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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 coordinatesa-b |
| 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 the line ob. the ray 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 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 points 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 points 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 point not on the line, then there is exactly 1 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 a 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 angle congruence theorem | all right angles are congruent |
| congruent supplements theorem | if two angle 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 congruent 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 |
| alternate interior angles theorem | if two parallel lines are cut by transversal, then the pairs of alternative interior angles are congruent |
| alternate exterior angles theorem | if two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congrunet |
| consecutive interior angles theorem | if two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary |
| corresponding angles converse | if two line are cut by a tranvesal so the 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 non vertical lines are parallel if and only if they have the same slop. Any two vertical lines are parallel |
| slopes of perpendicular lines | in coordinate plane, two non vertical lines are perpendicular if and only if the product of their slopes is -1. horizontal lines are perpendicular to vertical lines. |
Created by:
nathan gable