Lesson 2 3 Pairs of Lines Lesson 2

Lesson 2 -3 Pairs of Lines Lesson 2 -3: Pairs of Lines 1

Parallel Lines l l l 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, . Lesson 2 -3: Pairs of Lines 2

PERPENDICULAR LINES l l l Perpendicular lines are lines that intersect to form a right angle. The symbol used for perpendicular lines is . 4 right angles are formed. m In this figure line m is perpendicular to line n. n With symbols we denote, m n Lesson 2 -3: Pairs of Lines 3

OBLIQUE LINES l l Oblique lines are lines that intersect, but do NOT form a right angle. m n Lesson 2 -3: Pairs of Lines 4

Skew Lines and Parallel Planes l l 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 Lesson 2 -3: Pairs of Lines 5

Examples: 1. 2. 3. 4. 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: 1. Segments BC, FG, & EH. 2. Segments DH, DC, AE & AB. 3. Segments CG, BF, FE, & GH. 4. Plane FGH. Lesson 2 -3: Pairs of Lines 6

Slope of Parallel and Perpendicular lines l 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). Lesson 2 -3: Pairs of Lines 7

Examples: Find the slope of the line through the given points. a. (-4, 7) and (3, 7) b. (3, -1) and (3, 2) c. (1, -4) and (2, 5) d. (-2, 5) and (1, -1) Lesson 2 -3: Pairs of Lines 8

Examples Any line parallel to a line with slope has slope _____. Any line perpendicular to a line with slope has slope ___. 0 Any line parallel to a line with slope 0 has slope _____. Any line perpendicular to a line with undefined slope has slope. Zero Slope 2 Any line parallel to a line with slope 2 has slope _____. Lesson 2 -3: Pairs of Lines 9