Free Geometry Basics Course •Part 1  Terms in Geometry •Part 2  Types of Angles •Part 3 •Postulates • Part 4 • Measuring Angles • Part 5 • More On Angles • Geometry Help • Mathematicians Review • Conic Sections • Pythagorean Theorem • •

Related Resources • Measurement Formulas • Recommended Resources • Area Calculator • Introduction to Polygons

Background:
Euclid of Alexandria wrote 13 books called 'The Elements' around 300 BC. These books laid the foundation of geometry. Some of the postulates below were actually posed by Euclid in his 13 books. They were assumed as axioms, without proof. Euclid's postulates have been slightly corrected over a period of time. Some are listed here and continue to be part of 'Euclidean Geometry'.

Know this stuff! Learn it, memorize it and keep this page as a handy reference if you expect to understand Geometry.

There are some basic facts, information and postulates that are very important to know in geometry. Not everything is proved in Geometry, thus we use some postulates which are basic assumptions or unproved general statements that we accept. Here are a few of the basics and postulates that are intended for entry level Geometry. (Note: there are many more postulates than are stated here, these postulates are intended for beginner geometry)

The Basics and Important Postulates :

1. You can only draw one line between two points. You will not be able to draw a second line through points A and B:

2. There's 360° around a circle.

3. Two lines can instersect at ONLY one point. S is the only intersection of and in the figure below.

4. A line segment has ONLY one midpoint. M is the only Midpoint of in the figure below.

5. An angle can only have one bisector. (Bisector: a ray that's in the interior of an angle and forms two equal angles with the sides of that angle.)

In the figure below, is the bisector of A

6. Any geometric shape can be moved without changing its shape.

7. A line segment will always be the shortest distance between two points on a plane. The curved line and the bropken line segments are further in distance between A and B.

8. If two points lie in a plane, the line containing the points lie in the plane.

9. When two planes intersect, their intersection is a line.

10. ALL lines and planes are sets of points.

11. Every line has a coordinate system. (The Ruler Postulate)

 

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