ResxTranslationProvider.cs

public ResxTranslationProvider(ResourceManager resourceManager)
{
    _resourceManager = resourceManager;
    foreach (var culture in CultureInfo.GetCultures(CultureTypes.AllCultures))
    {
        var resourceSet = _resourceManager.GetResourceSet(culture, false, false);
        if (resourceSet != null)
        {
            _languages.Add(culture);
        }
    }
}

TranslateExtension.cs

public TranslateExtension(string key)
{
    if (key == null)
        throw new ArgumentNullException("key");
    if (DesignerProperties.GetIsInDesignMode(DependencyObject))
    {
        if (TranslationManager.Instance.TranslationProvider == null)
            throw new Exception("TranslationManager.Instance.TranslationProvider==null");
        var translate = TranslationManager.Instance.TranslationProvider.Translate(key);
        if (translate == null)
        {
            throw new Exception(string.Format(@"TranslationManager.Instance.Translate({0})", key));
        }
    }
    Key = key;
}