diff --git a/src/Perspex.Controls/Shapes/Polygon.cs b/src/Perspex.Controls/Shapes/Polygon.cs
index 99aab8a59c..4ff24d060f 100644
--- a/src/Perspex.Controls/Shapes/Polygon.cs
+++ b/src/Perspex.Controls/Shapes/Polygon.cs
@@ -1,11 +1,7 @@
 // Copyright (c) The Perspex Project. All rights reserved.
 // Licensed under the MIT license. See licence.md file in the project root for full license information.
 
-using System;
 using System.Collections.Generic;
-using System.Linq;
-using System.Text;
-using System.Threading.Tasks;
 using Perspex.Media;
 
 namespace Perspex.Controls.Shapes
@@ -15,12 +11,36 @@ namespace Perspex.Controls.Shapes
         public static readonly StyledProperty<IList<Point>> PointsProperty =
             PerspexProperty.Register<Polygon, IList<Point>>("Points");
 
+        private Geometry _geometry;
+
+        static Polygon()
+        {
+            PointsProperty.Changed.AddClassHandler<Polygon>(x => x.PointsChanged);
+        }
+
+        public override Geometry DefiningGeometry
+        {
+            get
+            {
+                if (_geometry == null)
+                {
+                    _geometry = new PolylineGeometry(Points, true);
+                }
+
+                return _geometry;
+            }
+        }
+
         public IList<Point> Points
         {
             get { return GetValue(PointsProperty); }
             set { SetValue(PointsProperty, value); }
         }
 
-        public override Geometry DefiningGeometry => new PolylineGeometry(Points, true);
+        private void PointsChanged(PerspexPropertyChangedEventArgs e)
+        {
+            _geometry = null;
+            InvalidateMeasure();
+        }
     }
 }
diff --git a/src/Perspex.Controls/Shapes/Polyline.cs b/src/Perspex.Controls/Shapes/Polyline.cs
index cac26ee873..eb0426b77b 100644
--- a/src/Perspex.Controls/Shapes/Polyline.cs
+++ b/src/Perspex.Controls/Shapes/Polyline.cs
@@ -1,11 +1,7 @@
 // Copyright (c) The Perspex Project. All rights reserved.
 // Licensed under the MIT license. See licence.md file in the project root for full license information.
 
-using System;
 using System.Collections.Generic;
-using System.Linq;
-using System.Text;
-using System.Threading.Tasks;
 using Perspex.Media;
 
 namespace Perspex.Controls.Shapes
@@ -15,9 +11,25 @@ namespace Perspex.Controls.Shapes
         public static readonly StyledProperty<IList<Point>> PointsProperty =
             PerspexProperty.Register<Polyline, IList<Point>>("Points");
 
+        private Geometry _geometry;
+
         static Polyline()
         {
             StrokeThicknessProperty.OverrideDefaultValue<Polyline>(1);
+            PointsProperty.Changed.AddClassHandler<Polyline>(x => x.PointsChanged);
+        }
+
+        public override Geometry DefiningGeometry
+        {
+            get
+            {
+                if (_geometry == null)
+                {
+                    _geometry = new PolylineGeometry(Points, false);
+                }
+
+                return _geometry;
+            }
         }
 
         public IList<Point> Points
@@ -26,6 +38,10 @@ namespace Perspex.Controls.Shapes
             set { SetValue(PointsProperty, value); }
         }
 
-        public override Geometry DefiningGeometry => new PolylineGeometry(Points, false);
+        private void PointsChanged(PerspexPropertyChangedEventArgs e)
+        {
+            _geometry = null;
+            InvalidateMeasure();
+        }
     }
 }