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 LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricParallel((Segment)parser.Get(tw), (Segment)parser.Get(sv)));
}
//Demonstrates: Use of AngleArc equation, Central angle equal to intercepted arc
public Test01(bool onoff, bool complete) : base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point a = new Point("A", -5, 0); points.Add(a);
Point b = new Point("B", 5, 0); points.Add(b);
Point c = new Point("C", 0, 5); points.Add(c);
Segment oc = new Segment(o, c); segments.Add(oc);
List <Point> pnts = new List <Point>();
pnts.Add(a);
pnts.Add(o);
pnts.Add(b);
collinear.Add(new Collinear(pnts));
Circle circle = new Circle(o, 5.0);
circles.Add(circle);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
MinorArc m1 = (MinorArc)parser.Get(new MinorArc(circle, a, c));
MinorArc m2 = (MinorArc)parser.Get(new MinorArc(circle, b, c));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(a, o, c)), (Angle)parser.Get(new Angle(b, o, c))));
goals.Add(new GeometricCongruentArcs(m1, m2));
}
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));
}
//Demonstrates: Minor Arcs Congruent if central angles congruent
public Test10(bool onoff, bool complete)
: base(onoff, complete)
{
//Circle center
Point o = new Point("O", 0, 0); points.Add(o);
//Vertices for angle TOV, a central angle of circle O, with one endpoint at 90 degrees and another at 30 degrees
Point t = new Point("T", -3, 4); points.Add(t);
Point v = new Point("V", 0, 5); points.Add(v);
//Vertices for angle VOA, a central angle of circle C, with one endpoint at 90 degrees and another at 30 degrees
Point a = new Point("A", 3, 4); points.Add(a);
Segment ot = new Segment(o, t); segments.Add(ot);
Segment ov = new Segment(o, v); segments.Add(ov);
Segment oa = new Segment(o, a); segments.Add(oa);
Circle circleO = new Circle(o, 5.0);
circles.Add(circleO);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentArcs((MinorArc)parser.Get(new MinorArc(circleO, t, v)), (MinorArc)parser.Get(new MinorArc(circleO, v, a))));
goals.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(t, o, v)), (Angle)parser.Get(new Angle(v, o, a))));
}
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 Page146Problem14(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 146 Problem 14";
Point g = new Point("G", 0, 0); points.Add(g);
Point d = new Point("D", 3, 2); points.Add(d);
Point e = new Point("E", 7, 0); points.Add(e);
Point h = new Point("H", 2, 0); points.Add(h);
Point k = new Point("K", 5, 0); points.Add(k);
Point f = new Point("F", 4, -2); points.Add(f);
Segment dg = new Segment(d, g); segments.Add(dg);
Segment de = new Segment(d, e); segments.Add(de);
Segment dh = new Segment(d, h); segments.Add(dh);
Segment fg = new Segment(f, g); segments.Add(fg);
Segment fk = new Segment(f, k); segments.Add(fk);
Segment ef = new Segment(e, f); segments.Add(ef);
List <Point> pts = new List <Point>();
pts.Add(g);
pts.Add(h);
pts.Add(k);
pts.Add(e);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricParallel(dg, ef));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(g, d, e)), (Angle)parser.Get(new Angle(g, f, e))));
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(g, h)), (Segment)parser.Get(new Segment(e, k))));
goals.Add(new GeometricParallel(dh, fk));
}
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 Page42Problem16(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 42 Problem 16";
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", 6, 0); points.Add(c);
Point x = new Point("X", -3, -2); points.Add(x);
Point y = new Point("Y", 0, -5); points.Add(y);
Point z = new Point("Z", 2, -3); points.Add(z);
Segment bx = new Segment(b, x); segments.Add(bx);
Segment by = new Segment(b, y); segments.Add(by);
Segment bz = new Segment(b, z); segments.Add(bz);
List <Point> pts = new List <Point>();
pts.Add(a);
pts.Add(b);
pts.Add(c);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new Complementary((Angle)parser.Get(new Angle(a, b, x)), (Angle)parser.Get(new Angle(x, b, y))));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(a, b, x)), (Angle)parser.Get(new Angle(y, b, z))));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(x, b, y)), (Angle)parser.Get(new Angle(c, b, z))));
goals.Add(new Complementary((Angle)parser.Get(new Angle(y, b, z)), (Angle)parser.Get(new Angle(z, b, c))));
}
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));
}
//Demonstrates: congruent chords have congruent arcs
public Page306Theorem7_4_1(bool onoff, bool complete) : base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point r = new Point("R", -3, 4); points.Add(r);
Point s = new Point("S", 2, Math.Sqrt(21)); points.Add(s);
Point t = new Point("T", 2, -Math.Sqrt(21)); points.Add(t);
Point u = new Point("U", -3, -4); points.Add(u);
Segment rt = new Segment(r, t);
Segment su = new Segment(s, u);
Point v = rt.FindIntersection(su); points.Add(v);
Segment rs = new Segment(r, s); segments.Add(rs);
Segment ut = new Segment(u, t); segments.Add(ut);
Circle c = new Circle(o, 5.0);
circles.Add(c);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments(rs, ut));
MinorArc a1 = (MinorArc)parser.Get(new MinorArc(c, r, s));
MinorArc a2 = (MinorArc)parser.Get(new MinorArc(c, t, u));
MajorArc ma1 = (MajorArc)parser.Get(new MajorArc(c, r, s));
MajorArc ma2 = (MajorArc)parser.Get(new MajorArc(c, t, u));
goals.Add(new GeometricCongruentArcs(a1, a2));
goals.Add(new GeometricCongruentArcs(ma1, ma2));
}
public Page76Problem8(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 76 Problem 8";
Point s = new Point("S", 2, 8); points.Add(s);
Point r = new Point("R", 1, 4); points.Add(r);
Point t = new Point("T", 5, 4); points.Add(t);
Point q = new Point("Q", 4, 0); points.Add(q);
Point p = new Point("P", 0, 0); points.Add(p);
// System.Diagnostics.Debug.WriteLine(new Segment(b, c).FindIntersection(new Segment(p, d)));
Segment st = new Segment(s, t); segments.Add(st);
Segment rt = new Segment(r, t); segments.Add(rt);
Segment rq = new Segment(r, q); segments.Add(rq);
Segment pq = new Segment(p, q); segments.Add(pq);
List <Point> pts = new List <Point>();
pts.Add(s);
pts.Add(r);
pts.Add(p);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricParallel(st, rq));
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(s, r)), (Segment)parser.Get(new Segment(r, p))));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(s, r, t)), (Angle)parser.Get(new Angle(r, p, q))));
goals.Add(new GeometricCongruentSegments(st, rq));
}
public Page170ClassroomExercise05(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 170 Classroom Exercise 05";
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", 10, 10); points.Add(c);
Point d = new Point("D", 0, 10); points.Add(d);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment cd = new Segment(c, d); segments.Add(cd);
Segment ad = new Segment(a, d); segments.Add(ad);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Quadrilateral quad = (Quadrilateral)parser.Get(new Quadrilateral(ad, bc, cd, ab));
Angle abc = (Angle)parser.Get(new Angle(a, b, c));
given.Add(new Strengthened(quad, new Parallelogram(quad)));
given.Add(new Strengthened(abc, new RightAngle(abc)));
given.Add(new GeometricCongruentSegments(ab, bc));
goals.Add(new Strengthened(quad, new Square(quad)));
}
public Page75Problem18(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 75 Problem 18";
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 2, 4); points.Add(b);
Point c = new Point("C", 3, 3); points.Add(c);
Point d = new Point("D", 4, 4); points.Add(d);
Point e = new Point("E", 6, 0); points.Add(e);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment de = new Segment(d, e); segments.Add(de);
Segment ae = new Segment(a, e); segments.Add(ae);
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 GeometricCongruentAngles((Angle)parser.Get(new Angle(a, b, e)), (Angle)parser.Get(new Angle(a, d, e))));
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(a, c)), (Segment)parser.Get(new Segment(c, e))));
goals.Add(new GeometricCongruentTriangles(new Triangle(a, b, c), new Triangle(e, d, c)));
}
public Page60Theorem22(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 60 Theorem 22";
Point a = new Point("A", -1, 3); points.Add(a);
Point b = new Point("B", 4, 3); points.Add(b);
Point c = new Point("C", 0, 0); points.Add(c);
Point d = new Point("D", 5, 0); points.Add(d);
Point x = new Point("X", 2, 3); points.Add(x);
Point y = new Point("Y", 1, 0); points.Add(y);
Segment xy = new Segment(x, y); segments.Add(xy);
List <Point> pts = new List <Point>();
pts.Add(a);
pts.Add(x);
pts.Add(b);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(c);
pts.Add(y);
pts.Add(d);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricParallel((Segment)parser.Get(new Segment(a, b)), (Segment)parser.Get(new Segment(c, d))));
goals.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(a, x, y)), (Angle)parser.Get(new Angle(x, y, d))));
}
public Page6Prob29(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 17); points.Add(a);
Point b = new Point("B", 0, 34); points.Add(b);
Point c = new Point("C", 0, -34); points.Add(c);
Point o = new Point("O", 0, 0); points.Add(o);
Segment bc = new Segment(b, c); segments.Add(bc);
List <Point> pts = new List <Point>();
pts.Add(b);
pts.Add(a);
pts.Add(o);
pts.Add(c);
collinear.Add(new Collinear(pts));
circles.Add(new Circle(o, 34));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
known.AddSegmentLength((Segment)parser.Get(new Segment(a, b)), 17);
known.AddAngleMeasureDegree((Angle)parser.Get(new Angle(b, o, c)), 180);
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(a, b)), (Segment)parser.Get(new Segment(a, o))));
List <Point> wanted = new List <Point>();
wanted.Add(new Point("", 19, 0));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(433.5 * System.Math.PI);
}
public Page284Example46(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 284 example 4.6";
Point e = new Point("E", 1, 0); points.Add(e);
Point f = new Point("F", 0, 8); points.Add(f);
Point g = new Point("G", 5, 3); points.Add(g);
Point h = new Point("H", 9, 6); points.Add(h);
Point j = new Point("J", 10, -2); points.Add(j);
Segment ef = new Segment(e, f); segments.Add(ef);
Segment hj = new Segment(h, j); segments.Add(hj);
List <Point> pts = new List <Point>();
pts.Add(f);
pts.Add(g);
pts.Add(j);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(e);
pts.Add(g);
pts.Add(h);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(g, f)), (Segment)parser.Get(new Segment(j, g))));
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(e, g)), (Segment)parser.Get(new Segment(h, g))));
goals.Add(new GeometricCongruentSegments(ef, hj));
}
public Page285Problem21(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 285 Problem 21";
Point a = new Point("A", 3, 4); points.Add(a);
Point b = new Point("B", 9, 4); points.Add(b);
Point c = new Point("C", 0, 0); points.Add(c);
Point d = new Point("D", 6, 0); points.Add(d);
Point e = new Point("E", 12, 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 bd = new Segment(b, d); segments.Add(bd);
Segment be = new Segment(b, e); segments.Add(be);
List <Point> pts = new List <Point>();
pts.Add(c);
pts.Add(d);
pts.Add(e);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(c, d)), (Segment)parser.Get(new Segment(d, e))));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(a, c, d)), (Angle)parser.Get(new Angle(b, e, d))));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(c, a, d)), (Angle)parser.Get(new Angle(d, b, e))));
goals.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(b, a, d)), (Angle)parser.Get(new Angle(d, b, a))));
}
public Page197Problem37(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 197 Problem 37";
Point a = new Point("A", 0, 5); points.Add(a);
Point b = new Point("B", 3, 8); points.Add(b);
Point c = new Point("C", 5, 0); points.Add(c);
Point d = new Point("D", 9000, 5); points.Add(d);
Point e = new Point("E", 0, 0); points.Add(e);
Point f = new Point("F", 0, 30); points.Add(f);
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(e);
pts.Add(a);
pts.Add(f);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(f, a, b)),
(Angle)parser.Get(new Angle(c, a, d))));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(d, a, b)),
(Angle)parser.Get(new Angle(e, a, c))));
goals.Add(new Strengthened(parser.GetIntersection(new Segment(a, b), new Segment(a, c)),
new Perpendicular(parser.GetIntersection(new Segment(a, b), new Segment(a, c)))));
}
public Page226Problem44(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 226 Problem 44";
Point v = new Point("V", 4, 12); points.Add(v);
Point w = new Point("W", 12, 6); points.Add(w);
Point x = new Point("X", 8, 4); points.Add(x);
Point y = new Point("Y", 10, 0); points.Add(y);
Point z = new Point("Z", 0, 0); points.Add(z);
Segment vw = new Segment(v, w); segments.Add(vw);
Segment yz = new Segment(y, z); segments.Add(yz);
List <Point> pts = new List <Point>();
pts.Add(z);
pts.Add(x);
pts.Add(w);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(v);
pts.Add(x);
pts.Add(y);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(x, v, w)), (Angle)parser.Get(new Angle(x, z, y))));
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(w, x)), (Segment)parser.Get(new Segment(x, y))));
goals.Add(new GeometricCongruentSegments(vw, yz));
}
public Page156Problem34(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 156 Problem 34";
Point s = new Point("S", 0, 10); points.Add(s);
Point t = new Point("T", 0, 0); points.Add(t);
Point u = new Point("U", 10, 0); points.Add(u);
Point v = new Point("V", 10, 10); points.Add(v);
Point w = new Point("W", 5, 5); points.Add(w);
Segment st = new Segment(s, t); segments.Add(st);
Segment uv = new Segment(u, v); segments.Add(uv);
List <Point> pts = new List <Point>();
pts.Add(t);
pts.Add(w);
pts.Add(v);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(s);
pts.Add(w);
pts.Add(u);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(w, v, u)), (Angle)parser.Get(new Angle(w, s, t))));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(w, t, s)), (Angle)parser.Get(new Angle(w, s, t))));
goals.Add(new GeometricParallel(st, uv));
}
public Page284Example44(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 284 Example 4.4";
Point d = new Point("D", 0, 4); points.Add(d);
Point e = new Point("E", 3, 0); points.Add(e);
Point f = new Point("F", 6, 0); points.Add(f);
Point g = new Point("G", 12, 4); points.Add(g);
Point h = new Point("H", 9, 0); points.Add(h);
Segment de = new Segment(d, e); segments.Add(de);
Segment df = new Segment(d, f); segments.Add(df);
Segment gh = new Segment(g, h); segments.Add(gh);
Segment fg = new Segment(f, g); segments.Add(fg);
List <Point> pts = new List <Point>();
pts.Add(e);
pts.Add(f);
pts.Add(h);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(f, e)), (Segment)parser.Get(new Segment(f, h))));
given.Add(new GeometricCongruentSegments(de, gh));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(d, e, f)), (Angle)parser.Get(new Angle(g, h, f))));
goals.Add(new GeometricCongruentTriangles(new Triangle(d, e, f), new Triangle(g, h, f)));
}
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))));
}
public Page76Problem8(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 76 Problem 8";
Point s = new Point("S", 2, 8); points.Add(s);
Point r = new Point("R", 1, 4); points.Add(r);
Point t = new Point("T", 5, 4); points.Add(t);
Point q = new Point("Q", 4, 0); points.Add(q);
Point p = new Point("P", 0, 0); points.Add(p);
// System.Diagnostics.Debug.WriteLine(new Segment(b, c).FindIntersection(new Segment(p, d)));
Segment st = new Segment(s, t); segments.Add(st);
Segment rt = new Segment(r, t); segments.Add(rt);
Segment rq = new Segment(r, q); segments.Add(rq);
Segment pq = new Segment(p, q); segments.Add(pq);
List<Point> pts = new List<Point>();
pts.Add(s);
pts.Add(r);
pts.Add(p);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricParallel(st, rq));
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(s, r)), (Segment)parser.Get(new Segment(r, p))));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(s, r, t)), (Angle)parser.Get(new Angle(r, p, q))));
goals.Add(new GeometricCongruentSegments(st, rq));
}
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 Page113Problem7(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 113 Problem 7";
Point a = new Point("A", -4, 3); points.Add(a);
Point b = new Point("B", -4.0 / 3.0, -1); points.Add(b);
Point c = new Point("C", 0, 0); points.Add(c);
Point p = new Point("P", 4, 3); points.Add(p);
Point q = new Point("Q", 4.0 / 3.0, -1); points.Add(q);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment pq = new Segment(p, q); segments.Add(pq);
List<Point> pts = new List<Point>();
pts.Add(a);
pts.Add(c);
pts.Add(q);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(p);
pts.Add(c);
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(b, c)), (Segment)parser.Get(new Segment(c, q))));
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(a, c)), (Segment)parser.Get(new Segment(c, p))));
goals.Add(new GeometricCongruentTriangles(new Triangle(a, b, c), new Triangle(p, q, c)));
}
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 LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
known.AddSegmentLength(new Segment(a, d), 3.5);
//known.AddSegmentLength(new Segment(b, d), 3.5);
//known.AddSegmentLength(new Segment(c, e), 3.5);
// The goal is the entire area of the figure.
goalRegions.Add(parser.implied.GetAtomicRegionByPoint(new Point("", 0, -1)));
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))));
SetSolutionArea(1.975367389);
}
public Page197Problem35(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 197 Problem 35";
Point a = new Point("A", 0, 5); points.Add(a);
Point b = new Point("B", 3, 8); points.Add(b);
Point c = new Point("C", 5, 0); points.Add(c);
Point d = new Point("D", 9000, 5); points.Add(d);
Point e = new Point("E", 0, 0); points.Add(e);
Point f = new Point("F", 0, 30); points.Add(f);
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(e);
pts.Add(a);
pts.Add(f);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(f, a, b)),
(Angle)parser.Get(new Angle(d, a, b))));
goals.Add(new Strengthened(parser.GetIntersection(new Segment(a, b), new Segment(a, c)),
new Perpendicular(parser.GetIntersection(new Segment(a, b), new Segment(a, c)))));
}
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 LiveGeometry.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);
}
public Page145Problem10(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 145 Problem 10";
Point a = new Point("A", 0, 5); points.Add(a);
Point b = new Point("B", 1, 6); points.Add(b);
Point c = new Point("C", 5, 7); points.Add(c);
Point d = new Point("D", 6, 5); points.Add(d);
Point e = new Point("E", 5, 3); points.Add(e);
Point f = new Point("F", 1, 4); points.Add(f);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment cd = new Segment(c, d); segments.Add(cd);
Segment de = new Segment(d, e); segments.Add(de);
Segment ef = new Segment(e, f); segments.Add(ef);
Segment af = new Segment(a, f); segments.Add(af);
Segment ad = new Segment(a, d); segments.Add(ad);
// Constructed
Segment ae = new Segment(a, e); segments.Add(ae);
Segment ac = new Segment(a, c); segments.Add(ac);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments(ab, af));
given.Add(new GeometricCongruentSegments(cd, de));
given.Add(new GeometricCongruentSegments(bc, ef));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(e, d, a)), (Angle)parser.Get(new Angle(c, d, a))));
goals.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(a, b, c)), (Angle)parser.Get(new Angle(a, f, e))));
}
public Page75Problem17(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 75 Problem 17";
Point v = new Point("V", 3, -7); points.Add(v);
Point z = new Point("Z", 0, 0); points.Add(z);
Point y = new Point("Y", 6, 0); points.Add(y);
Point x = new Point("X", 7, 0); points.Add(x);
Point u = new Point("U", 10, -7); points.Add(u);
Point w = new Point("W", 13, 0); points.Add(w);
// System.Diagnostics.Debug.WriteLine(new Segment(b, c).FindIntersection(new Segment(a, d)));
Segment vz = new Segment(v, z); segments.Add(vz);
Segment vy = new Segment(v, y); segments.Add(vy);
Segment ux = new Segment(u, x); segments.Add(ux);
Segment uw = new Segment(u, w); segments.Add(uw);
List<Point> pts = new List<Point>();
pts.Add(z);
pts.Add(y);
pts.Add(x);
pts.Add(w);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricParallel(vz, ux));
given.Add(new GeometricParallel(vy, uw));
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(w, x)), (Segment)parser.Get(new Segment(y, z))));
goals.Add(new GeometricCongruentTriangles(new Triangle(w, x, u), new Triangle(y, z, v)));
}
public Page243Problem15(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 243 Problem 15";
Point d = new Point("D", 4, 24); points.Add(d);
Point f = new Point("F", 3, 18); points.Add(f);
Point h = new Point("H", 1, 6); points.Add(h);
Point e = new Point("E", 5, 24); points.Add(e);
Point g = new Point("G", 8, 18); points.Add(g);
Point j = new Point("J", 14, 6); points.Add(j);
Segment de = new Segment(d, e); segments.Add(de);
Segment fg = new Segment(f, g); segments.Add(fg);
Segment hj = new Segment(h, j); segments.Add(hj);
List<Point> pts = new List<Point>();
pts.Add(d);
pts.Add(f);
pts.Add(h);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(e);
pts.Add(g);
pts.Add(j);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricParallel((Segment)parser.Get(de), (Segment)parser.Get(fg)));
given.Add(new GeometricParallel((Segment)parser.Get(hj), (Segment)parser.Get(fg)));
}
public IPage120Problem7(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Book I Page 120 Problem 7";
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 10, 0); points.Add(b);
Point p = new Point("P", 5, 0); points.Add(p);
Point d = new Point("D", 7, 8); points.Add(d);
Point e = new Point("E", 3, 8); points.Add(e);
// System.Diagnostics.Debug.Write(new Segment(q, r).FindIntersection(new Segment(p, s)));
Segment ad = new Segment(a, d); segments.Add(ad);
Segment be = new Segment(b, e); segments.Add(be);
Segment ep = new Segment(e, p); segments.Add(ep);
Segment dp = new Segment(d, p); segments.Add(dp);
List <Point> pts = new List <Point>();
pts.Add(a);
pts.Add(p);
pts.Add(b);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new Midpoint((InMiddle)parser.Get(new InMiddle(p, (Segment)parser.Get(new Segment(a, b))))));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(b, a, d)), (Angle)parser.Get(new Angle(a, b, e))));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(e, p, a)), (Angle)parser.Get(new Angle(d, p, b))));
goals.Add(new GeometricCongruentTriangles(new Triangle(d, a, p), new Triangle(e, b, p)));
goals.Add(new GeometricCongruentSegments(ad, be));
}
public Page7Prob26(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 4); points.Add(b);
Point c = new Point("C", 4, 4); points.Add(c);
Point d = new Point("D", 4, 0); points.Add(d);
Point o = new Point("O", 2, 2); points.Add(o);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment cd = new Segment(c, d); segments.Add(cd);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment da = new Segment(d, a); segments.Add(da);
circles.Add(new Circle(o, 2));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
known.AddSegmentLength(da, 4);
known.AddSegmentLength(cd, 4);
given.Add(new RightAngle((Angle)parser.Get(new Angle(a, b, c))));
given.Add(new RightAngle((Angle)parser.Get(new Angle(b, c, d))));
given.Add(new RightAngle((Angle)parser.Get(new Angle(c, d, a))));
given.Add(new RightAngle((Angle)parser.Get(new Angle(d, a, b))));
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 2, 1));
wanted.Add(new Point("", 0.5, 0.5));
wanted.Add(new Point("", 3.5, 0.5));
wanted.Add(new Point("", 2, -1));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(8 + 2 * System.Math.PI);
}
public Page6Prob30(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point p = new Point("P", 2, 0); points.Add(p);
Point q = new Point("Q", 4, 0); points.Add(q);
Point r = new Point("R", 6, 0); points.Add(r);
Point s = new Point("S", 8, 0); points.Add(s);
Segment rs = new Segment(r, s); segments.Add(rs);
List<Point> pts = new List<Point>();
pts.Add(o);
pts.Add(p);
pts.Add(q);
pts.Add(r);
pts.Add(s);
collinear.Add(new Collinear(pts));
circles.Add(new Circle(o, 8));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
known.AddSegmentLength(rs, 2);
given.Add(new GeometricCongruentSegments(rs, (Segment)parser.Get(new Segment(o, p))));
given.Add(new GeometricCongruentSegments(rs, (Segment)parser.Get(new Segment(p, q))));
given.Add(new GeometricCongruentSegments(rs, (Segment)parser.Get(new Segment(q, r))));
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 3, 0));
wanted.Add(new Point("", 7, 0));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(40 * System.Math.PI);
}
public Page243Problem15(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 243 Problem 15";
Point d = new Point("D", 4, 24); points.Add(d);
Point f = new Point("F", 3, 18); points.Add(f);
Point h = new Point("H", 1, 6); points.Add(h);
Point e = new Point("E", 5, 24); points.Add(e);
Point g = new Point("G", 8, 18); points.Add(g);
Point j = new Point("J", 14, 6); points.Add(j);
Segment de = new Segment(d, e); segments.Add(de);
Segment fg = new Segment(f, g); segments.Add(fg);
Segment hj = new Segment(h, j); segments.Add(hj);
List <Point> pts = new List <Point>();
pts.Add(d);
pts.Add(f);
pts.Add(h);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(e);
pts.Add(g);
pts.Add(j);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricParallel((Segment)parser.Get(de), (Segment)parser.Get(fg)));
given.Add(new GeometricParallel((Segment)parser.Get(hj), (Segment)parser.Get(fg)));
}
//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 LiveGeometry.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)));
}
public Page2Prob19(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point a = new Point("A", -6, 0); points.Add(a);
Point b = new Point("B", 6, 0); points.Add(b);
Point p = new Point("P", -3, 6.0 * System.Math.Sqrt(3) / 2.0); points.Add(p);
Segment pa = new Segment(p, a); segments.Add(pa);
Segment pb = new Segment(p, b); segments.Add(pb);
List<Point> pts = new List<Point>();
pts.Add(a);
pts.Add(o);
pts.Add(b);
collinear.Add(new Collinear(pts));
circles.Add(new Circle(o, 6));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricAngleEquation((Angle)parser.Get(new Angle(o, a, p)), new NumericValue(60.0)));
known.AddSegmentLength((Segment)parser.Get(new Segment(o, b)), 6);
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 3, 4));
wanted.Add(new Point("", -5.19, 2.9));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(25.37175323);
problemName = "Jurgensen Page 2 Problem 19";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public Page284Example44(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 284 Example 4.4";
Point d = new Point("D", 0, 4); points.Add(d);
Point e = new Point("E", 3, 0); points.Add(e);
Point f = new Point("F", 6, 0); points.Add(f);
Point g = new Point("G", 12, 4); points.Add(g);
Point h = new Point("H", 9, 0); points.Add(h);
Segment de = new Segment(d, e); segments.Add(de);
Segment df = new Segment(d, f); segments.Add(df);
Segment gh = new Segment(g, h); segments.Add(gh);
Segment fg = new Segment(f, g); segments.Add(fg);
List<Point> pts = new List<Point>();
pts.Add(e);
pts.Add(f);
pts.Add(h);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(f, e)), (Segment)parser.Get(new Segment(f, h))));
given.Add(new GeometricCongruentSegments(de, gh));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(d, e, f)), (Angle)parser.Get(new Angle(g, h, f))));
goals.Add(new GeometricCongruentTriangles(new Triangle(d, e, f), new Triangle(g, h, f)));
}
public Page284Example46(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 284 example 4.6";
Point e = new Point("E", 1, 0); points.Add(e);
Point f = new Point("F", 0, 8); points.Add(f);
Point g = new Point("G", 5, 3); points.Add(g);
Point h = new Point("H", 9, 6); points.Add(h);
Point j = new Point("J", 10, -2); points.Add(j);
Segment ef = new Segment(e, f); segments.Add(ef);
Segment hj = new Segment(h, j); segments.Add(hj);
List<Point> pts = new List<Point>();
pts.Add(f);
pts.Add(g);
pts.Add(j);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(e);
pts.Add(g);
pts.Add(h);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(g, f)), (Segment)parser.Get(new Segment(j, g))));
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(e, g)), (Segment)parser.Get(new Segment(h, g))));
goals.Add(new GeometricCongruentSegments(ef, hj));
}
public Page60Theorem22(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 60 Theorem 22";
Point a = new Point("A", -1, 3); points.Add(a);
Point b = new Point("B", 4, 3); points.Add(b);
Point c = new Point("C", 0, 0); points.Add(c);
Point d = new Point("D", 5, 0); points.Add(d);
Point x = new Point("X", 2, 3); points.Add(x);
Point y = new Point("Y", 1, 0); points.Add(y);
Segment xy = new Segment(x, y); segments.Add(xy);
List<Point> pts = new List<Point>();
pts.Add(a);
pts.Add(x);
pts.Add(b);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(c);
pts.Add(y);
pts.Add(d);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricParallel((Segment)parser.Get(new Segment(a, b)), (Segment)parser.Get(new Segment(c, d))));
goals.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(a, x, y)), (Angle)parser.Get(new Angle(x, y, d))));
}
//Demonstrates: congruent chords have congruent arcs
public Page306Theorem7_4_1(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point r = new Point("R", -3, 4); points.Add(r);
Point s = new Point("S", 2, Math.Sqrt(21)); points.Add(s);
Point t = new Point("T", 2, -Math.Sqrt(21)); points.Add(t);
Point u = new Point("U", -3, -4); points.Add(u);
Segment rt = new Segment(r, t);
Segment su = new Segment(s, u);
Point v = rt.FindIntersection(su); points.Add(v);
Segment rs = new Segment(r, s); segments.Add(rs);
Segment ut = new Segment(u, t); segments.Add(ut);
Circle c = new Circle(o, 5.0);
circles.Add(c);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments(rs, ut));
MinorArc a1 = (MinorArc)parser.Get(new MinorArc(c, r, s));
MinorArc a2 = (MinorArc)parser.Get(new MinorArc(c, t, u));
MajorArc ma1 = (MajorArc)parser.Get(new MajorArc(c, r, s));
MajorArc ma2 = (MajorArc)parser.Get(new MajorArc(c, t, u));
goals.Add(new GeometricCongruentArcs(a1, a2));
goals.Add(new GeometricCongruentArcs(ma1, ma2));
}
public Page160Problem43(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 160 Problem 43";
Point t = new Point("T", 15.0 - 5.0 * Math.Sqrt(3.0), 0); points.Add(t);
Point s = new Point("S", 10, 0); points.Add(s);
Point f = new Point("F", 15, 5.0 * Math.Sqrt(3.0)); points.Add(f); // This is the wrong coordinate pair......
Point e = new Point("E", 15, 5.0 * Math.Sqrt(3.0)); points.Add(e);
Point r = new Point("R", 20, 0); points.Add(r);
Segment er = new Segment(e, r); segments.Add(er);
Segment fs = new Segment(f, s); segments.Add(fs);
Segment se = new Segment(s, e); segments.Add(se);
List<Point> pts = new List<Point>();
pts.Add(t);
pts.Add(s);
pts.Add(r);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(t);
pts.Add(f);
pts.Add(e);
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, e, r)), (Angle)parser.Get(new Angle(s, r, e))));
given.Add(new AngleBisector((Angle)parser.Get(new Angle(r, s, f)), se));
//goals.Add(new GeometricAngleEquation((Angle)parser.Get(new Angle(f, s, t)), new NumericValue(60)));
}
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 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 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 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 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 LiveGeometry.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 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 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 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 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 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));
}
//Demonstrates: Minor Arcs Congruent if central angles congruent
public Test10(bool onoff, bool complete)
: base(onoff, complete)
{
//Circle center
Point o = new Point("O", 0, 0); points.Add(o);
//Vertices for angle TOV, a central angle of circle O, with one endpoint at 90 degrees and another at 30 degrees
Point t = new Point("T", -3, 4); points.Add(t);
Point v = new Point("V", 0, 5); points.Add(v);
//Vertices for angle VOA, a central angle of circle C, with one endpoint at 90 degrees and another at 30 degrees
Point a = new Point("A", 3, 4); points.Add(a);
Segment ot = new Segment(o, t); segments.Add(ot);
Segment ov = new Segment(o, v); segments.Add(ov);
Segment oa = new Segment(o, a); segments.Add(oa);
Circle circleO = new Circle(o, 5.0);
circles.Add(circleO);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentArcs((MinorArc)parser.Get(new MinorArc(circleO, t, v)), (MinorArc)parser.Get(new MinorArc(circleO, v, a))));
goals.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(t, o, v)), (Angle)parser.Get(new Angle(v, o, a))));
}
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 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 Page135Problem21(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 135 Problem 21";
Point f = new Point("F", -3, 4); points.Add(f);
Point l = new Point("L", -1, 4); points.Add(l);
Point a = new Point("A", 1, 4); points.Add(a);
Point k = new Point("K", 3, 4); points.Add(k);
Point m = new Point("M", -1.5, 2); points.Add(m);
Point n = new Point("N", 1.5, 2); points.Add(n);
Point s = new Point("S", 0, 0); points.Add(s);
Point x = new Point("X", 0, 3.2); points.Add(x);
List <Point> pts = new List <Point>();
pts.Add(f);
pts.Add(m);
pts.Add(s);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(f);
pts.Add(l);
pts.Add(a);
pts.Add(k);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(l);
pts.Add(x);
pts.Add(n);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(a);
pts.Add(x);
pts.Add(m);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(k);
pts.Add(n);
pts.Add(s);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(f, l)),
(Segment)parser.Get(new Segment(a, k))));
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(s, f)),
(Segment)parser.Get(new Segment(s, k))));
given.Add(new Midpoint((InMiddle)parser.Get(new InMiddle(m, (Segment)parser.Get(new Segment(s, f))))));
given.Add(new Midpoint((InMiddle)parser.Get(new InMiddle(n, (Segment)parser.Get(new Segment(s, k))))));
goals.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(a, m)),
(Segment)parser.Get(new Segment(l, n))));
}
public Page168Problem35(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 168 Problem 35";
Point a = new Point("A", 1, 0); points.Add(a);
Point b = new Point("B", 5, 0); points.Add(b);
Point c = new Point("C", 9, 0); points.Add(c);
Point d = new Point("D", 0, 2); points.Add(d);
Point e = new Point("E", 4, 2); points.Add(e);
Point f = new Point("F", 3, 4); points.Add(f);
Point g = new Point("G", 7, 4); points.Add(g);
Point h = new Point("H", 6, 6); points.Add(h);
Point i = new Point("I", 0, 10); points.Add(i);
Point j = new Point("J", 4, 10); points.Add(j);
Point k = new Point("K", 12, 10); points.Add(k);
Point l = new Point("L", 16, 10); points.Add(l);
List <Point> pts = new List <Point>();
pts.Add(a);
pts.Add(e);
pts.Add(g);
pts.Add(l);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(d);
pts.Add(f);
pts.Add(h);
pts.Add(k);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(b);
pts.Add(e);
pts.Add(f);
pts.Add(i);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(c);
pts.Add(g);
pts.Add(h);
pts.Add(j);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(f, h, g)),
(Angle)parser.Get(new Angle(f, e, g))));
given.Add(new GeometricParallel((Segment)parser.Get(new Segment(a, l)), (Segment)parser.Get(new Segment(d, k))));
goals.Add(new GeometricParallel(new Segment(b, i), new Segment(c, j)));
}
public Page62Problem2(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 62 Problem 2";
Point a = new Point("A", -1, 3); points.Add(a);
Point b = new Point("B", 4, 3); points.Add(b);
Point c = new Point("C", 0, 0); points.Add(c);
Point d = new Point("D", 5, 0); points.Add(d);
Point e = new Point("E", -3, 3); points.Add(e);
Point f = new Point("F", -2, 6); points.Add(f);
Point g = new Point("G", 3, 6); points.Add(g);
Point h = new Point("H", 8, 3); points.Add(h);
Point i = new Point("I", 10, 0); points.Add(i);
Point j = new Point("J", 7, -6); points.Add(j);
Point k = new Point("K", 1, -3); points.Add(k);
Point l = new Point("L", -5, 0); points.Add(l);
List <Point> pts = new List <Point>();
pts.Add(f);
pts.Add(a);
pts.Add(c);
pts.Add(k);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(e);
pts.Add(a);
pts.Add(b);
pts.Add(h);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(g);
pts.Add(b);
pts.Add(d);
pts.Add(j);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(l);
pts.Add(c);
pts.Add(d);
pts.Add(i);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricParallel((Segment)parser.Get(new Segment(a, b)), (Segment)parser.Get(new Segment(c, d))));
goals.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(e, a, f)), (Angle)parser.Get(new Angle(c, a, b))));
goals.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(e, a, f)), (Angle)parser.Get(new Angle(a, c, l))));
goals.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(e, a, f)), (Angle)parser.Get(new Angle(k, c, d))));
}
public Page175ClassroomExercise12(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 175 CLassroom Ex 12";
//Point z = new Point("Z", 0, 12); points.Add(z);
//Point y = new Point("Y", 12, 0); points.Add(y);
//Point x = new Point("X", 0, 0); points.Add(x);
//Point m = new Point("M", 6, 0); points.Add(m);
//Point n = new Point("N", 6, 6); points.Add(n);
//Point t = new Point("T", 0, 6); points.Add(t);
Point z = new Point("Z", 0, 6); points.Add(z);
Point y = new Point("Y", 8, 0); points.Add(y);
Point x = new Point("X", 4, 0); points.Add(x);
Point m = new Point("M", 6, 0); points.Add(m);
Point n = new Point("N", 4, 3); points.Add(n);
Point t = new Point("T", 2, 3); points.Add(t);
Segment mt = new Segment(m, t); segments.Add(mt);
Segment mn = new Segment(m, n); segments.Add(mn);
Segment nt = new Segment(n, t); segments.Add(nt);
List <Point> pts = new List <Point>();
pts.Add(x);
pts.Add(m);
pts.Add(y);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(y);
pts.Add(n);
pts.Add(z);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(z);
pts.Add(t);
pts.Add(x);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new Midpoint((InMiddle)parser.Get(new InMiddle(m, new Segment(x, y)))));
given.Add(new Midpoint((InMiddle)parser.Get(new InMiddle(n, new Segment(z, y)))));
given.Add(new Midpoint((InMiddle)parser.Get(new InMiddle(t, new Segment(z, x)))));
goals.Add(new GeometricCongruentTriangles(new Triangle(z, t, n), new Triangle(t, x, m)));
goals.Add(new GeometricCongruentTriangles(new Triangle(z, t, n), new Triangle(n, m, y)));
goals.Add(new GeometricCongruentTriangles(new Triangle(z, t, n), new Triangle(m, n, t)));
goals.Add(new GeometricCongruentTriangles(new Triangle(m, n, t), new Triangle(n, m, y)));
goals.Add(new GeometricCongruentTriangles(new Triangle(m, n, t), new Triangle(t, x, m)));
goals.Add(new GeometricCongruentTriangles(new Triangle(t, x, m), new Triangle(n, m, y)));
}
