public Page6Prob32b(bool onoff, bool complete)
: base(onoff, complete)
{
Point r = new Point("R", -8 * System.Math.Sin(0.3 * System.Math.PI), 8 * System.Math.Cos(0.3 * System.Math.PI)); points.Add(r);
Point p = new Point("P", 0, 0); points.Add(p);
Point s = new Point("S", 8 * System.Math.Sin(0.3 * System.Math.PI), 8 * System.Math.Cos(0.3 * System.Math.PI)); points.Add(s);
Point q = new Point("Q", 0, -4); points.Add(q);
Segment rp = new Segment(r, p); segments.Add(rp);
Segment ps = new Segment(p, s); segments.Add(ps);
Segment pq = new Segment(p, q); segments.Add(pq);
circles.Add(new Circle(p, 8));
circles.Add(new Circle(q, 4));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
known.AddSegmentLength(pq, 4);
known.AddAngleMeasureDegree((Angle)parser.Get(new Angle(r, p, s)), 108);
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 0.5, -4));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(16 * System.Math.PI);
}
public Page6Row3Prob32c(bool onoff, bool complete)
: base(onoff, complete)
{
Point r = new Point("R", -8 * System.Math.Sin(0.3 * System.Math.PI), 8 * System.Math.Cos(0.3 * System.Math.PI)); points.Add(r);
Point p = new Point("P", 0, 0); points.Add(p);
Point s = new Point("S", 8 * System.Math.Sin(0.3 * System.Math.PI), 8 * System.Math.Cos(0.3 * System.Math.PI)); points.Add(s);
Point q = new Point("Q", 0, -4); points.Add(q);
Segment rp = new Segment(r, p); segments.Add(rp);
Segment ps = new Segment(p, s); segments.Add(ps);
Segment pq = new Segment(p, q); segments.Add(pq);
circles.Add(new Circle(p, 8));
circles.Add(new Circle(q, 4));
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
known.AddSegmentLength(pq, 4);
known.AddAngleMeasureDegree((Angle)parser.Get(new Angle(r, p, s)), 108);
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 7, 0));
wanted.Add(new Point("", -7, 0));
wanted.Add(new Point("", -2, 1));
wanted.Add(new Point("", 2, 1));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(28.8 * System.Math.PI);
problemName = "McDougall Page 6 Row 3 Problem 32c";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public Page145Problem07(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 145 Problem 7";
Point f = new Point("F", 0, 5); points.Add(f);
Point l = new Point("L", 4, 7); points.Add(l);
Point k = new Point("K", 4, 3); points.Add(k);
Point a = new Point("A", 5, 5); points.Add(a);
Point j = new Point("J", 3, 5); points.Add(j);
Segment fl = new Segment(f, l); segments.Add(fl);
Segment fk = new Segment(f, k); segments.Add(fk);
Segment al = new Segment(a, l); segments.Add(al);
Segment ak = new Segment(a, k); segments.Add(ak);
Segment jl = new Segment(j, l); segments.Add(jl);
Segment jk = new Segment(j, k); segments.Add(jk);
List<Point> pts = new List<Point>();
pts.Add(f);
pts.Add(j);
pts.Add(a);
collinear.Add(new Collinear(pts));
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments(al, ak));
given.Add(new GeometricCongruentSegments(fl, fk));
goals.Add(new GeometricCongruentSegments(jl, jk));
}
public Page226Problem42(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 226 Problem 42";
Point j = new Point("J", 0, 0); points.Add(j);
Point k = new Point("K", 0, 12); points.Add(k);
Point l = new Point("L", 3, 2); points.Add(l);
Point m = new Point("M", 3, 10); points.Add(m);
Point n = new Point("N", 9, 6); points.Add(n);
Segment jk = new Segment(j, k); segments.Add(jk);
Segment lm = new Segment(l, m); segments.Add(lm);
List<Point> pts = new List<Point>();
pts.Add(j);
pts.Add(l);
pts.Add(n);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(k);
pts.Add(m);
pts.Add(n);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new IsoscelesTriangle((Segment)parser.Get(new Segment(k, n)), (Segment)parser.Get(new Segment(j, n)), jk));
given.Add(new GeometricParallel(jk, lm));
goals.Add(new Strengthened((Triangle)parser.Get(new Triangle(n, m, l)), new IsoscelesTriangle((Triangle)parser.Get(new Triangle(n, m, l)))));
}
public Page301Problem42(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 301 Problem 42";
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 6); points.Add(b);
Point c = new Point("C", 4, 3); points.Add(c);
Point d = new Point("D", 8, 0); points.Add(d);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment ac = new Segment(a, c); segments.Add(ac);
Segment ad = new Segment(a, d); segments.Add(ad);
List<Point> pts = new List<Point>();
pts.Add(b);
pts.Add(c);
pts.Add(d);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new Midpoint((InMiddle)parser.Get(new InMiddle( c, (Segment)parser.Get(new Segment(b, d))))));
given.Add(new RightAngle(b, a, d));
goals.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(b, c)), ac));
goals.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(d, c)), ac));
}
public Page223Problem24(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 223 Problem 24";
Point b = new Point("B", 2, 4); points.Add(b);
Point n = new Point("N", 8, 4); points.Add(n);
Point l = new Point("L", 0, 0); points.Add(l);
Point c = new Point("C", 10, 0); points.Add(c);
Point m = new Point("M", 5, 2.5); points.Add(m);
Segment cl = new Segment(c, l); segments.Add(cl);
Segment bn = new Segment(b, n); segments.Add(bn);
List<Point> pts = new List<Point>();
pts.Add(l);
pts.Add(m);
pts.Add(n);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(b);
pts.Add(m);
pts.Add(c);
collinear.Add(new Collinear(pts));
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(m, b, n)), (Angle)parser.Get(new Angle(m, c, l))));
}
public Page2Prob15(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point a = new Point("A", 0, 4); points.Add(a);
Point b = new Point("B", -4, 0); points.Add(b);
Segment oa = new Segment(o, a); segments.Add(oa);
Segment ob = new Segment(o, b); segments.Add(ob);
Segment ab = new Segment(a, b); segments.Add(ab);
circles.Add(new Circle(o, 4.0));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new RightAngle((Angle)parser.Get(new Angle(a, o, b))));
known.AddSegmentLength(oa, 4);
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", -2.828, 2.8));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(4.566370614);
}
public Page164Problem36(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 164 Problem 36";
Point a = new Point("A", 11, 8); points.Add(a);
Point b = new Point("B", 10, 8); points.Add(b);
Point c = new Point("C", 10, 11); points.Add(c);
Point d = new Point("D", 0, 8); points.Add(d);
Point e = new Point("E", 0, 0); points.Add(e);
Point f = new Point("F", 10, 0); points.Add(f);
Segment de = new Segment(d, e); segments.Add(de);
Segment ef = new Segment(e, f); segments.Add(ef);
List<Point> pts = new List<Point>();
pts.Add(f);
pts.Add(b);
pts.Add(c);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(d);
pts.Add(b);
pts.Add(a);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(b, d, e)), (Angle)parser.Get(new Angle(c, b, d))));
goals.Add(new GeometricParallel(de, new Segment(f, c)));
}
public Page223Problem23(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 223 Problem 23";
Point j = new Point("J", 0, 0); points.Add(j);
Point i = new Point("I", 3, 3); points.Add(i);
Point y = new Point("Y", 7, 7); points.Add(y);
Point g = new Point("G", 6, 0); points.Add(g);
Point z = new Point("Z", 7, 0); points.Add(z);
Segment ig = new Segment(i, g); segments.Add(ig);
Segment yz = new Segment(y, z); segments.Add(yz);
List<Point> pts = new List<Point>();
pts.Add(j);
pts.Add(i);
pts.Add(y);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(j);
pts.Add(g);
pts.Add(z);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(j, g, i)), (Angle)parser.Get(new Angle(j, y, z))));
goals.Add(new GeometricSimilarTriangles((Triangle)parser.Get(new Triangle(j, i, g)), (Triangle)parser.Get(new Triangle(j, z, y))));
}
public Page316Problem42(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 316 Problem 42";
Point p = new Point("P", 10, 0); points.Add(p);
Point q = new Point("Q", 0, 0); points.Add(q);
Point l = new Point("L", 0, 6); points.Add(l);
Point m = new Point("M", 10, 6); points.Add(m);
Point n = new Point("N", 3, 3); points.Add(n);
Segment lm = new Segment(l, m); segments.Add(lm);
Segment ln = new Segment(l, n); segments.Add(ln);
Segment mn = new Segment(m, n); segments.Add(mn);
Segment np = new Segment(n, p); segments.Add(np);
Segment nq = new Segment(n, q); segments.Add(nq);
Segment pq = new Segment(p, q); segments.Add(pq);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(m, l, n)), (Angle)parser.Get(new Angle(n, q, p))));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(n, m, l)), (Angle)parser.Get(new Angle(n, p, q))));
given.Add(new GeometricCongruentSegments(ln, nq));
goals.Add(new GeometricCongruentTriangles(new Triangle(l, m, n), new Triangle(q, p, n)));
}
public Page73Problem8(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 73 Problem 8";
Point t = new Point("T", -4, 5); points.Add(t);
Point n = new Point("N", 0, 5); points.Add(n);
Point s = new Point("S", 0, 0); points.Add(s);
Point h = new Point("H", 0, -5); points.Add(h);
Point u = new Point("U", 4, -5); points.Add(u);
Segment nt = new Segment(n, t); segments.Add(nt);
Segment hu = new Segment(h, u); segments.Add(hu);
List<Point> pts = new List<Point>();
pts.Add(t);
pts.Add(s);
pts.Add(u);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(n);
pts.Add(s);
pts.Add(h);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(s, u, h)), (Angle)parser.Get(new Angle(n, t, s))));
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(n, s)), (Segment)parser.Get(new Segment(s, h))));
goals.Add(new GeometricCongruentTriangles(new Triangle(s, n, t), new Triangle(s, h, u)));
}
public Page66Problem16(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 66 Problem 16";
Point a = new Point("A", 1, 5); points.Add(a);
Point b = new Point("B", 8, 5); points.Add(b);
Point c = new Point("C", 7, 0); points.Add(c);
Point d = new Point("D", 0, 0); points.Add(d);
Segment ba = new Segment(b, a); segments.Add(ba);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment ad = new Segment(a, d); segments.Add(ad);
Segment bd = new Segment(b, d); segments.Add(bd);
Segment cd = new Segment(c, d); segments.Add(cd);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments(ba, cd));
given.Add(new GeometricCongruentSegments(bc, ad));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(a, b, d)), (Angle)parser.Get(new Angle(c, d, b))));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(a, d, b)), (Angle)parser.Get(new Angle(c, b, d))));
goals.Add(new GeometricCongruentTriangles(new Triangle(a, b, d), new Triangle(c, d, b)));
}
public Page273Problem39(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 273 Problem 39";
Point a = new Point("A", 1, 0); points.Add(a);
Point b = new Point("B", 0, 5); points.Add(b);
Point c = new Point("C", 3, 3); points.Add(c);
Point d = new Point("D", 5, 6); points.Add(d);
Point e = new Point("E", 6, 1); points.Add(e);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment de = new Segment(d, e); segments.Add(de);
List<Point> pts = new List<Point>();
pts.Add(a);
pts.Add(c);
pts.Add(d);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(b);
pts.Add(c);
pts.Add(e);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new SegmentBisector(parser.GetIntersection(new Segment(a, d), new Segment(b, e)), (Segment)parser.Get(new Segment(a, d))));
given.Add(new GeometricParallel(ab, de));
goals.Add(new GeometricCongruentTriangles(new Triangle(a, b, c), new Triangle(d, e, c)));
}
public Page69Problem14(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 69 Problem 14";
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 7, -6); points.Add(b);
Point c = new Point("C", 14, 0); points.Add(c);
Point d = new Point("D", 7, 0); points.Add(d);
Segment ba = new Segment(b, a); segments.Add(ba);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment bd = new Segment(b, d); segments.Add(bd);
List<Point> pts = new List<Point>();
pts.Add(a);
pts.Add(d);
pts.Add(c);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments(ba, bc));
given.Add(new Midpoint((InMiddle)parser.Get(new InMiddle(d, (Segment)parser.Get(new Segment(a, c))))));
goals.Add(new GeometricCongruentTriangles(new Triangle(a, b, d), new Triangle(c, b, d)));
}
public Page223Problem22(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 223 Problem 22";
Point x = new Point("X", 1, 0); points.Add(x);
Point f = new Point("F", 3, 4); points.Add(f);
Point s = new Point("S", 4, 6); points.Add(s);
Point e = new Point("E", 5, 0); points.Add(e);
Point r = new Point("R", 7, 0); points.Add(r);
Segment rs = new Segment(r, s); segments.Add(rs);
Segment ef = new Segment(e, f); segments.Add(ef);
List<Point> pts = new List<Point>();
pts.Add(x);
pts.Add(e);
pts.Add(r);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(x);
pts.Add(f);
pts.Add(s);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricParallel(rs, ef));
goals.Add(new GeometricSimilarTriangles((Triangle)parser.Get(new Triangle(f, x, e)), (Triangle)parser.Get(new Triangle(s, x, r))));
}
public Page231Problem14(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 231 Problem 14";
Point j = new Point("J", 0, 0); points.Add(j);
Point k = new Point("K", 3, 2); points.Add(k);
Point l = new Point("L", 9, 0); points.Add(l);
Point m = new Point("M", 5, 0); points.Add(m);
Point n = new Point("N", 3, -2); points.Add(n);
Segment jk = new Segment(j, k); segments.Add(jk);
Segment jn = new Segment(j, n); segments.Add(jn);
Segment kl = new Segment(k, l); segments.Add(kl);
Segment km = new Segment(k, m); segments.Add(km);
Segment ln = new Segment(l, n); segments.Add(ln);
Segment mn = new Segment(m, n); segments.Add(mn);
List<Point> pts = new List<Point>();
pts.Add(j);
pts.Add(m);
pts.Add(l);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentTriangles(new Triangle(j, k, m), new Triangle(j, n, m)));
goals.Add(new GeometricCongruentTriangles(new Triangle(j, k, l), new Triangle(j, n, l)));
}
public Page145Problem04(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 145 Problem 4";
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 5, 0); points.Add(b);
Point d = new Point("D", 1, 4); points.Add(d);
Point c = new Point("C", 6, 4); points.Add(c);
Point l = new Point("L", 2, 3); points.Add(l);
Point m = new Point("M", 4, 1); points.Add(m);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment cd = new Segment(c, d); segments.Add(cd);
Segment ad = new Segment(a, d); segments.Add(ad);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment al = new Segment(a, l); segments.Add(al);
Segment cm = new Segment(c, m); segments.Add(cm);
List<Point> pts = new List<Point>();
pts.Add(d);
pts.Add(l);
pts.Add(m);
pts.Add(b);
collinear.Add(new Collinear(pts));
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments(ab, cd));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(c, d, l)), (Angle)parser.Get(new Angle(m, b, a))));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(d, a, l)), (Angle)parser.Get(new Angle(m, c, b))));
goals.Add(new GeometricCongruentSegments(al, cm));
}
/// <summary>
/// Create a new triangle bounded by the 3 given segments. The set of points that define these segments should have only 3 distinct elements.
/// </summary>
/// <param name="a">The segment opposite point a</param>
/// <param name="b">The segment opposite point b</param>
/// <param name="c">The segment opposite point c</param>
public Triangle(Segment a, Segment b, Segment c)
: base(a, b, c)
{
SegmentA = a;
SegmentB = b;
SegmentC = c;
Point1 = SegmentA.Point1;
Point2 = SegmentA.Point2;
Point3 = Point1.Equals(SegmentB.Point1) || Point2.Equals(SegmentB.Point1) ? SegmentB.Point2 : SegmentB.Point1;
AngleA = new Angle(Point1, Point2, Point3);
AngleB = new Angle(Point2, Point3, Point1);
AngleC = new Angle(Point3, Point1, Point2);
isRight = isRightTriangle();
provenRight = false;
givenRight = false;
isIsosceles = IsIsosceles();
provenIsosceles = false;
isEquilateral = IsEquilateral();
provenEquilateral = false;
congruencePairs = new List<Triangle>();
similarPairs = new List<Triangle>();
addSuperFigureToDependencies();
}
public IPage119Problem3(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "I Page 119 Problem 3";
Point a = new Point("A", 4, 0); points.Add(a);
Point b = new Point("B", 4, 10); points.Add(b);
Point c = new Point("C", 8, 10); points.Add(c);
Point d = new Point("D", 0, 0); points.Add(d);
Point o = new Point("O", 4, 5); points.Add(o);
Segment ad = new Segment(a, d); segments.Add(ad);
Segment bc = new Segment(b, c); segments.Add(bc);
List<Point> pts = new List<Point>();
pts.Add(d);
pts.Add(o);
pts.Add(c);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(b);
pts.Add(o);
pts.Add(a);
collinear.Add(new Collinear(pts));
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments(ad, bc));
given.Add(new Perpendicular(parser.GetIntersection(ad, new Segment(a, b))));
given.Add(new Perpendicular(parser.GetIntersection(bc, new Segment(a, b))));
goals.Add(new SegmentBisector(parser.GetIntersection((Segment)parser.Get(new Segment(c, d)), (Segment)parser.Get(new Segment(a, b))), (Segment)parser.Get(new Segment(c, d))));
}
public BasicPolygonTester(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", -2, 0); points.Add(a);
Point b = new Point("B", 0, 6); points.Add(b);
Point c = new Point("C", 2, 0); points.Add(c);
Point d = new Point("D", 3, -1); points.Add(d);
Point e = new Point("E", 1, 3); points.Add(e);
Point f = new Point("F", 0, 0); points.Add(f);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment ca = new Segment(c, a); segments.Add(ca);
Segment de = new Segment(d, e); segments.Add(de);
Segment ef = new Segment(e, f); segments.Add(ef);
Segment fd = new Segment(f, d); segments.Add(fd);
Segment cd = new Segment(c, d); segments.Add(cd);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
// The goal is the entire area of the figure.
goalRegions = new List<GeometryTutorLib.Area_Based_Analyses.Atomizer.AtomicRegion>(parser.implied.atomicRegions);
}
public Page156Problem36(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 156 Problem 36";
Point j = new Point("J", 0, 10); points.Add(j);
Point k = new Point("K", 10, 10); points.Add(k);
Point l = new Point("L", 20, 10); points.Add(l);
Point m = new Point("M", 5, 0); points.Add(m);
Point n = new Point("N", 15, 0); points.Add(n);
Segment jm = new Segment(j, m); segments.Add(jm);
Segment km = new Segment(k, m); segments.Add(km);
Segment kn = new Segment(k, n); segments.Add(kn);
Segment ln = new Segment(l, n); segments.Add(ln);
List<Point> pts = new List<Point>();
pts.Add(j);
pts.Add(k);
pts.Add(l);
collinear.Add(new Collinear(pts));
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(m, j, k)), (Angle)parser.Get(new Angle(m, k, j))));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(n, k, l)), (Angle)parser.Get(new Angle(n, l, k))));
given.Add(new GeometricParallel(jm, kn));
goals.Add(new GeometricParallel(km, ln));
}
public IPage120Problem6(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Book I Page 120 Problem 6";
Point a = new Point("A", 2, 6); points.Add(a);
Point b = new Point("B", 0, 0); points.Add(b);
Point c = new Point("C", 10, 0); points.Add(c);
Point d = new Point("D", 4, 0); points.Add(d);
Point e = new Point("E", 12, 6); points.Add(e);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment ad = new Segment(a, d); segments.Add(ad);
Segment ac = new Segment(a, c); segments.Add(ac);
Segment ae = new Segment(a, e); segments.Add(ae);
Segment ec = new Segment(e, c); segments.Add(ec);
Segment de = new Segment(d, e); segments.Add(de);
List<Point> pts = new List<Point>();
pts.Add(b);
pts.Add(d);
pts.Add(c);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments(ac, ae));
given.Add(new GeometricCongruentSegments(ab, ad));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(b, a, d)), (Angle)parser.Get(new Angle(e, a, c))));
goals.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(b, c)), de));
}
public Page2Col1Prob3(bool onoff, bool complete)
: base(onoff, complete)
{
Point d = new Point("D", 60, 0); points.Add(d);
Point b = new Point("B", 0, 60); points.Add(b);
Point o = new Point("O", 0, 0); points.Add(o);
Segment bo = new Segment(b, o); segments.Add(bo);
Segment od = new Segment(o, d); segments.Add(od);
circles.Add(new Circle(o, 60.0));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new RightAngle(new Angle(b, o, d)));
known.AddSegmentLength(bo, 60);
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 0, -1));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(8482.300165);
problemName = "Page 2 Col 1 Problem 3";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public Page243Problem16(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 243 Problem 16";
Point a = new Point("A", 1.6, 1.2); points.Add(a);
Point b = new Point("B", 2, 6); points.Add(b);
Point c = new Point("C", 17, 6); points.Add(c);
Point d = new Point("D", 17.6, 13.2); points.Add(d);
Point x = new Point("X", 8, 6); points.Add(x);
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(b);
pts.Add(x);
pts.Add(c);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(a);
pts.Add(x);
pts.Add(d);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
}
public Page242Problem21(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 242 Problem 21";
Point t = new Point("T", 0, 0); points.Add(t);
Point s = new Point("S", 6, 8); points.Add(s);
Point o = new Point("O", 9, 12); points.Add(o);
Point v = new Point("V", 13, 8); points.Add(v);
Point w = new Point("W", 21, 0); points.Add(w);
Segment tw = new Segment(t, w); segments.Add(tw);
Segment sv = new Segment(s, v); segments.Add(sv);
List<Point> pts = new List<Point>();
pts.Add(t);
pts.Add(s);
pts.Add(o);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(o);
pts.Add(v);
pts.Add(w);
collinear.Add(new Collinear(pts));
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricParallel((Segment)parser.Get(tw), (Segment)parser.Get(sv)));
}
public Page229Problem05(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 229 Problem 05";
Point a = new Point("A", 13.0 / 2.0, 3.0); points.Add(a);
Point b = new Point("B", 0, 3); points.Add(b);
Point c = new Point("C", 2, 0); points.Add(c);
Point e = new Point("E", 13.0 / 3.0, 3); points.Add(e);
Point f = new Point("F", 5, 2); points.Add(f);
Segment bc = new Segment(c, b); segments.Add(bc);
Segment ef = new Segment(e, f); segments.Add(ef);
List<Point> pts = new List<Point>();
pts.Add(a);
pts.Add(f);
pts.Add(c);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(b);
pts.Add(e);
pts.Add(a);
collinear.Add(new Collinear(pts));
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
}
public Page168Problem34(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 168 Problem 34";
Point a = new Point("A", 1, 7); points.Add(a);
Point b = new Point("B", 1, 4); points.Add(b);
Point c = new Point("C", 8, 0); points.Add(c);
Point d = new Point("D", 8, 4); points.Add(d);
Point e = new Point("E", 4, 4); points.Add(e);
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(e);
pts.Add(c);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(b);
pts.Add(e);
pts.Add(d);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(b, a, e)),
(Angle)parser.Get(new Angle(a, e, b))));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(d, e, c)),
(Angle)parser.Get(new Angle(e, c, d))));
goals.Add(new GeometricParallel(ab, cd));
}
public IPage123Example6(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Book I Page 123 Example 6";
Point a = new Point("A", 3.5, 4); points.Add(a);
Point b = new Point("B", 0, 0); points.Add(b);
Point c = new Point("C", 7, 0); points.Add(c);
Point d = new Point("D", 2, 0); points.Add(d);
Point e = new Point("E", 5, 0); points.Add(e);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment ac = new Segment(a, c); segments.Add(ac);
Segment ad = new Segment(a, d); segments.Add(ad);
Segment ae = new Segment(a, e); segments.Add(ae);
List<Point> pts = new List<Point>();
pts.Add(b);
pts.Add(d);
pts.Add(e);
pts.Add(c);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new IsoscelesTriangle((Triangle)parser.Get(new Triangle(a, b, c))));
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(b, e)), (Segment)parser.Get(new Segment(c, d))));
goals.Add(new GeometricCongruentSegments(ad, ae));
}
public Page145Problem08(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 145 Problem 8";
Point f = new Point("F", 0, 5); points.Add(f);
Point l = new Point("L", 4, 7); points.Add(l);
Point k = new Point("K", 4, 3); points.Add(k);
Point a = new Point("A", 5, 5); points.Add(a);
Point j = new Point("J", 3, 5); points.Add(j);
Segment fl = new Segment(f, l); segments.Add(fl);
Segment fk = new Segment(f, k); segments.Add(fk);
Segment al = new Segment(a, l); segments.Add(al);
Segment ak = new Segment(a, k); segments.Add(ak);
Segment jl = new Segment(j, l); segments.Add(jl);
Segment jk = new Segment(j, k); segments.Add(jk);
List<Point> pts = new List<Point>();
pts.Add(f);
pts.Add(j);
pts.Add(a);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new AngleBisector((Angle)parser.Get(new Angle(l, f, k)), (Segment)parser.Get(new Segment(f, a))));
given.Add(new AngleBisector((Angle)parser.Get(new Angle(l, a, k)), (Segment)parser.Get(new Segment(f, a))));
goals.Add(new AngleBisector((Angle)parser.Get(new Angle(l, j, k)), (Segment)parser.Get(new Segment(f, a))));
}
//Demonstrates: If a quad is inscribed in a circle, then its opposite angles are supplementary
public Page312Corollary2(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
//Points and segments for an inscribed rectangle
Point r = new Point("R", -3, 4); points.Add(r);
Point s = new Point("S", 3, 4); points.Add(s);
Point t = new Point("T", 3, -4); points.Add(t);
Point u = new Point("U", -3, -4); points.Add(u);
Segment rs = new Segment(r, s); segments.Add(rs);
Segment st = new Segment(s, t); segments.Add(st);
Segment tu = new Segment(t, u); segments.Add(tu);
Segment ur = new Segment(u, r); segments.Add(ur);
Circle c = new Circle(o, 5.0);
circles.Add(c);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Angle angle1 = (Angle)parser.Get(new Angle(r, s, t));
Angle angle2 = (Angle)parser.Get(new Angle(u, r, s));
Angle angle3 = (Angle)parser.Get(new Angle(s, t, u));
given.Add(new Strengthened(angle1, new RightAngle(angle1)));
given.Add(new GeometricCongruentAngles(angle2, angle3));
Quadrilateral quad = (Quadrilateral)parser.Get(new Quadrilateral(ur, st, rs, tu));
goals.Add(new Strengthened(quad, new Rectangle(quad)));
}
/// <summary>
/// This event is called when the segment1 combo box changes its selction.
/// The method will update the segment2 combo box to reflect viable combinations with segment1.
/// </summary>
/// <param name="sender"></param>
/// <param name="e"></param>
private void Segment1_SelectionChanged(object sender, SelectionChangedEventArgs e)
{
segment2.ItemsSource = null;
GeometryTutorLib.ConcreteAST.Segment selection = segment1.SelectedValue as GeometryTutorLib.ConcreteAST.Segment;
if (selection != null)
{
segment2.ItemsSource = options[selection];
}
}
public static ConcreteAST.Point AcquireRestrictedPoint(List <ConcreteAST.Point> points, ConcreteAST.Point that,
ConcreteAST.Segment seg, ConcreteAST.Arc arc)
{
ConcreteAST.Point pt = AcquirePoint(points, that);
if (pt == null)
{
return(null);
}
return(!seg.PointLiesOnAndBetweenEndpoints(pt) || !arc.PointLiesOn(pt) ? null : pt);
}
protected override GroundedClause MakeClause()
{
GeometryTutorLib.ConcreteAST.Segment s1 = segment1.SelectedValue as GeometryTutorLib.ConcreteAST.Segment;
GeometryTutorLib.ConcreteAST.Segment s2 = segment2.SelectedValue as GeometryTutorLib.ConcreteAST.Segment;
if (s1 != null && s2 != null)
{
return(new GeometricParallel(s1, s2));
}
else
{
return(null);
}
}
private static int GetComposableCycleWithSegment(UndirectedPlanarGraph.PlanarGraph graph,
List <MinimalCycle> cycles,
GeometryTutorLib.ConcreteAST.Segment segment)
{
for (int c = 0; c < cycles.Count; c++)
{
if (cycles[c].HasThisExtendedSegment(graph, segment))
{
return(c);
}
}
return(-1);
}
/// <summary>
/// Figure out what possible segment combinations are before showing the window.
/// </summary>
protected override void OnShow()
{
options = new Dictionary <GeometryTutorLib.ConcreteAST.Segment, List <GeometryTutorLib.ConcreteAST.Segment> >();
//Get a list of all congruent segment givens
List <GroundedClause> psegs = new List <GroundedClause>();
foreach (GroundedClause gc in currentGivens)
{
GeometricParallel pseg = gc as GeometricParallel;
if (pseg != null)
{
psegs.Add(pseg);
}
}
//Pick a first segment...
foreach (GeometryTutorLib.ConcreteAST.Segment ts1 in parser.backendParser.implied.segments)
{
List <GeometryTutorLib.ConcreteAST.Segment> possible = new List <GeometryTutorLib.ConcreteAST.Segment>();
GeometryTutorLib.ConcreteAST.Segment s1 = new GeometryTutorLib.ConcreteAST.Segment(ts1.Point1, ts1.Point2);
//... and see what other segments are viable second options.
foreach (GeometryTutorLib.ConcreteAST.Segment ts2 in parser.backendParser.implied.segments)
{
GeometryTutorLib.ConcreteAST.Segment s2 = new GeometryTutorLib.ConcreteAST.Segment(ts2.Point1, ts2.Point2);
if (s1.IsParallelWith(s2))
{
GeometricParallel pseg = new GeometricParallel(s1, s2);
if (!s1.StructurallyEquals(s2) && !StructurallyContains(psegs, pseg))
{
possible.Add(s2);
}
}
}
//If we found a possible list of combinations, add it to the dictionary
if (possible.Count > 0)
{
options.Add(s1, possible);
}
}
//Set the options of the segment1 combo box
segment1.ItemsSource = null; //Graphical refresh
segment1.ItemsSource = options.Keys;
}
/// <summary>
/// Parse a line.
/// </summary>
/// <param name="line">The line to parse.</param>
private void ParseLine(ILine uiLine)
{
//
// Parse the constituent points.
//
IPoint p1 = uiLine.Dependencies.FindPoint(uiLine.Coordinates.P1, 0);
IPoint p2 = uiLine.Dependencies.FindPoint(uiLine.Coordinates.P2, 0);
Parse(p1);
Parse(p2);
// Create the tutor segments
GeometryTutorLib.ConcreteAST.Segment tutorSeg = new GeometryTutorLib.ConcreteAST.Segment(uiToEngineMap[p1] as Point, uiToEngineMap[p2] as Point);
// TempSegs.Add(new TempSegment(s.Point1, s.Point2));
uiToEngineMap.Add(uiLine, tutorSeg);
definedSegments.Add(tutorSeg);
}
//
// If a cycle has an edge that is EXTENDED, there exist two regions, one on each side of the segment; compose the two segments.
//
// Fixed point algorithm: while there exists a cycle with an extended segment, compose.
private static void ComposeCycles(UndirectedPlanarGraph.PlanarGraph graph, List <MinimalCycle> cycles)
{
for (int cycleIndex = HasComposableCycle(graph, cycles); cycleIndex != -1; cycleIndex = HasComposableCycle(graph, cycles))
{
// Get the cycle and remove it from the list.
MinimalCycle thisCycle = cycles[cycleIndex];
cycles.RemoveAt(cycleIndex);
// Get the extended segment which is the focal segment of composition.
GeometryTutorLib.ConcreteAST.Segment extendedSeg = thisCycle.GetExtendedSegment(graph);
// Find the matching cycle that has the same Extended segment
int otherIndex = GetComposableCycleWithSegment(graph, cycles, extendedSeg);
MinimalCycle otherCycle = cycles[otherIndex];
cycles.RemoveAt(otherIndex);
// Compose the two cycles into a single cycle.
MinimalCycle composed = thisCycle.Compose(otherCycle, extendedSeg);
// Add the new, composed cycle
cycles.Add(composed);
}
}
// Simple function for creating a point (if needed since it is not labeled by the UI).
private Point HandleIntersectionPoint(List <Point> containment, List <Point> toAdd, GeometryTutorLib.ConcreteAST.Segment segment, Point pt)
{
if (pt == null)
{
return(null);
}
// The point must be between the endpoints of the segment
if (!segment.PointLiesOnAndBetweenEndpoints(pt))
{
return(null);
}
return(HandleIntersectionPoint(containment, toAdd, pt));
}
//public PerpendicularBisector(Point i, Segment l, Segment bisector, string just) : base(i, l, bisector, just)
//{
// this.bisector = bisector;
//}
public PerpendicularBisector(Intersection inter, Segment bisector) : base(inter)
{
this.bisector = bisector;
}
public Intersection GetIntersection(GeometryTutorLib.ConcreteAST.Segment segment1, GeometryTutorLib.ConcreteAST.Segment segment2)
{
Point inter = (Point)Get(segment1.FindIntersection(segment2));
return((Intersection)Get(new Intersection(inter, segment1, segment2)));
}