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.
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