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High school Geometry is pretty different from what students study about Geometry in earlier math classes. Whenever I ask students what they think they'll study in high school the general response is 'Shapes and stuff!' Well, there's a place in high school for the 2-D and 3-D shapes students come into Geometry already knowing. Unfortunately, most of that material is reserved for the end of the course because to truly understand where those came from you have to go way back to the very beginning. The analogy I like to use is an iceberg. The information students come into Geometry with is just the tip of the iceberg. Most of what we study in high school is all of the stuff that's hidden below the surface.

Geometry is referred to as an 'axiomatic system'. What does that even mean? Well, first of all, an axiom and a postulate are synonyms for each other. We usually use the word 'postulate' in Geometry and a postulate is simply a statement you can accept to be true without having to explain why it's true. Euclid of Alexandria, known as the Father of Geometry, developed what we generally think of as Geometry based on 5 postulates. In fact, what we generally refer to as Geometry is really called Euclidean Geometry, named after Euclid of Alexandria. Euclid's 5 Postulates

1) A straight line segment can be drawn between any two points.

2) A line segment can be extended indefinitely in a straight line.

3) Given any line segment, a circle can be made with the segment as a radius and one endpoint as its center.

4) All right angles are congruent.

5) If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two Right Angles, then the two lines inevitably must intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the Parallel Postulate.

The 5th postulate caused a lot of problems with mathematicians for a long time. Euclid himself only used the first four postulates to develop the rest of his system of Geometry. After postulates we move on to theorems, which are true statements but they have to be proven or explained. From there come conjectures, which are statements based on observations, giving us inductive reasoning... and it just keeps on going until we get back to the tip of that iceberg students come into Geometry already knowing.