Example1 - $scope inheritance
Note) The ChildCtrl is nested within MainCtrl in the html. AngularJS responds to this by ensuring that the $scope passed to ChildCtrl inherits properties and methods from the $scope passed to and decorated by MainCtrl.
Also Note) AngularJS does not introduce any inheritance (prototypical or otherwise) between the actual controllers themselves.
Example 2 - Rolling your own Controller Inheritance
Note) I changed for the way I create my controllers from an anonymous approach utilising the controller method to a named function approach. This is necessary because you need the named function in order to access and extend its prototype.
Also Note) I forced the ChildCtrl to inherit from the main MainCtrl using prototypical inheritance. I was then able to do is extend the $scope of the ChildCtrl with a method that made use of the inherited method.