Mandy, Do you realize that every course in axiomatic geometry has a slightly different set of axioms? We do not know what yours are.

That said, you should have axioms somewhat like these.

Axiom:There are three non-collinear points.

Axiom:Given two points there is a line containing the points.

So you could say something like this.

Given a point P, by the first axiom there is another point Q.

By the second axiom there is a line .

Again by the first axiom . Why is that true?

So . Why is that true?

Can you find a second line .