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postulates/thorems
| Term | Definition |
|---|---|
| ruler postulate | The points on a line can be matched one by one with real numbers, The real number that corresponds to a point is the coordinate of the point. |
| 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 postulates | consider Ray ob and a point a on one side of the line ob. the rays of the form Ray oa can be matched one to one with 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 two measures of angle rsp and angle pst |
| two point postulates | through any two points, there exists exactly one line |
| line-point postulates | a line contains at least two points |
| line intersection postulates | if two lines intersect, then their intersection is exactly one point |
| three point postulate | through any three noncollinear points, there exists exactly one plane |
| plane line postulate | a plane contains at least three noncollinear points |
| plane poit postulates | if two points lie in a plane, then the line containing them lies in the plane |
| parallel postulate | if two lines intersect, then their intersection is a line |
| linear pair postulates | if two angles from a linear pair, the 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 |
| perpenducular postulate | for any segment ab segment ab is congruent to segment ab. for any angle a, angle a congruent to angle a |
| refkexitive property | if segment ab is currengurent 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 |
| symmetric property | if segment ab is congruent to segment cd and segment dc is congruent to segment ef then segment ab is congurent to segment ef if angle a is congurent to angle b and angle b and angle b is congurent to angle c, then angle a is congurent to angle c |
| transitive property | all right angles are congurent |
| right angles congruence theorem | if two angles are supplemantry to the same angle then they are congurent |
| congruent supplements therom | if to angles are commplentary to the same angle then they are congurent |
| vertical angles congruence theorem | vertical angles are congruent |
| corresponding angles theorem | if two parallel lines are cut by a transveral, then the pairs of corresponding angles are congurrent |
| alternate interior angles theorem | if two parallel lines are cut by transversal, the the pais of alternative interior angles are congurent |
| consecutive interior angles theorem | if two parallel lines are cut by a transversal, then the paid of consecutive interior angles are supplementary |
| alternate exterior angles theorem | if two parallel lines aew cut by a transversal, then the pair of alternate exterior angles are congurrent |
| corresponding angles converse | if two lines are cut by a transversal, so the corresponding angles are congurent, then the lines are parallel |
| alternate inteior angles converse | if two lines are cut by a transveral so the alternate exterior angles are congurent, then the lines are parallel |
| alternate exterior angles converse | if two lines are cut by a transnserval so the alternate interior angles are congurent the the lines are parallel |
| conssecutave inteior angles converse | if two lines are cut by a transversal so the consecutive interior angles are supplementary, the 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 |
| line pair perpendicular theorem | if two lines intersect to form a linear pair of congurent to angles, then the lines are pperpenducliar |
| perpenducular transervsal theorem | in a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to other line |
| lines of perpendicular to 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 the same slope. 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 slope is -1. horizontal lines are perpendicular to vertical lines |
| plane intersection postulate | if two planes intersect, the their intersection is a line |
Created by:
Atamplen