MainPage.xaml.cs

using System;
using System.Linq;
using Windows.UI.Xaml.Controls;
using Windows.UI.Xaml.Media;
using Windows.UI.Xaml.Shapes;
using Windows.UI;
using Windows.Foundation;

namespace ManyLinesTestCs
{
    public sealed partial class MainPage : Page
    {
        public MainPage()
        {
            this.InitializeComponent();

            var geometryGroup = new GeometryGroup();

            canvas.Children.Add(
                new Path()
                {
                    Stroke = new SolidColorBrush(Colors.SteelBlue),
                    StrokeThickness = 1.0,
                    Data = geometryGroup
                });

            var random = new Random();

            button.Click += (s, e) =>
                {
                    foreach (var elt in Enumerable.Range(0, 2000))
                        geometryGroup.Children.Add(
                            new LineGeometry()
                            {
                                StartPoint = new Point(random.Next((int)canvas.Width), random.Next((int)canvas.Width)),
                                EndPoint = new Point(random.Next((int)canvas.Width), random.Next((int)canvas.Width))
                            });
                };
        }
    }
}