how to show/hide a div on the basis of a checkbox selection in angular js

I think you are looking for ng-true-value and ng-false-value

<div ng-app>
    <div >
        <input type="checkbox" ng-true-value="A" ng-false-value="B" ng-model="check"/>        
    </div>

    <div ng-show="check == 'A'">
        Checked
    </div>
</div>

Fiddle

Have you tried it this way? Here's the fiddle It works great.

<input type="checkbox" id="Animals" name="Animals" ng-model="ModelData.Animals" />
<div class="form-group" ng-show="ModelData.Animals">
  <label for="FirstName" class="col-md-9">
    Are you interested in Animal Liability Coverage?
  </label>
  <div class="col-md-3">
    <label>
      <input type="radio" id="AnimalLiabCovY" name="AnimalLiabilityCoverageRadio" ng-model="ModelData.AnimalLiabCov" value="Y" /> Yes
      <input type="radio" id="AnimalLiabCovN" name="AnimalLiabilityCoverageRadio" ng-model="ModelData.AnimalLiabCov" value="N" /> No
    </label>
  </div>
</div>