Foundations of Geometry

When Euclid organized his thoughts on geometry, he chose four undefined terms and five axioms or postulates to be the foundation of Euclidean geometry. Every other part of geometry is built upon this foundation.

Undefined terms

• point
• line
• plane
• space

Five axioms

• The shortest distance between any two points is a straight line
• Any line segment can be extended infinitely in either direction
• A circle can be made with any center and any radius
• All right angles are equal to each other
• Given a point and a line not on the point, only one line can be drawn parallel to the given line through the given point