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
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 startPoint = firsLineSegment.StartPoint;