Parallel lines are two coplanar lines that never intersect. They always have an equal distance between them. stands for "is parallel to". That's all there is to it. However, parallel lines AND angles, well, that's a different story. There are lots of postulates and theorums that have to do with them.
- Alternate exterior angles
- Alternate interior angles
- Corresponding angles
Corresponding Angles Postulate: If two coplanar lines are cut by a transversal so that two corresponding angles have the same measure, then those lines are parallel.
Parallel Lines Postulate: If two lines are parallel and are cut by a transversal, corresponding angles have the same measure.
Alternate Exterior Angles Theorum: If two parallel lines are cut by a transversal, the alternate exterior angles are congruent. See proof.Note: While you can usually get away with not knowing the names of theorums, your Geometry teacher will generally require you to know them.
Alternate Interior Angles Theorum: If two parallel lines are cut by a transversal, the alternate interior angles are congruent. See proof.
Interior Angle Theorum: If two parallel lines are cut by a transversal, interior angles on the same side of the transveral are supplementary. See proof.
Note: Your teachers may not recognize the names of the above theorums.
Parallel Lines and Slopes Theorum: Two nonvertical lines are parallel if and only if they have the same slope.
Transivity of Parallelism Theorum: In a plane, if l m and m n, than l n.
- Jaime III
When you stop to think, don't forget to start up again!