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 LiveGeometry.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))));
}
//Demonstrates: A segment perpendicular to a radius is a tangent, tangents from point are congruent
public Page296Theorem7_1_Test3(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
//Intersection point for two tangents
Point c = new Point("C", 0, 6.25); points.Add(c);
//Points for two tangents
Point a = new Point("A", 3, 4); points.Add(a);
Point b = new Point("B", -3, 4); points.Add(b);
//Tangent and Radii segments
Segment ac = new Segment(a, c); segments.Add(ac);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment oa = new Segment(o, a); segments.Add(oa);
Segment ob = new Segment(o, b); segments.Add(ob);
Circle circle = new Circle(o, 5.0);
circles.Add(circle);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Intersection inter1 = parser.GetIntersection(ac, oa);
Intersection inter2 = parser.GetIntersection(bc, ob);
given.Add(new Strengthened(inter1, new Perpendicular(inter1)));
given.Add(new Strengthened(inter2, new Perpendicular(inter2)));
//CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(a, circle, ap));
//given.Add(new Strengthened(cInter, new Tangent(cInter)));
goals.Add(new GeometricCongruentSegments(ac, bc));
}
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)))));
}
//Demonstrates: A segment perpendicular to a radius is a tangent, tangents from point are congruent
public Page296Theorem7_1_Test3(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
//Intersection point for two tangents
Point c = new Point("C", 0, 6.25); points.Add(c);
//Points for two tangents
Point a = new Point("A", 3, 4); points.Add(a);
Point b = new Point("B", -3, 4); points.Add(b);
//Tangent and Radii segments
Segment ac = new Segment(a, c); segments.Add(ac);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment oa = new Segment(o, a); segments.Add(oa);
Segment ob = new Segment(o, b); segments.Add(ob);
Circle circle = new Circle(o, 5.0);
circles.Add(circle);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Intersection inter1 = parser.GetIntersection(ac, oa);
Intersection inter2 = parser.GetIntersection(bc, ob);
given.Add(new Strengthened(inter1, new Perpendicular(inter1)));
given.Add(new Strengthened(inter2, new Perpendicular(inter2)));
//CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(a, circle, ap));
//given.Add(new Strengthened(cInter, new Tangent(cInter)));
goals.Add(new GeometricCongruentSegments(ac, bc));
}
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 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 LiveGeometry.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))));
}
// Demonstration of theorem "Median of a trapezoid is half the sum of the bases"
/*
* D_______E
* / \
* L______/M________\N
* / \
* /_____________\
* A B
*/
public Page174Theorem416_2(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 174 Theorem 4-16 Part 2";
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 10, 0); points.Add(b);
Point c = new Point("C", 8, 4); points.Add(c);
Point d = new Point("D", 2, 4); points.Add(d);
Point l = new Point("L", -7, 2); points.Add(l);
Point m = new Point("M", 1, 2); points.Add(m);
Point n = new Point("N", 9, 2); points.Add(n);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment cd = new Segment(c, d); segments.Add(cd);
List <Point> pts = new List <Point>();
pts.Add(a);
pts.Add(m);
pts.Add(d);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(b);
pts.Add(n);
pts.Add(c);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(l);
pts.Add(m);
pts.Add(n);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment ad = (Segment)parser.Get(new Segment(a, d));
Segment bc = (Segment)parser.Get(new Segment(b, c));
Segment ln = (Segment)parser.Get(new Segment(l, n));
Quadrilateral quad = (Quadrilateral)parser.Get(new Quadrilateral(ad, bc, cd, ab));
Addition sum = new Addition(ab, cd);
//If segment MN is the median of the trapezoid, and segment LN is congruent to the sum of AB and CD, then
//segment AD must bisect segment LN
given.Add(new Strengthened(quad, new Trapezoid(quad)));
given.Add(new SegmentBisector(parser.GetIntersection(ln, ad), ln));
given.Add(new SegmentBisector(parser.GetIntersection(ln, bc), ln));
given.Add(new GeometricSegmentEquation(ln, sum));
goals.Add(new SegmentBisector(parser.GetIntersection(ad, ln), ad));
}
public Page146Problem15(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 146 Problem 15";
Point t = new Point("T", 0, 0); points.Add(t);
Point p = new Point("P", 0.5, 1.5); points.Add(p);
Point s = new Point("S", 1, 3); points.Add(s);
Point x = new Point("X", 3, 1); points.Add(x);
Point q = new Point("Q", 3.5, 2.5); points.Add(q);
Point y = new Point("Y", 4, 4); points.Add(y);
Point o = new Point("O", 2, 2); points.Add(o);
List <Point> pts = new List <Point>();
pts.Add(t);
pts.Add(o);
pts.Add(y);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(s);
pts.Add(o);
pts.Add(x);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(s);
pts.Add(p);
pts.Add(t);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(y);
pts.Add(q);
pts.Add(x);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(p);
pts.Add(o);
pts.Add(q);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new SegmentBisector(parser.GetIntersection(new Segment(s, x), new Segment(t, y)), (Segment)parser.Get(new Segment(s, x))));
given.Add(new SegmentBisector(parser.GetIntersection(new Segment(s, x), new Segment(t, y)), (Segment)parser.Get(new Segment(t, y))));
InMiddle goalIm = (InMiddle)parser.Get(new InMiddle(o, new Segment(p, q)));
goals.Add(new Strengthened(goalIm, new Midpoint(goalIm)));
}
// Demonstration of theorem "Median of a trapezoid is half the sum of the bases"
/*
* D_______E
* / \
* L______/M________\N
* / \
* /_____________\
* A B
*/
public Page174Theorem416_2(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 174 Theorem 4-16 Part 2";
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 10, 0); points.Add(b);
Point c = new Point("C", 8, 4); points.Add(c);
Point d = new Point("D", 2, 4); points.Add(d);
Point l = new Point("L", -7, 2); points.Add(l);
Point m = new Point("M", 1, 2); points.Add(m);
Point n = new Point("N", 9, 2); points.Add(n);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment cd = new Segment(c, d); segments.Add(cd);
List<Point> pts = new List<Point>();
pts.Add(a);
pts.Add(m);
pts.Add(d);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(b);
pts.Add(n);
pts.Add(c);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(l);
pts.Add(m);
pts.Add(n);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment ad = (Segment)parser.Get(new Segment(a, d));
Segment bc = (Segment)parser.Get(new Segment(b, c));
Segment ln = (Segment)parser.Get(new Segment(l, n));
Quadrilateral quad = (Quadrilateral)parser.Get(new Quadrilateral(ad, bc, cd, ab));
Addition sum = new Addition(ab, cd);
//If segment MN is the median of the trapezoid, and segment LN is congruent to the sum of AB and CD, then
//segment AD must bisect segment LN
given.Add(new Strengthened(quad, new Trapezoid(quad)));
given.Add(new SegmentBisector(parser.GetIntersection(ln, ad), ln));
given.Add(new SegmentBisector(parser.GetIntersection(ln, bc), ln));
given.Add(new GeometricSegmentEquation(ln, sum));
goals.Add(new SegmentBisector(parser.GetIntersection(ad, ln), ad));
}
public Page146Problem15(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 146 Problem 15";
Point t = new Point("T", 0, 0); points.Add(t);
Point p = new Point("P", 0.5, 1.5); points.Add(p);
Point s = new Point("S", 1, 3); points.Add(s);
Point x = new Point("X", 3, 1); points.Add(x);
Point q = new Point("Q", 3.5, 2.5); points.Add(q);
Point y = new Point("Y", 4, 4); points.Add(y);
Point o = new Point("O", 2, 2); points.Add(o);
List<Point> pts = new List<Point>();
pts.Add(t);
pts.Add(o);
pts.Add(y);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(s);
pts.Add(o);
pts.Add(x);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(s);
pts.Add(p);
pts.Add(t);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(y);
pts.Add(q);
pts.Add(x);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(p);
pts.Add(o);
pts.Add(q);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new SegmentBisector(parser.GetIntersection(new Segment(s, x), new Segment(t, y)), (Segment)parser.Get(new Segment(s, x))));
given.Add(new SegmentBisector(parser.GetIntersection(new Segment(s, x), new Segment(t, y)), (Segment)parser.Get(new Segment(t, y))));
InMiddle goalIm = (InMiddle)parser.Get(new InMiddle( o, new Segment(p, q)));
goals.Add(new Strengthened(goalIm, new Midpoint(goalIm)));
}
//Demonstrates: Tangents are perpendicular to radii
public Page296Theorem7_1(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point r = new Point("R", -3, -5); points.Add(r);
Point s = new Point("S", 8, -5); points.Add(s);
Point t = new Point("T", 0, -5); points.Add(t);
Segment ot = new Segment(o, t); segments.Add(ot);
List<Point> pnts = new List<Point>();
pnts.Add(r);
pnts.Add(t);
pnts.Add(s);
collinear.Add(new Collinear(pnts));
Circle c = new Circle(o, 5.0);
circles.Add(c);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment rs = (Segment)parser.Get(new Segment(r, s));
CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(t, c, rs));
given.Add(new Strengthened(cInter, new Tangent(cInter)));
Intersection inter = parser.GetIntersection(ot, rs);
goals.Add(new Strengthened(inter, new Perpendicular(inter)));
}
public Page90Problem22(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 90 Problem 22";
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 5, 0); points.Add(b);
Point c = new Point("C", 2.5, 20); points.Add(c);
Point d = new Point("D", 2.5, 0); points.Add(d);
Segment ac = new Segment(a, c); segments.Add(ac);
Segment cb = new Segment(c, b); segments.Add(cb);
Segment cd = new Segment(c, d); segments.Add(cd);
List<Point> pts = new List<Point>();
pts.Add(a);
pts.Add(d);
pts.Add(b);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new PerpendicularBisector(parser.GetIntersection(cd, new Segment(a, b)), cd));
goals.Add(new GeometricCongruentTriangles(new Triangle(a, c, d), new Triangle(b, c, d)));
}
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 Page90Problem22(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 90 Problem 22";
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 5, 0); points.Add(b);
Point c = new Point("C", 2.5, 20); points.Add(c);
Point d = new Point("D", 2.5, 0); points.Add(d);
Segment ac = new Segment(a, c); segments.Add(ac);
Segment cb = new Segment(c, b); segments.Add(cb);
Segment cd = new Segment(c, d); segments.Add(cd);
List <Point> pts = new List <Point>();
pts.Add(a);
pts.Add(d);
pts.Add(b);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new PerpendicularBisector(parser.GetIntersection(cd, new Segment(a, b)), cd));
goals.Add(new GeometricCongruentTriangles(new Triangle(a, c, d), new Triangle(b, c, d)));
}
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)));
}
//Demonstrates: Tangents are perpendicular to radii
public Page296Theorem7_1(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point r = new Point("R", -3, -5); points.Add(r);
Point s = new Point("S", 8, -5); points.Add(s);
Point t = new Point("T", 0, -5); points.Add(t);
Segment ot = new Segment(o, t); segments.Add(ot);
List <Point> pnts = new List <Point>();
pnts.Add(r);
pnts.Add(t);
pnts.Add(s);
collinear.Add(new Collinear(pnts));
Circle c = new Circle(o, 5.0);
circles.Add(c);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment rs = (Segment)parser.Get(new Segment(r, s));
CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(t, c, rs));
given.Add(new Strengthened(cInter, new Tangent(cInter)));
Intersection inter = parser.GetIntersection(ot, rs);
goals.Add(new Strengthened(inter, new Perpendicular(inter)));
}
public IPage119Problem5(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "I Page 119 Problem 5";
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", 8, -4); points.Add(p);
Point q = new Point("Q", 8, 4); points.Add(q);
Point x = new Point("X", 16, 8); points.Add(x);
Point y = new Point("Y", 16, 0); points.Add(y);
Point z = new Point("Z", 24, -12); points.Add(z);
Point o = new Point("O", -100, 0); points.Add(o);
Segment bq = new Segment(b, q); segments.Add(bq);
Segment bp = new Segment(b, p); segments.Add(bp);
List <Point> pts = new List <Point>();
pts.Add(o);
pts.Add(a);
pts.Add(b);
pts.Add(y);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(a);
pts.Add(q);
pts.Add(x);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(a);
pts.Add(p);
pts.Add(z);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new AngleBisector((Angle)parser.Get(new Angle(q, a, p)), (Segment)parser.Get(new Segment(o, y))));
given.Add(new Perpendicular(parser.GetIntersection(new Segment(b, p), new Segment(a, z))));
given.Add(new Perpendicular(parser.GetIntersection(new Segment(b, q), new Segment(a, x))));
goals.Add(new GeometricCongruentTriangles(new Triangle(a, p, b), new Triangle(a, q, b)));
goals.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(b, p)), (Segment)parser.Get(new Segment(b, q))));
}
public IPage119Problem5(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "I Page 119 Problem 5";
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", 8, -4); points.Add(p);
Point q = new Point("Q", 8, 4); points.Add(q);
Point x = new Point("X", 16, 8); points.Add(x);
Point y = new Point("Y", 16, 0); points.Add(y);
Point z = new Point("Z", 24, -12); points.Add(z);
Point o = new Point("O", -100, 0); points.Add(o);
Segment bq = new Segment(b, q); segments.Add(bq);
Segment bp = new Segment(b, p); segments.Add(bp);
List<Point> pts = new List<Point>();
pts.Add(o);
pts.Add(a);
pts.Add(b);
pts.Add(y);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(a);
pts.Add(q);
pts.Add(x);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(a);
pts.Add(p);
pts.Add(z);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new AngleBisector((Angle)parser.Get(new Angle(q, a, p)), (Segment)parser.Get(new Segment(o, y))));
given.Add(new Perpendicular(parser.GetIntersection(new Segment(b, p), new Segment(a, z))));
given.Add(new Perpendicular(parser.GetIntersection(new Segment(b, q), new Segment(a, x))));
goals.Add(new GeometricCongruentTriangles(new Triangle(a, p, b), new Triangle(a, q, b)));
goals.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(b, p)), (Segment)parser.Get(new Segment(b, q))));
}
// Simple demonstration of theorem "Median of a trapezoid is parallel to the bases"
public Page174Theorem416_1(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 174 Theorem 4-16 Part 1";
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 11, 0); points.Add(b);
Point c = new Point("C", 7, 4); points.Add(c);
Point d = new Point("D", 2, 4); points.Add(d);
Point m = new Point("M", 1, 2); points.Add(m);
Point n = new Point("N", 9, 2); points.Add(n);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment cd = new Segment(c, d); segments.Add(cd);
Segment mn = new Segment(m, n); segments.Add(mn);
List <Point> pts = new List <Point>();
pts.Add(a);
pts.Add(m);
pts.Add(d);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(b);
pts.Add(n);
pts.Add(c);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment ad = (Segment)parser.Get(new Segment(a, d));
Segment bc = (Segment)parser.Get(new Segment(b, c));
Quadrilateral quad = (Quadrilateral)parser.Get(new Quadrilateral(ad, bc, cd, ab));
//given.Add(new Strengthened(quad, new Trapezoid(ad, bc, cd, ab)));
given.Add(new Parallel(ab, cd));
given.Add(new SegmentBisector(parser.GetIntersection(mn, ad), mn));
given.Add(new SegmentBisector(parser.GetIntersection(mn, bc), mn));
goals.Add(new Parallel(mn, cd));
goals.Add(new Parallel(mn, ab));
}
// Simple demonstration of theorem "Median of a trapezoid is parallel to the bases"
public Page174Theorem416_1(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 174 Theorem 4-16 Part 1";
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 11, 0); points.Add(b);
Point c = new Point("C", 7, 4); points.Add(c);
Point d = new Point("D", 2, 4); points.Add(d);
Point m = new Point("M", 1, 2); points.Add(m);
Point n = new Point("N", 9, 2); points.Add(n);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment cd = new Segment(c, d); segments.Add(cd);
Segment mn = new Segment(m, n); segments.Add(mn);
List<Point> pts = new List<Point>();
pts.Add(a);
pts.Add(m);
pts.Add(d);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(b);
pts.Add(n);
pts.Add(c);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment ad = (Segment)parser.Get(new Segment(a, d));
Segment bc = (Segment)parser.Get(new Segment(b, c));
Quadrilateral quad = (Quadrilateral)parser.Get(new Quadrilateral(ad, bc, cd, ab));
//given.Add(new Strengthened(quad, new Trapezoid(ad, bc, cd, ab)));
given.Add(new Parallel(ab, cd));
given.Add(new SegmentBisector(parser.GetIntersection(mn, ad), mn));
given.Add(new SegmentBisector(parser.GetIntersection(mn, bc), mn));
goals.Add(new Parallel(mn, cd));
goals.Add(new Parallel(mn, ab));
}
public Page48Problem23To31(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 48 Problem 23-31";
Point a = new Point("A", 0, 5); points.Add(a);
Point b = new Point("B", 2, 4); points.Add(b);
Point c = new Point("C", 4, 3); points.Add(c);
Point m = new Point("M", 3, 6); points.Add(m);
Point x = new Point("X", -2, 1); points.Add(x);
Point y = new Point("Y", 0, 0); points.Add(y);
Point z = new Point("Z", 2, -1); points.Add(z);
Point q = new Point("Q", -1, -2); points.Add(q);
List <Point> pts = new List <Point>();
pts.Add(a);
pts.Add(b);
pts.Add(c);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(x);
pts.Add(y);
pts.Add(z);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(q);
pts.Add(y);
pts.Add(b);
pts.Add(m);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new Perpendicular(parser.GetIntersection(new Segment(m, q), new Segment(a, c))));
given.Add(new GeometricParallel((Segment)parser.Get(new Segment(a, c)), (Segment)parser.Get(new Segment(x, z))));
goals.Add(new Perpendicular(parser.GetIntersection(new Segment(m, q), new Segment(x, z))));
}
public Page48Problem23To31(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 48 Problem 23-31";
Point a = new Point("A", 0, 5); points.Add(a);
Point b = new Point("B", 2, 4); points.Add(b);
Point c = new Point("C", 4, 3); points.Add(c);
Point m = new Point("M", 3, 6); points.Add(m);
Point x = new Point("X", -2, 1); points.Add(x);
Point y = new Point("Y", 0, 0); points.Add(y);
Point z = new Point("Z", 2, -1); points.Add(z);
Point q = new Point("Q", -1, -2); points.Add(q);
List<Point> pts = new List<Point>();
pts.Add(a);
pts.Add(b);
pts.Add(c);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(x);
pts.Add(y);
pts.Add(z);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(q);
pts.Add(y);
pts.Add(b);
pts.Add(m);
collinear.Add(new Collinear(pts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new Perpendicular(parser.GetIntersection(new Segment(m, q), new Segment(a, c))));
given.Add(new GeometricParallel((Segment)parser.Get(new Segment(a, c)), (Segment)parser.Get(new Segment(x, z))));
goals.Add(new Perpendicular(parser.GetIntersection(new Segment(m, q), new Segment(x, z))));
}
public Page156Problem35(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 156 Problem 35";
Point a = new Point("A", 9, 0); points.Add(a);
Point b = new Point("B", 0, 3); points.Add(b);
Point c = new Point("C", 0, 9); points.Add(c);
Point d = new Point("D", 9, 9); points.Add(d);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment ad = new Segment(a, d); segments.Add(ad);
Segment bc = new Segment(b, c); segments.Add(bc);
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 GeometricCongruentAngles((Angle)parser.Get(new Angle(a, d, b)), (Angle)parser.Get(new Angle(d, b, c))));
given.Add(new Perpendicular(parser.GetIntersection(new Segment(a, d), new Segment(c, d))));
goals.Add(new Strengthened(parser.GetIntersection(new Segment(b, c), new Segment(c, d)),
new Perpendicular(parser.GetIntersection(new Segment(b, c), new Segment(c, d)))));
}
public Page156Problem35(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 156 Problem 35";
Point a = new Point("A", 9, 0); points.Add(a);
Point b = new Point("B", 0, 3); points.Add(b);
Point c = new Point("C", 0, 9); points.Add(c);
Point d = new Point("D", 9, 9); points.Add(d);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment ad = new Segment(a, d); segments.Add(ad);
Segment bc = new Segment(b, c); segments.Add(bc);
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 GeometricCongruentAngles((Angle)parser.Get(new Angle(a, d, b)), (Angle)parser.Get(new Angle(d, b, c))));
given.Add(new Perpendicular(parser.GetIntersection(new Segment(a, d), new Segment(c, d))));
goals.Add(new Strengthened(parser.GetIntersection(new Segment(b, c), new Segment(c, d)),
new Perpendicular(parser.GetIntersection(new Segment(b, c), new Segment(c, d)))));
}
public Page160Problem42(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Page 160 Problem 42";
Point a = new Point("A", -3, -1); points.Add(a);
Point b = new Point("B", 0, 0); points.Add(b);
Point c = new Point("C", 6, 2); points.Add(c);
Point d = new Point("D", 1, -3); points.Add(d);
Point x = new Point("X", -5, 5); points.Add(x);
Point y = new Point("Y", -2, 6); points.Add(y);
Point z = new Point("Z", 1, 7); points.Add(z);
Point q = new Point("Q", -3, 9); points.Add(q);
List <Point> pts = new List <Point>();
pts.Add(q);
pts.Add(y);
pts.Add(b);
pts.Add(d);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(x);
pts.Add(y);
pts.Add(z);
collinear.Add(new Collinear(pts));
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 GeometricParallel((Segment)parser.Get(new Segment(a, c)), (Segment)parser.Get(new Segment(x, z))));
given.Add(new Perpendicular(parser.GetIntersection((Segment)parser.Get(new Segment(q, d)), (Segment)parser.Get(new Segment(x, z)))));
goals.Add(new Supplementary((Angle)parser.Get(new Angle(c, b, y)), (Angle)parser.Get(new Angle(z, y, b))));
}
//Demonstrates: Tangents are perpendicular to radii
public Page296Theorem7_1_Test2(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point a = new Point("A", 3, 4); points.Add(a);
Point p = new Point("P", 0, 6.25); points.Add(p);
Segment ap = new Segment(a, p); segments.Add(ap);
Segment ao = new Segment(a, o); segments.Add(ao);
Circle circle = new Circle(o, 5.0);
circles.Add(circle);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(a, circle, ap));
given.Add(new Strengthened(cInter, new Tangent(cInter)));
Intersection inter = parser.GetIntersection(ao, ap);
goals.Add(new Strengthened(inter, new Perpendicular(inter)));
}
public IPage128Problem01(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Book I Page 128 Problem 1";
Point a = new Point("A", 2, 7); points.Add(a);
Point b = new Point("B", 0, 0); points.Add(b);
Point c = new Point("C", 4, 0); points.Add(c);
Point d = new Point("D", 2, 3); points.Add(d);
Point p = new Point("P", 2, 0); points.Add(p);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment ac = new Segment(a, c); segments.Add(ac);
Segment bd = new Segment(b, d); segments.Add(bd);
Segment cd = new Segment(c, d); segments.Add(cd);
List<Point> pts = new List<Point>();
pts.Add(b);
pts.Add(p);
pts.Add(c);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(a);
pts.Add(d);
pts.Add(p);
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 IsoscelesTriangle((Triangle)parser.Get(new Triangle(d, b, c))));
goals.Add(new GeometricCongruentTriangles(new Triangle(a, b, d), new Triangle(a, c, d)));
goals.Add(new GeometricCongruentTriangles(new Triangle(a, b, p), new Triangle(a, c, p)));
goals.Add(new AngleBisector((Angle)parser.Get(new Angle(b, a, c)), (Segment)parser.Get(new Segment(a, p))));
goals.Add(new AngleBisector((Angle)parser.Get(new Angle(b, d, c)), (Segment)parser.Get(new Segment(a, p))));
goals.Add(new PerpendicularBisector(parser.GetIntersection(new Segment(a, p), new Segment(b, c)),
(Segment)parser.Get(new Segment(a, p))));
}
public ExtraSquareProblem(bool onoff, bool complete) : base(onoff, complete)
{
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);
Point m = new Point("M", 5, 5); points.Add(m);
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);
List <Point> pnts = new List <Point>();
pnts.Add(a);
pnts.Add(m);
pnts.Add(c);
collinear.Add(new Collinear(pnts));
pnts = new List <Point>();
pnts.Add(b);
pnts.Add(m);
pnts.Add(d);
collinear.Add(new Collinear(pnts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Quadrilateral quad = (Quadrilateral)parser.Get(new Quadrilateral(ad, bc, cd, ab));
Segment bd = (Segment)parser.Get(new Segment(b, d));
Segment ac = (Segment)parser.Get(new Segment(a, c));
given.Add(new Strengthened(quad, new Parallelogram(quad)));
given.Add(new Perpendicular(parser.GetIntersection(ac, bd)));
given.Add(new GeometricCongruentSegments(ac, bd));
goals.Add(new Strengthened(quad, new Square(quad)));
}
public Page160Problem42(bool onoff, bool complete)
: base(onoff, complete)
{
problemName = "Page 160 Problem 42";
Point a = new Point("A", -3, -1); points.Add(a);
Point b = new Point("B", 0, 0); points.Add(b);
Point c = new Point("C", 6, 2); points.Add(c);
Point d = new Point("D", 1, -3); points.Add(d);
Point x = new Point("X", -5, 5); points.Add(x);
Point y = new Point("Y", -2, 6); points.Add(y);
Point z = new Point("Z", 1, 7); points.Add(z);
Point q = new Point("Q", -3, 9); points.Add(q);
List<Point> pts = new List<Point>();
pts.Add(q);
pts.Add(y);
pts.Add(b);
pts.Add(d);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(x);
pts.Add(y);
pts.Add(z);
collinear.Add(new Collinear(pts));
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 GeometricParallel((Segment)parser.Get(new Segment(a, c)), (Segment)parser.Get(new Segment(x, z))));
given.Add(new Perpendicular(parser.GetIntersection((Segment)parser.Get(new Segment(q, d)), (Segment)parser.Get(new Segment(x, z)))));
goals.Add(new Supplementary((Angle)parser.Get(new Angle(c, b, y)), (Angle)parser.Get(new Angle(z, y, b))));
}
public IPage128Problem01(bool onoff, bool complete) : base(onoff, complete)
{
problemName = "Book I Page 128 Problem 1";
Point a = new Point("A", 2, 7); points.Add(a);
Point b = new Point("B", 0, 0); points.Add(b);
Point c = new Point("C", 4, 0); points.Add(c);
Point d = new Point("D", 2, 3); points.Add(d);
Point p = new Point("P", 2, 0); points.Add(p);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment ac = new Segment(a, c); segments.Add(ac);
Segment bd = new Segment(b, d); segments.Add(bd);
Segment cd = new Segment(c, d); segments.Add(cd);
List <Point> pts = new List <Point>();
pts.Add(b);
pts.Add(p);
pts.Add(c);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(a);
pts.Add(d);
pts.Add(p);
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 IsoscelesTriangle((Triangle)parser.Get(new Triangle(d, b, c))));
goals.Add(new GeometricCongruentTriangles(new Triangle(a, b, d), new Triangle(a, c, d)));
goals.Add(new GeometricCongruentTriangles(new Triangle(a, b, p), new Triangle(a, c, p)));
goals.Add(new AngleBisector((Angle)parser.Get(new Angle(b, a, c)), (Segment)parser.Get(new Segment(a, p))));
goals.Add(new AngleBisector((Angle)parser.Get(new Angle(b, d, c)), (Segment)parser.Get(new Segment(a, p))));
goals.Add(new PerpendicularBisector(parser.GetIntersection(new Segment(a, p), new Segment(b, c)),
(Segment)parser.Get(new Segment(a, p))));
}
public ExtraSquareProblem(bool onoff, bool complete)
: base(onoff, complete)
{
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);
Point m = new Point("M", 5, 5); points.Add(m);
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);
List<Point> pnts = new List<Point>();
pnts.Add(a);
pnts.Add(m);
pnts.Add(c);
collinear.Add(new Collinear(pnts));
pnts = new List<Point>();
pnts.Add(b);
pnts.Add(m);
pnts.Add(d);
collinear.Add(new Collinear(pnts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Quadrilateral quad = (Quadrilateral)parser.Get(new Quadrilateral(ad, bc, cd, ab));
Segment bd = (Segment)parser.Get(new Segment(b, d));
Segment ac = (Segment)parser.Get(new Segment(a,c));
given.Add(new Strengthened(quad, new Parallelogram(quad)));
given.Add(new Perpendicular(parser.GetIntersection(ac, bd)));
given.Add(new GeometricCongruentSegments(ac, bd));
goals.Add(new Strengthened(quad, new Square(quad)));
}
//Demonstrates: Tangents are perpendicular to radii
public Page296Theorem7_1_Test2(bool onoff, bool complete) : base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point a = new Point("A", 3, 4); points.Add(a);
Point p = new Point("P", 0, 6.25); points.Add(p);
Segment ap = new Segment(a, p); segments.Add(ap);
Segment ao = new Segment(a, o); segments.Add(ao);
Circle circle = new Circle(o, 5.0);
circles.Add(circle);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(a, circle, ap));
given.Add(new Strengthened(cInter, new Tangent(cInter)));
Intersection inter = parser.GetIntersection(ao, ap);
goals.Add(new Strengthened(inter, new Perpendicular(inter)));
}