find(Var)	Find the value of the varible
18	UseTheorem	N	UseTheorem(A_B_C)