Understanding Lines and Angles in Geometry
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Learn about parallel, perpendicular, oblique lines, skew lines, and parallel planes in geometry. Understand slope of lines and their relationships. Practice examples for better comprehension.
Understanding Lines and Angles in Geometry
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Pairs of Lines Lesson 3-1 Lesson 2-3: Pairs of Lines
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, . Lesson 2-3: Pairs of Lines
m n 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. In this figure line m is perpendicular to line n. With symbols we denote, m n Lesson 2-3: Pairs of Lines
OBLIQUE LINES • Oblique lines are lines that intersect, but do NOT form a right angle. • m n Lesson 2-3: Pairs of Lines
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 Lesson 2-3: Pairs of Lines
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. Lesson 2-3: Pairs of Lines
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). Lesson 2-3: Pairs of Lines
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) Lesson 2-3: Pairs of Lines
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 Lesson 2-3: Pairs of Lines
