Geometry postulates

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

Postulate 1.1

Through two points, there is exactly 1 line. 

Line t is the only line passing through E and F

Postulate 1.1Postulate 1.1

Postulate 1.2

Two lines can intersect in exactly 1 point.

Postulate 1.2Postulate 1.2

Postulate 1.3

Two planes can intersect in exactly 1 line. The figure on the right has 2 planes. Plane ZXY in yellow and plane PXY in blue intersect in line XY shown in red.

Postulate 1.3Postulate 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.

The 3 black points determine exactly 1 plane

The 3 red points determine exactly 1 plane.

Postulate 1.4Postulate 1.4

Postulate 1.5 or ruler postulate

Each point on a line can be assigned a real number. The distance between any 2 points is the absolute value of the difference of the corresponding numbers.

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

If   ∠ AOB is a straight angle, then 

m ∠ AOC + m ∠ COB = 180

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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