| A | B |
|---|
| Coplanar | in the same plane |
| Parallel lines | coplanar lines that do not intersect |
| Intersecting lines | coplanar lines that have exactly one point in common |
| Perpendicular lines | lines that intersect at right angles |
| Right angle | an angle that measures 90° |
| Oblique lines | lines that do not intersect at 90° |
| Transitivity of Parallel Lines | If two lines are parallel to the same line, then they are parallel to each other |
| Algebraic Property | two nonvertical lines are perpendicular if and only if the product of their slopes is –1 |
| Property of Perpendicular Lines | If two coplanar lines are perpendicular to the same line, then they are parallel to each other |
| Skew lines | lines that do not lie on the same plane |
| Parallel planes | planes that do not intersect |
| Postulate 12 | If two distinct lines intersect, then their intersection is exactly one point |
| Coincident | lines that are parallel and have all points in common |
| Intersecting lines have | one solution |
| Parallel lines have | no solutions |
| Coincident lines have | many solutions |
| 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 |
| Theorem 3.3 | If two lines are perpendicular, then they intersect to form four right angles |
| Theorem 3.4 | All right angles are congruent |
| Theorem 3.5 | If two lines intersect to form a pair of adjacent congruent angles, then the lines are perpendicular |
| Corresponding Angles Postulate | 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. |
| Consecutive Interior Angles Theorem | If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. |
| Alternate Exterior Angles Theorem | If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. |
| Perpendicular Transversal Theorem | If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the second. |
| Corresponding Angles Converse | If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel. |
| Alternate Interior Angles Converse | If two lines are cut by a transversal so that the alternate interior angles are congruent, then the lines are parallel. |
| Consecutive Interior Angles Converse | If two lines are cut by a transversal so that the consecutive interior angles are supplementary, then the lines are parallel. |
| Alternate Exterior Angles Converse | If two lines are cut by a transversal so that the alternate exterior angles are congruent, then the lines are parallel. |
