For line and polygons you should not be putting anything but a "Path" object in your template, and it must have the name "Element". You can place the visual states inside it:
<ControlTemplate>
<Path x:Name="Member" Stroke="Blue" Fill="Black"
StrokeStartLineCap="Round" StrokeThickness="2"
StrokeLineJoin="Round" StrokeEndLineCap="Round" >
<VisualStateManager>
...
</VisualStateManager>
</Path>
</ControlTemplate>
This is a limitation for polygons and polylines (since they are paths and not just any UIElement).