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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 differenceofthecoordinatesofA, 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 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 | Through any three noncollinear points, there exists exactly one point. |
| Plane-Point Postulate | If two points lie in a plane, then their intersection is a line. |
| 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 EF, then the segment AB 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. |
| Alternate interior angles theorem | If two parallel lines are cut by a 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 congruent. |
| 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 lines are cut by a transversal 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 the 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 vertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel. |
| Slope of perpendicular lines | In a coordinate plane, two no vertical lines are perpendicular if and only if the product of their slopes is -1. Horizontal lines are perpendicular to vertical lines. |
| Plane-Line postulate | If two points lie in a plain, then the lines containing them lies in the plane. |
| Transitive property | If segment Ab is congruent to segment Cd and segment CD is congruent to segment EF, Then the segment AB is congruent to segment EF. If angle A is congruent to angle B and angle B is congruent to angle Cm then angle A is congruent to angle C. |
Created by:
Riverduke