//
// Take the angle congruence and bisector and create the AngleBisector relation
//
private static List<EdgeAggregator> InstantiateToMedian(Triangle tri, SegmentBisector sb, GroundedClause original)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// The Bisector cannot be a side of the triangle.
if (tri.CoincidesWithASide(sb.bisector) != null) return newGrounded;
// Acquire the intersection segment that coincides with the base of the triangle
Segment triangleBaseCandidate = sb.bisected.OtherSegment(sb.bisector);
Segment triangleBase = tri.CoincidesWithASide(triangleBaseCandidate);
if (triangleBase == null) return newGrounded;
// The candidate base and the actual triangle side must equate exactly
if (!triangleBase.HasSubSegment(triangleBaseCandidate) || !triangleBaseCandidate.HasSubSegment(triangleBase)) return newGrounded;
// The point opposite the base of the triangle must be within the endpoints of the bisector
Point oppPoint = tri.OtherPoint(triangleBase);
if (!sb.bisector.PointLiesOnAndBetweenEndpoints(oppPoint)) return newGrounded;
// -> Median(Segment(V, C), Triangle(A, B, C))
Median newMedian = new Median(sb.bisector, tri);
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(tri);
antecedent.Add(original);
newGrounded.Add(new EdgeAggregator(antecedent, newMedian, annotation));
return newGrounded;
}