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postulates theorums
| Term | Definition |
|---|---|
| Ruler Postulate | The points on a line can be matched one to one with real numbers. The real number that corresponds 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 of the coordinates of |
| Segment Addition Postulate | If B is between A and C, then AB + BC = AC. If AB + BC = AC, then B is between A and C |
| Protractor Postulate | Consider ray OB and a point A on one side of line OB. The rays of the form ray OA can be matched one to one with the real numbers from 0 to 180. |
| Angle Addition Postulate | If P is in the interior of angle RST, then the measure of angle RST is equal to the sum of the measures of angle RSP and angle PST |
| Two Point Postulate | Through any two points, there exists exactly one line |
| Line-Point Postulate | A line contains at least two points |
| Line Intersection Postulate | If two lines intersect, then their intersection is exactly one point |
| Three Point Postulate | Though any three noncollinear points, there exists exactly one plane |
| Plane-Point Postulate | A plane contains at least three noncollinear points |
| Plane-Line Postulate | If two points lie in a plane, then the line containing them lies in the plane |
| Plane Intersection Postulate | If two planes intersect, then their intersection is a line |
| Linear Pair Postulate | If two angles form a linear pair, then they are supplementary |
| Parallel Postulate | If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line |
| Perpendicular Postulate | If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line |
| Reflexive Property | For any segment AB, segment AB is congruent to segment AB. For any angle A, angle A is congruent to angle A. |
| Symmetric Property | If segment AB is congruent to segment CD, the segment CD is congruent to segment AB. If angle A is congruent to angle B, then angle B is congruent to angle A. |
| Transitive Property | If segment AB is congruent to segment CD and segment CD is congruent to segment EF, then segment AB is congruent to segment EF. If angle A is congruent to angle B and angle B is congruent to angle C, then angle A is congruent to angle C. |
| Right Angles Congruence Theorem | All right angles are congruent |
| Congruent Supplements Theorem | If two angles are supplementary to the same angle (or to congruent angles) then they are congruent |
| Congruent Complements Theorem | If two angles are complementary to the same angle (or to congruent angles) then they are congruent |
| Vertical Angles Congruence Theorem | Vertical angles are congruent |
| Corresponding Angles Theorem | If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent |
Created by:
Jonathon B