public Page37Problem2(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 37 Problem 2";
Point a = new Point("A", -4, 0); points.Add(a);
Point b = new Point("B", 0, 0); points.Add(b);
Point c = new Point("C", -4, 7); points.Add(c);
Point x = new Point("X", 1, 3); points.Add(x);
Point y = new Point("Y", 1, 0); points.Add(y);
Point z = new Point("Z", 7, 0); points.Add(z);
Point p = new Point("P", 5, 7); points.Add(p);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment xy = new Segment(x, y); segments.Add(xy);
Segment yz = new Segment(y, z); segments.Add(yz);
Segment yp = new Segment(y, p); segments.Add(yp);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new Complementary((Angle)parser.Get(new Angle(a, b, c)), (Angle)parser.Get(new Angle(x, y, p))));
Addition sum = new Addition((Angle)parser.Get(new Angle(p, y, z)), (Angle)parser.Get(new Angle(x, y, p)));
given.Add(new GeometricAngleEquation(sum, new NumericValue(90)));
goals.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(a, b, c)), (Angle)parser.Get(new Angle(p, y, z))));
}
// Demonstration of theorem "Median of a trapezoid is half the sum of the bases"
/*
* D_______E
* / \
* L______/M________\N
* / \
* /_____________\
* A B
*/
public Page174Theorem416_2(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 174 Theorem 4-16 Part 2";
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 10, 0); points.Add(b);
Point c = new Point("C", 8, 4); points.Add(c);
Point d = new Point("D", 2, 4); points.Add(d);
Point l = new Point("L", -7, 2); points.Add(l);
Point m = new Point("M", 1, 2); points.Add(m);
Point n = new Point("N", 9, 2); points.Add(n);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment cd = new Segment(c, d); segments.Add(cd);
List<Point> pts = new List<Point>();
pts.Add(a);
pts.Add(m);
pts.Add(d);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(b);
pts.Add(n);
pts.Add(c);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(l);
pts.Add(m);
pts.Add(n);
collinear.Add(new Collinear(pts));
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment ad = (Segment)parser.Get(new Segment(a, d));
Segment bc = (Segment)parser.Get(new Segment(b, c));
Segment ln = (Segment)parser.Get(new Segment(l, n));
Quadrilateral quad = (Quadrilateral)parser.Get(new Quadrilateral(ad, bc, cd, ab));
Addition sum = new Addition(ab, cd);
//If segment MN is the median of the trapezoid, and segment LN is congruent to the sum of AB and CD, then
//segment AD must bisect segment LN
given.Add(new Strengthened(quad, new Trapezoid(quad)));
given.Add(new SegmentBisector(parser.GetIntersection(ln, ad), ln));
given.Add(new SegmentBisector(parser.GetIntersection(ln, bc), ln));
given.Add(new GeometricSegmentEquation(ln, sum));
goals.Add(new SegmentBisector(parser.GetIntersection(ad, ln), ad));
}
public static List<EdgeAggregator> Instantiate(GroundedClause c)
{
annotation.active = EngineUIBridge.JustificationSwitch.SEGMENT_ADDITION_AXIOM;
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
InMiddle im = c as InMiddle;
if (im == null) return newGrounded;
Segment s1 = new Segment(im.segment.Point1, im.point);
Segment s2 = new Segment(im.point, im.segment.Point2);
Addition sum = new Addition(s1, s2);
GeometricSegmentEquation eq = new GeometricSegmentEquation(sum, im.segment);
eq.MakeAxiomatic();
// For hypergraph
List<GroundedClause> antecedent = Utilities.MakeList<GroundedClause>(im);
newGrounded.Add(new EdgeAggregator(antecedent, eq, annotation));
return newGrounded;
}
private static List<EdgeAggregator> InstantiateToTheorem(Trapezoid trapezoid, GroundedClause original)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// If median has not been checked, check now
if (!trapezoid.IsMedianChecked()) trapezoid.FindMedian();
// Generate only if the median is valid (exists in the original figure)
if (!trapezoid.IsMedianValid()) return newGrounded;
Addition sum = new Addition(trapezoid.baseSegment, trapezoid.oppBaseSegment);
Multiplication product = new Multiplication(new NumericValue(2), trapezoid.median);
GeometricSegmentEquation gseq = new GeometricSegmentEquation(product, sum);
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(original);
newGrounded.Add(new EdgeAggregator(antecedent, gseq, annotation));
return newGrounded;
}
private static List<EdgeAggregator> InstantiateAngles(Angle angle1, Angle angle2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// An angle may have multiple names
if (angle1.Equates(angle2)) return newGrounded;
if (!angle1.GetVertex().Equals(angle2.GetVertex())) return newGrounded;
// Determine the shared segment if we have an adjacent situation
Segment shared = angle1.IsAdjacentTo(angle2);
if (shared == null) return newGrounded;
//
// If we combine these two angles, the result is a third angle, which, when measured,
// would be less than 180; this is contradictory since we measuare angles greedily and no circular angle is measured as > 180
//
if (angle1.measure + angle2.measure > 180) return newGrounded;
// Angle(A, B, C), Angle(C, B, D) -> Angle(A, B, C) + Angle(C, B, D) = Angle(A, B, D)
Point vertex = angle1.GetVertex();
Point exteriorPt1 = angle2.OtherPoint(shared);
Point exteriorPt2 = angle1.OtherPoint(shared);
Angle newAngle = new Angle(exteriorPt1, vertex, exteriorPt2);
Addition sum = new Addition(angle1, angle2);
GeometricAngleEquation geoAngEq = new GeometricAngleEquation(sum, newAngle);
geoAngEq.MakeAxiomatic(); // This is an axiomatic equation
// For hypergraph construction
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(angle1);
antecedent.Add(angle2);
newGrounded.Add(new EdgeAggregator(antecedent, geoAngEq, annotation));
return newGrounded;
}
//
// Triangle(A, B, C) -> m\angle ABC + m\angle CAB + m\angle BCA = 180^o
//
public static List<EdgeAggregator> Instantiate(GroundedClause c)
{
annotation.active = EngineUIBridge.JustificationSwitch.SUM_ANGLES_IN_TRIANGLE_180;
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
Triangle tri = c as Triangle;
if (tri == null) return newGrounded;
// Generate, by definition the sum of the three angles equal 180^o
Angle a1 = new Angle(tri.Point1, tri.Point2, tri.Point3);
Angle a2 = new Angle(tri.Point3, tri.Point1, tri.Point2);
Angle a3 = new Angle(tri.Point2, tri.Point3, tri.Point1);
Addition add = new Addition(a1, a2);
Addition overallAdd = new Addition(add, a3);
NumericValue value = new NumericValue(180); // Sum is 180^o
GeometricAngleEquation eq = new GeometricAngleEquation(overallAdd, value);
List<GroundedClause> antecedent = Utilities.MakeList<GroundedClause>(tri);
newGrounded.Add(new EdgeAggregator(antecedent, eq, annotation));
return newGrounded;
}
//
// Inflate am entire flattened side of an equation
//
private static GroundedClause InflateEntireSide(List<GroundedClause> side)
{
GroundedClause singleExp;
if (side.Count <= 1)
{
singleExp = InflateTerm(side[0]);
}
else
{
singleExp = new Addition(InflateTerm(side[0]), InflateTerm(side[1]));
for (int i = 2; i < side.Count; i++)
{
singleExp = new Addition(singleExp, InflateTerm(side[i]));
}
}
return singleExp;
}
private static EdgeAggregator ConstructExteriorRelationship(Triangle tri, Angle extAngle)
{
//
// Acquire the remote angles
//
Angle remote1 = null;
Angle remote2 = null;
tri.AcquireRemoteAngles(extAngle.GetVertex(), out remote1, out remote2);
//
// Construct the new equation
//
Addition sum = new Addition(remote1, remote2);
GeometricAngleEquation eq = new GeometricAngleEquation(extAngle, sum);
//
// For the hypergraph
//
List<GroundedClause> antecedent = Utilities.MakeList<GroundedClause>(tri);
antecedent.Add(extAngle);
return new EdgeAggregator(antecedent, eq, annotation);
}