1. Parallel and perpendicular lines Parallel lines are lines that are coplanar and do not intersect Skew lines are lines that do not intersect and are not coplanar

2. Transversal angle pair relationships A transversal, or a line that intersects two or more coplanar lines. Transversal Postulate: If two parallel lines are intersected by a transversal, then the corresponding angles are congruent.

3. Converse of parallel line conjecture If two lines are cut by a transversal to form congruent corresponding angles or congruent alternate interior angles or congruent alternate exterior angles, Then the lines are parallel

4. Alternate interior angles theorem: If two parallel lines are cut by a transversal, the alternate interior angles are congruent. Consecutive interior angles theorem: If two parallel lines are cut by a transversal them each pair of consecutive interior angles is supplementary Alternate exterior angles theorem: If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent.

5. Slope of a line Ratio of the change along the y-axis to the change along the x-axis The slope m of the line through the points (x 1, y 1 ) and (x 2, y 2 ) is given by

6. Classifying slopes

7. Parallel and perpendicular line postulates Two non vertical lines have the same slope if and only if they are parallel Two non vertical lines are perpendicular if and only if the product of their slopes is -1

8. Equation of lines The slope-intercept form of a linear equation is y=mx+b, where m is the slope of the line and b is the y-intercept The point-slope form of a linear equation is

9. Parallel postulate If given a line and a point not on the line, then there exists exactly one point through the line that is parallel to the given line

10. Proving lines parallel Alternate exterior angles converse: If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles is congruent, the two lines are a parallel

11. Consecutive interior angles converse : If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel

12. Alternate interior angles converse : If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the lines are parallel

13. Perpendicular transversal converse: In a plane, if two lines are perpendicular to the same line, then they are parallel

14. Perpendicular postulate If given a line and a point not on the line, then there exists exactly one line through the point that is perpendicular to the given line

15. Distance between a point and a line The distance between a point and a line is the length of the segment perpendicular to the line from the point