Geometry postulates, or axioms are accepted statements or fact. Therefore, there is no need to prove them.
Postulate 1.1

Postulate 1.1

Postulate 1.2

Postulate 1.2

Postulate 1.3

Postulate 1.3

Postulate 1.4
Through any three points that are not on the same line, there is exactly one plane. Notice that we don't need 4 points to define a plane. This makes sense since a chair with only 3 legs will not fall over.

Postulate 1.4

Postulate 1.5 or ruler postulate

Postulate 1.6 or segment addition postulate
If A, B, and C are collinear, and B is between A and C, AB + BC = AC
A more thorough coverage of the ruler postulate can be found here
Postulate 1.7 or protractor postulate
Let O be the midpoint of line AB. Rays OA, OB, and all the rays with endpoints O that can be drawn on one side of line AB can be paired with the real numbers from 0 to 180 such that that
OA is paired with 0 and OB is paired with 180.
Postulate 1.8 or angle addition postulate

Postulate 1.9
If two shapes are congruent, then their areas are equal.
Postulate 1.10
The area of a shape is the sum of the areas of its nonoverlapping parts.
Jul 06, 18 12:29 PM
Learn how to solve two types of logarithmic equations
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
Jul 06, 18 12:29 PM
Learn how to solve two types of logarithmic equations
Our Top Pages
Formula for percentage
Compatible numbers
Basic math test
Basic math formulas
Types of angles
Math problem solver
Algebra word problems
Surface area of a cube
Finding the average
Scale drawings
Everything you need to prepare for an important exam!
K12 tests, GED math test, basic math tests, geometry tests, algebra tests.
Real Life Math Skills
Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.