Q:

Creating a class in Angular

How to create a class in angularjs with a constructor, getter, setter, variables and methods?
Here is example of what I want to make in angulajs
class Abc {
int a;
string str ="Hello world";

  public Abc(){
  }

  public show(){
   return str;
  }

  public setStr(string str){
  this.str = str;
  }

  public getStr(){
  return this.str;
  }
}

I don't want to use any type script.
Just want to know how to make a class in angularjs with the following abilities.

A:

That is not the way JS or angular work.

Update

Since what you are trying to do is to be able to create new instances, you should probably create this in a service, and then in the controller you can inject your service.
For example:
angular.module('app', function(){

});

angular.module('app').factory('Abc', function(){
    return {
        a: 0,
        str: "Hello world",
        show:  function() {
            return str;
        },
        setStr: function(str) {
            this.str = str;
        },
        getStr: function() {
            return str;
        }
    }
});

angular.module('app').controller('myController', function(Abc) {
     $scope.newClass = new Abc;
});

Old answer.

Instead you create objects which have there own properties, usually inside the $scope of your controller.
An equivalent angular code to your code would be:
angular.module('app', function(){

});

angular.module('app').controller('Abc', function(){
    $scope.a;

    var str = "Hello world";

    $scope.show = function() {
        return str;
    };

    $scope.setStr = function(str) {
        str = str;
    };

    $scope.getStr = function() {
        return str;
    };
});

