//
        // Creates a Topped F-Shape
        //            top
        // oppSide __________       <--- Stands on
        //             |
        //             |_____ off   <--- Stands on
        //             |
        //             |
        //           bottom
        //
        //   Returns: <bottom, off>
        private static List<EdgeAggregator> GenerateToppedFShape(Parallel parallel, Intersection inter1, Intersection inter2, Intersection bottom, Point off)
        {
            List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();

            Intersection top = inter1.Equals(bottom) ? inter2 : inter1;

            // Determine the side of the top intersection needed for the angle
            Segment transversal = inter1.AcquireTransversal(inter2);

            Segment parallelTop = top.OtherSegment(transversal);
            Segment parallelBottom = bottom.OtherSegment(transversal);

            Segment crossingTester = new Segment(off, parallelTop.Point1);
            Point intersection = transversal.FindIntersection(crossingTester);

            Point oppSide = transversal.PointLiesOnAndBetweenEndpoints(intersection) ? parallelTop.Point1 : parallelTop.Point2;

            //
            // Generate the new congruence
            //
            List<CongruentAngles> newAngleRelations = new List<CongruentAngles>();

            GeometricCongruentAngles gca = new GeometricCongruentAngles(new Angle(off, bottom.intersect, top.intersect),
                                                                        new Angle(oppSide, top.intersect, bottom.intersect));
            newAngleRelations.Add(gca);

            return MakeRelations(newAngleRelations, parallel, inter1, inter2);
        }
        //
        // Creates a shape like a crazy person flying
        //
        //            top   top
        //             |     |
        // larger      |_____|___ off
        //             |     |
        //             |     |
        //
        // Similar to H-shape with an extended point
        // Returns the 'larger' intersection that contains the point: off
        private static List<EdgeAggregator> InstantiateFlyingIntersection(Parallel parallel, Intersection inter1, Intersection inter2, Intersection larger, Point off)
        {
            List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();

            Intersection smallerInter = inter1.Equals(larger) ? inter2 : inter1;

            Segment transversal = inter1.AcquireTransversal(inter2);

            Segment parallel1 = inter1.OtherSegment(transversal);
            Segment parallel2 = inter2.OtherSegment(transversal);

            Point largerTop = parallel1.Point1;
            Point largerBottom = parallel1.Point2;

            Point otherTop = null;
            Point otherBottom = null;

            Segment crossingTester = new Segment(parallel1.Point1, parallel2.Point1);
            Point intersection = transversal.FindIntersection(crossingTester);
            // opposite sides
            if (transversal.PointLiesOnAndBetweenEndpoints(intersection))
            {
                otherTop = parallel2.Point2;
                otherBottom = parallel2.Point1;
            }
            // same sides
            else
            {
                otherTop = parallel2.Point1;
                otherBottom = parallel2.Point2;
            }

            //
            // Generate the new congruence
            //
            List<CongruentAngles> newAngleRelations = new List<CongruentAngles>();

            GeometricCongruentAngles gca1 = new GeometricCongruentAngles(new Angle(off, smallerInter.intersect, otherTop),
                                                                         new Angle(smallerInter.intersect, larger.intersect, largerTop));
            newAngleRelations.Add(gca1);
            GeometricCongruentAngles gca2 = new GeometricCongruentAngles(new Angle(off, smallerInter.intersect, otherBottom),
                                                                         new Angle(smallerInter.intersect, larger.intersect, largerBottom));
            newAngleRelations.Add(gca2);

            return MakeRelations(newAngleRelations, parallel, inter1, inter2);
        }