1 Notes 9/4/12 Pairs of Lines

2 Parallel Lines Parallel lines are coplanar lines that do not intersect. Arrows are used to indicate lines are parallel. The symbol used for parallel lines is ||. In the above figure, the arrows show that line AB is parallel to line CD. With symbols we denote,.

3 PERPENDICULAR LINES Perpendicular lines are lines that intersect to form a right angle. The symbol used for perpendicular lines is . 4 right angles are formed. m n In this figure line m is perpendicular to line n. With symbols we denote, m  n

4 OBLIQUE LINES Oblique lines are lines that intersect, but do NOT form a right angle. m  n 

5 Skew Lines and Parallel Planes Two lines are skew if they do not intersect and are not in the same plane (not coplanar). Ex: All planes are either parallel or intersecting. Parallel planes are two planes that do not intersect. Ex: Plane ABC and Plane EFG

6 Examples: 1.Name all segments that are parallel to 2.Name all segments that intersect 3.Name all segments that are skew to 4.Name all planes that are parallel to plane ABC. Answers: 1.Segments BC, FG, & EH. 2.Segments DH, DC, AE & AB. 3.Segments CG, BF, FE, & GH. 4.Plane FGH.

7 Examples: a.(-4, 7) and (3, 7) b.(3, -1) and (3, 2) c.(1, -4) and (2, 5) d.(-2, 5) and (1, -1) Find the slope of the line through the given points.

8 Examples Any line parallel to a line with slope has slope _____. Any line perpendicular to a line with slope has slope ___. Any line parallel to a line with slope 0 has slope _____. Any line perpendicular to a line with undefined slope has slope. Any line parallel to a line with slope 2 has slope _____. 0 Zero Slope 2