You have to assign the MenuItem's Style
property by declaring the <Style>
as child element of a <MenuItem.Style>
element.
<MenuItem IsCheckable="True" IsChecked="True">
<MenuItem.Style>
<Style TargetType="MenuItem">
<Style.Triggers>
<Trigger Property="IsChecked" Value="True">
<Setter Property="Header" Value="Metric"/>
</Trigger>
<Trigger Property="IsChecked" Value="False">
<Setter Property="Header" Value="Imperial"/>
</Trigger>
</Style.Triggers>
</Style>
</MenuItem.Style>
</MenuItem>