Questions on Platonic Idealism

1. When Socrates gets the slave to describe how to double a square, he's showing that the slave already knew how to do this. Plato's explanation is that he can do this because he's come in contact with that mathematical truth before as one of the Forms. You may think that's odd and incredible, but if these Forms don't exist, then what are we studying when we study triangles, parallel lines, rational numbers, irrational numbers, imaginary numbers(!), and all the other bizarre things that mathematicians study? In what way are they 'real' things?

2. If we know a thing only through acquaintance with the Forms that that thing 'participates in', do we ever really know the thing itself, or only the Forms involved?