chapter 3
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21 terms
Terms | Definitions |
|---|---|
 parallel lines | they do not intersect and are coplanar |
| skew lines | do not intersect and are not coplanar |
| parallel planes | two planes that do not intersect |
| 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 |
| transversal | is a line that intersects two or more coplanar lines at different points |
| corresponding angles | if they have corresponding positions. if two angles are above the lines and to the right of the transversal |
| alternate interior angles | if they lie between the two lines and on opposite sides of the transversal |
| alternate exterior angles | if they lie outside the two lines and on opposite sides of the transversal |
| consecutive interior angles | if they lie between the two lines and on the same side of the transversal |
| 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 |
| 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 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 |
| slopes of parallel lines | in a coordinate plane two 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 an only if the product of their slopes is -1. Horizontal lines are perpendicular to vertical lines. |
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