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Postulates/Theorems
| 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 o |
| 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 point on one side of line OB. The rays of the form Ray OA can be matched one to one with real number 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 measure of angle rsp and angle pst |
| Two point Postulate | Through any two points there exist exactly one line |
| Line Point Postulate | A line contains at least two points |
| Line Intersection Postulate | If two lines intersect then their intersection is a line |
| Three point Postulate | though any three nonconllinear points there exist exactly one plane |
| plane point Postulate | A plane contains at least three nonconllinear points |
| Plane line Postulate | if two points lie in a plane then the line containing them lies in a 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 |
| 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 |
| reflective property | for any segment ab segment ab is congruent to segment ab for any angel A angle 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 ed 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 supplementry 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 theorems | vertical angles are congruent |
| corresponding angles theorem | if two parallel lines are cut by a transversal then the pairs of corresponding angles are congruent |
| alternate interior angles theorem | if two parallel lines are cut by a transversal then the pairs of alternate interior angles are congruent |
| alternate exterior angles theorem | if two parallel lines are cut by a transversal then pair of alternate exterior angels are congruent |
| consecutive interior angles theorem | if two parallel lines are cut by a transversal then pair of consecutive intertoir angles are supplementary |
| corresponding angles converse | if two lines are cut by a transversal so corresponding angles are congruent then the lines are parallel |
| alternate interior angles converse | if two lines are cut by a transversal so the alternate interior angles are congruent then the lines are parallel |
| alternate exterior angles converse | if two lines are cut by a transversal so the alternate exterior angles are congruent then the lines are parallel |
| consecutive interior angles converse | if two lines are cut by a transversal so the consecutive interior angles are supplementary then the lines are parallel |
| transitive property of parallel lines | if two lines are parallel to the same line then they are parallel to each other |
| linear pair perpendicular theorem | if two lines intersect to form a linear pair of congruent angles then the lines are perpendicular |
| perpendicular transversal theorem | in a plane if a transversal is perpendicular to one of two parallel lines then it is perpendicular to the other line |
| lines perpendicular to a transversal theorem | in a plane if two lines are perpendicular to the same line then they are parallel to each other |
| slopes of parallel lines | in a coordinate plane two distinct no vertical lines are parallel if and only if they have any two vertical lines are parallel |
| slopes of perpendicular lines | in a coordinate plane two nonvertical lines are perpendicular if and only if the product of their slopes is -1 horizontal lines are perpendicular to vertical lines |
Created by:
Kyle GG