## 7.1 Outline

- Greek (Euclidean) geometry
- undefined terms
- point
- line
- plane
- surface

- categories
- traditional (Euclidean) geometry
- transformational geometry

- Euclid’s postulates
- postulate
- axiom
- theorem
- five postulates

- parallel lines
- non-Euclidean geometries
- straightedge
- line segment
- congruent figures
- construct a figure
- construct a circle
- construct a line parallel to a given line through a given point

- undefined terms
- Transformational geometry
- transformation
- reflection
- line of symmetry

- Similarity
- definition
- similar

## 7.1 Essential Ideas

Geometry can be separated into two categories:

- Traditional (which is the geometry of Euclid)
- Transformational (which is more algebraic than the traditional approach)

When Euclid was formalizing traditional geometry, he based it on the following five postulates:

- A straight line can be drawn from any point to any other point.
- A straight line extends infinitely far in either direction.
- A circle can be described with any point as center and with a radius equal to any finite straight line drawn from the center.
- All right angles are equal to each other.
- Given a straight line and any point not on this line, there is one and only one line through that point that is parallel to the given line.