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pGeo C3 Post/The/Cor
pGeometry C3 Postulates/Theorems/Corollaries
| Term | Definition |
|---|---|
| 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 |
| 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 pair of alternate exterior angles are congruent |
| Consecutive Interior Angles Theorem | If two parallel lines are cut by a transversal, then the pair 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 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. |