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Geometry Honors: Notes on Postulates and Theorems Postulate: Statement accepted without proof. 4 Postulates we already have: 1. The Ruler Postulate (to calculate distance) 2. The Protractor Postulate (to calculate angles) 3. The Segment Addition Postulate 4. The Angle Addition Postulate Other Postulates : * A line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points not all in one plane. * Through any two points there is exactly one line. * Through any three points there is at least one plane, and through any three non-collinear points there is exactly one plane. * If two points are in a plane, then the line that contains the points is in that plane. * If two planes intersect, then their intersection is a line. Theorem: An important statement that we can PROVE to be true. * If two lines intersect, then they intersect in exactly one point. * Through a line and a point not in the line there is exactly one plane. * If two lines intersect, then exactly one plane contains the lines.