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Theorem:
Vertical angles are congruent.

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Postulates
	Description		Example
1.	Ruler Postulate: The points on a line can be matched one to one with the real numbers. The real numbers that correspond to a point is the coordinate of the point. The distance between points A and B, written as AB, is the absolute value of the difference between the coordinates A and B.
2.	Segment Addition Postulate: If B is between A and C, then AB+BC=AC, then B is between the coordinates of A and C.
3.	Angle Addition Postulate: If P is in the interior of RST, then mRSP+mPST=mRST.
4.	Through any two points there exists exactly one line.
5.	A line contains at least two points.
6.	If two lines intersect, then their intersection is exactly one point.
7.	Through any three noncollinear points there exists exactly one plane.
8.	A plane contains at least three noncollinear points.
9.	If two points lie in a plane, then the line containing them lies in the plane.
10.	If two planes intersect, then their intersection is a line.
Theorems
1.	Right Angle Congruence Theorem: All right angles are congruent.
2.	Congruent Supplements Theorem: If two angles are supplementary to the same angle (or to congruent angles) then the two angles are congruent.
3.	Congruent Complements Theorem: If two angles are complementary to the same angle (or to congruent angles) then the two angles are congruent.

5.	Alternate Interior Angles: If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
6.	Consecutive Interior Angles: If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.
7.	Alternate Exterior Angles: If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.
8.	Perpendicular Transversal: If a transversal is perpendicular to one of two perpendicular lines, then it is perpendicular to the other.
9.	Alternate Interior Angles Converse: If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.
10.	Consecutive Interior Angles Converse: If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.