In order to enhance the functionality of the RadMenu control, the RadMenuItem can behave like a checkable item. This means that it can be checked and unchecked like a simple CheckBox. In order to toggle this behavior you have to set the IsCheckable property of the RadMenuItem to either True or False. The default value is False.
To learn how to group the checkable items into radio groups read here.
Upon checking and unchecking the respective events are raised - Checked and Unchecked. You can subscribe to them in order to implement your custom logic against the respective action. To learn more about them read here.
Here is an example of a definition of a checkable RadMenuItem:
<telerik:RadMenuItem Header="Status Bar" IsCheckable="True" />
Note that after clicking on the item the menu will collapse. In order to keep the menu open you can set the StaysOpenOnClick property of the RadMenuItem to True. This will keep the menu open when this item is clicked.
If you want to programmatically mark an item as checked, you have to set the IsChecked property to True.