Difference between dass, die, der meaning "that"
I know that "das", "der" und "die" are articles, but in some cases I see them meaning "dass" (as that).
Ein Showmaster ist ein Moderator, jemand, "der" eine Fernsehshow präsentiert. Die zwar Englisch klingen, "die" aber kein Engländer oder Amerikaner versteht.
How do I know when to use "dass", "der" or "die" in those cases?
Let's look at the first example. 'der' is not an article in this situation. It is a relative pronoun. 'der' and everything that follows is a relative clause that expands on something that has gone before, in this case 'ein Moderator', which is called the antecedent. The relative pronoun must agree in number and gender with the antecedent, so masculine singular. The case can be different, but here they're both nominative. Basically a relative pronoun links the relative clause to the antecedent. In this example 'der' can translate as 'that' or 'who'.
In the second example the 'die' after the comma is another relative pronoun. The 'Die' at the start of the sentence is the antecedent.
'dass' is a conjunction usually translated as 'that'. 'Ich weiß, dass das Auto kaputt ist.' Notice that 'dass' doesn't agree with anything. It just connects the two clauses.
Oh, I know this -- I seem to be the first one who replies, and then I find that other people have posted while I've been typing.
It's great that you've added the aspect of "number" to the list. In my reply, I only thought about "gender" and "case", and I was sure that "case" was not a feature that the relative pronoun has to be aligned with. But I missed "number" (I somehow included it in my choice of examples, but you stated it clearly).