|Postulate 1||1. Any two distinct points on a line can be
assigned coordinates0 and 1.
2. There is a one-to-one correspondence between the real numbers and all points on the line.
3. To every pair of points, there corresponds exactly one positive number called the distance between the two points.
|Postulate 2||Segment Addition Postulate: If C is between A and B, then AC + CB = AB.|
|Postulate 3||Any segment has exactly one midpoint.|
|Postulate 4||Protractor Postulate: In a given plane,
select any line AB and any point C between A and B. Also select any two points R and S on
the same side of AB such that S is not on CR. Then there is a pairing of rays to real
numbers from 0 to 180 as follows.
1. CA is paired with 0 and CB is paired with 180.
2. If CR is paired with x, then 0 < x < 180.
3. If CR is paired with x and CS is paired with y, then angle RCS = |x - y|.
|Postulate 5||Angle Addition Postulate: If D is in the interior of angle ABC, then m angle ABC = m angle ABD + m angle LDBC.|
|Postulate 6||Every angle, except a straight angle, has exactly one bisector.|
|Postulate 7||If the outer rays of two adjacent angles form a straight angle, then the sum of the measures of the angles is 180.|
|Theorem 1.1||If the outer rays of two acute adjacent angles are perpendicular, then the sum of the measures of the angles is 90.|
|Theorem 2.1||If two angles are supplements of congruent angles, then they are congruent. (Supplements of congruent angles are congruent.)|
|Corollary||If two angles are supplements of the same angle, then they are congruent. (Supplements of the same angle are congruent.)|
|Theorem 2.2||If two angles are complements of congruent angles, then they are congruent. (Complements of congruent angles are congruent.)|
|Corollary||If two angles are complements of the same angle, then they are congruent. (Complements of congruent angles are congruent.)|
|Theorem 2.3||If two angles are right angles, then they are congruent.|
|Theorem 2.4||Vertical Angles Theorem: Vertical angles are congruent.|
|Corollary||If two lines are perpendicular, then four right angles are formed.|
|Postulate 8||A line contains at least two points. A plane contains at least three noncolinear points. Space contains at least four noncoplaner points|
Note: The concepts in this collection may
not be entirely accurate.
They are for reference only.