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Postulates/Theorems
Postulates/Theorems/Corollaries
| Question | Answer |
|---|---|
| Ruler Postulate | The points on a line can be matched one-to-one with real numbers. The number that corresponds to a point is its coordinate. The distance between points A and B is written as AB. If C is between A and B, then AC + CB = AB. |
| Segment Addition Postulate | If B is between A and C, then AB + BC = AC and B is between A and C. |
| Protractor Postulate | Consider ray OB and a point A on one side of line OB. The rays from OB can be matched one-to-one with real numbers. |
| Angle Addition Postulate | If P is in the interior of angle RST, then the measure of angle RST equals 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 | 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-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 | A segment is congruent to itself. Example: AB ≅ AB An angle is congruent to itself. |
| Symmetric Property | If AB ≅ CD, then CD ≅ AB. If angle A ≅ angle B, then angle B ≅ 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. |
| 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 the pairs of alternate exterior angles are congruent. |
| Consecutive Interior Angles Theorem | If two parallel lines are cut by a transversal, then the 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 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 nonvertical 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 slopes is −1. Horizontal lines are perpendicular to vertical lines. |
Created by:
augustmartinez