Section 3.1 Pairs of Lines

PERPENDICULAR LINES m n 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

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, .

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

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

Slope of Parallel and Perpendicular lines The slope of the non vertical line through the points and is m = The slope of a vertical line is not defined. The slope of a horizontal line is zero. Two lines are parallel if and only if they have equal slopes. Two lines are perpendicular if and only if the product of their slopes is -1 (reciprocals and opposite signs).

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

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 _____. Zero Slope 2