Geometry was the first system of ideas in which a few simple statements were assumed and then used to derive more complex ones. A system such as this is referred to as a deductive system. Geometry introduces you to the ideas of deduction and logical consequences, ideas you will continue to use throughout your life.
Ready to get your logical, geometric brain warmed up? A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven. Listed below are the first six postulates and the theorems that can be proven from these postulates.
Postulate 1: A line contains at least two points.
Postulate 2: A plane contains at least three non collinear points.
Postulate 3: Through any two points, there is exactly one line.
Postulate 4: Through any three noncollinear points, there is exactly one plane.
Postulate 5: If two points lie in a plane, then the line joining them lies in that plane.
Postulate 6: If two planes intersect, then their intersection is a line.
Theorem 1: If two lines intersect, then they intersect in exactly one point.
Theorem 2: If a point lies outside a line then exactly one plane contains both the line and the point.
Theorem 3: If two lines intersect, then exactly one plane contains both lines.