public sealed class LineSegment : Segment 

{
  // Method 1: Get the start point of the polyline by converting the polyline 
  //    into a collection of points and getting the first point

  // sketchGeometry is a Polyline
  // get the sketch as a point collection
  Geometry sketchGeometry = polyline; // for example
  var pointCol = ((Multipart)sketchGeometry).Points;
  // Get the start point of the line
  var firstPoint = pointCol[0];

  // Method 2: Convert polyline into a collection of line segments 
  //   and get the "StartPoint" of the first line segment.
  var polylineGeom = sketchGeometry as ArcGIS.Core.Geometry.Polyline;
  var polyLineParts = polylineGeom.Parts;

  ReadOnlySegmentCollection polylineSegments = polyLineParts.First();

  //get the first segment as a LineSegment
  var firsLineSegment = polylineSegments.First() as LineSegment;

  //Now get the start Point
  var startPointOfSegment = firsLineSegment.StartPoint;
}