Axioms

This course is based on Euclidian plane geometry which is an axiom system.  An axiomatic system is a set of specific statements which can be used to derive theorems. Axioms, also known as postulates, are statements that are taken to be true without proof. Euclidean geometry is based on the following five postulates from Euclid's book Elements:

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

2.  Any line segment can extend indefinitely in a line.

3.  Given a segment, a circle can be drawn with the segment as its radius and one endpoint as the center.

4.  All right angles are congruent.

5.  If a line that meets two other lines makes the interior angles on the same side less than two right angles, then those two straight lines, if extended, will meet on that same side.

ParallelPostulate

Since the measure of angles

1 and 2 are each less than 900,

 then lines AB and CD

will eventually intersect

on the side of line XY

that angles 1 and 2 are on.

The last postulate is known as the Parallel Postulate.  If the postulate is assumed true, then the type of Geometry is known as Euclidean Geometry.  If the postulate is assumed false, then the type of Geometry is known as non-Euclidean Geometry.  For this course, the Parallel Postulate is assumed to be true.

 

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