Thanks, kdub. I mean I should know one point is lie on one linesegment. I enclosed my working video.
As you can see in my video I moved two points to one Polyline. But my code returns two polylines are not touched eachother. Followings are my code. 
BlockTable acBlkTbl;
acBlkTbl = acCurrTrans.GetObject(db.BlockTableId, OpenMode.ForWrite) as BlockTable;
BlockTableRecord acBlkTblRec;
acBlkTblRec = acCurrTrans.GetObject(acBlkTbl[BlockTableRecord.ModelSpace],OpenMode.ForWrite) as BlockTableRecord;
Point3d acPt3d = new Point3d(right1.X, 0, 0);
Vector3d acVec3d = acPt3d.GetVectorTo(new Point3d(left2.X, 0, 0));
for (int i = 0; i < pln1.NumberOfVertices; i++)
{
    Point3d pt = pln1.GetPoint3dAt(i);
    if (pt.X == right1.X)
    {
       pln1.SetPointAt(i, new Point2d(left2.X, pt.Y));
    }
}
bool istch = NBCrelate.checkTwoPlineTouch(pln2, pln1);
if (istch)
  Application.ShowAlertDialog("Two Polyline touched");
public static bool checkTwoPlineTouch(Polyline pl1, Polyline pl2)            // this checks two polyline is close.
        {
            bool btch = false;
            int tchcnt = 0;
            for (int i = 0; i < pl2.NumberOfVertices; i++)
            {
                if (IsPointOnPolyline(pl1, pl2.GetPoint3dAt(i)))
                {
                    tchcnt++;
                }
            }
            if (tchcnt >= 2)
                btch = true;
            tchcnt = 0;
            if (!btch)
            {
                for (int i = 0; i < pl1.NumberOfVertices; i++)
                {
                    if (IsPointOnPolyline(pl2, pl1.GetPoint3dAt(i)))
                    {
                        tchcnt++;
                    }
                }
                if (tchcnt >= 2)
                    btch = true;
            }
            return btch;
        }
public static bool IsPointOnPolyline(Polyline pl, Point3d pt)           // this returns point is on polyline or not.
        {            
            bool isOn = false;
            for (int i = 0; i < pl.NumberOfVertices; i++)
            {
                Curve3d seg = null;
                Curve seg1 = null;
                SegmentType segType = pl.GetSegmentType(i);
                if (segType == SegmentType.Arc)
                    seg = pl.GetArcSegmentAt(i);
                else
                if (segType == SegmentType.Line)
                    seg = pl.GetLineSegmentAt(i);
                    //seg1 = pl.GetLineSegment2dAt(i);
                if (seg != null)
                {
                    //isOn = seg.IsOn(pt);      
                    isOn= IsPointOnCurveGDAP(seg, pt);
                    if (isOn)
                        break;
                }
            }
            return isOn;
        }
I saw moved Polyline's Point is equal to target polylines's left vertex X coordinate.
But IsPointOnPolyline function does not return true. I dont know cause. Could you tell me?