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 Page1Col1Prob5(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", -3.5, 0); points.Add(a);
Point b = new Point("B", 3.5, 0); points.Add(b);
Point c = new Point("C", 0, -3.5 * System.Math.Sqrt(3)); points.Add(c);
Point d = new Point("D", 0, 0); points.Add(d);
Point e = new Point("E", -1.75, -3.5 * System.Math.Sqrt(3.0) / 2.0); points.Add(e);
Point f = new Point("F", 1.75, -3.5 * System.Math.Sqrt(3.0) / 2.0); points.Add(f);
//Segment ad = new Segment(a, d); segments.Add(ad);
//Segment bd = new Segment(b, d); segments.Add(bd);
//Segment ce = new Segment(c, e); segments.Add(ce);
circles.Add(new Circle(a, 3.5));
circles.Add(new Circle(b, 3.5));
circles.Add(new Circle(c, 3.5));
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(a, d)), (Segment)parser.Get(new Segment(b, d))));
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(a, d)), (Segment)parser.Get(new Segment(e, c))));
known.AddSegmentLength(new Segment(a, d), 3.5);
goalRegions.Add(parser.implied.GetAtomicRegionByPoint(new Point("", 0, -1)));
SetSolutionArea(1.975367389);
problemName = "Class X Page 1 Col 1 Problem 5";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public Page3Prob23(bool onoff, bool complete)
: base(onoff, complete)
{
Point q = new Point("Q", -2, 0); points.Add(q);
Point p = new Point("P", 2, 0); points.Add(p);
Point o = new Point("O", 0, 0); points.Add(o);
List<Point> pts = new List<Point>();
pts.Add(q);
pts.Add(o);
pts.Add(p);
collinear.Add(new Collinear(pts));
circles.Add(new Circle(o, 4));
circles.Add(new Circle(p, 2));
circles.Add(new Circle(q, 2));
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
known.AddSegmentLength((Segment)parser.Get(new Segment(o, q)), 2);
known.AddSegmentLength((Segment)parser.Get(new Segment(p, o)), 2);
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 0, -3));
wanted.Add(new Point("", -2, -1));
wanted.Add(new Point("", -2, 1));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(8 * System.Math.PI);
problemName = "Jurgensen Page 3 Problem 23";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
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 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 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));
}
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 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 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 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 Page146Problem17(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 146 Problem 17";
Point d = new Point("D", 2, 3); points.Add(d);
Point b = new Point("B", 10, 0); points.Add(b);
Point a = new Point("A", 0, 0); points.Add(a);
Point c = new Point("C", 8, 3); points.Add(c);
Point m = new Point("M", 5, 0); points.Add(m);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment ad = new Segment(a, d); segments.Add(ad);
Segment cd = new Segment(c, d); segments.Add(cd);
Segment bd = new Segment(b, d); segments.Add(bd);
Segment ac = new Segment(a, c); segments.Add(ac);
Segment dm = new Segment(d, m); segments.Add(dm);
Segment cm = new Segment(c, m); segments.Add(cm);
List<Point> pts = new List<Point>();
pts.Add(a);
pts.Add(m);
pts.Add(b);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(a, m)), (Segment)parser.Get(new Segment(b, m))));
given.Add(new GeometricCongruentSegments(ad, bc));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(m, d, c)), (Angle)parser.Get(new Angle(m, c, d))));
}
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))));
}
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 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 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 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 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 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 Page4Prob8(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", -1 * System.Math.Sqrt(27), -3); points.Add(a);
Point b = new Point("B", 0, 6); points.Add(b);
Point c = new Point("C", System.Math.Sqrt(27), -3); points.Add(c);
Point p = new Point("P", 0, 0); points.Add(p);
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 ap = new Segment(a, p); segments.Add(ap);
Segment bp = new Segment(b, p); segments.Add(bp);
Segment cp = new Segment(c, p); segments.Add(cp);
circles.Add(new Circle(p, 6.0));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Triangle tri = (Triangle)parser.Get(new Triangle(a, b, c));
given.Add(new Strengthened(tri, new EquilateralTriangle(tri)));
known.AddSegmentLength(ap, 6);
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 0, -4));
wanted.Add(new Point("", -5, 0));
wanted.Add(new Point("", 5, 0));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(36 * System.Math.PI - 27 * System.Math.Sqrt(3));
}
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 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 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 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 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 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 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 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 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 static ConcreteAST.Point AcquireRestrictedPoint(List <ConcreteAST.Point> points, ConcreteAST.Point that,
ConcreteAST.Arc arc1, ConcreteAST.Arc arc2)
{
ConcreteAST.Point pt = AcquirePoint(points, that);
if (pt == null)
{
return(null);
}
return(!arc1.PointLiesOn(pt) || !arc2.PointLiesOn(pt) ? null : pt);
}
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);
}
//
// Get a point in the given list OR create a new list.
//
public static ConcreteAST.Point AcquirePoint(List <ConcreteAST.Point> points, ConcreteAST.Point that)
{
if (that == null)
{
return(null);
}
// Avoid parallel line intersections at infinity
if (double.IsInfinity(that.X) || double.IsInfinity(that.Y) || double.IsNaN(that.X) || double.IsNaN(that.Y))
{
return(null);
}
ConcreteAST.Point pt = GetStructurally <ConcreteAST.Point>(points, that);
if (pt == null)
{
pt = PointFactory.GeneratePoint(that.X, that.Y);
}
return(pt);
}
public void AddIntersectingPoint(Point pt) { Utilities.AddStructurallyUnique<Point>(intersectingPoints, pt); }
public virtual void AddCollinearPoint(Point newPt) { throw new ArgumentException("Only segments or arcs have 'collinearity'"); }
public virtual bool PointLiesOn(Point pt) { return false; }
public virtual void FindIntersection(Arc that, out Point inter1, out Point inter2) { inter1 = null; inter2 = null; }
public virtual bool PointLiesInside(Point pt) { return false; }
public virtual bool PointLiesInOrOn(Point pt)
{
if (pt == null) return false;
return PointLiesOn(pt) || PointLiesInside(pt);
}
