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Unformatted text preview: Section 2.4 Parallel and Perpendicular Lines Given any two distinct lines in the Cartesian plane, the two lines will either intersect or they will not. In this section, we will investigate the nature of two lines that do not intersect ( parallel lines ) and then discuss the special case of two lines that intersect at a right angle ( perpendicular lines ). These two cases are interesting because we need only know the slope of the two lines to determine whether or not the lines are parallel, perpendicular or neither. Objective 1: Understanding the Definition of Parallel Lines Two lines are parallel if they do not intersect, or in other words the lines do not share any common points. Since parallel lines do not intersect, the ratio of the vertical change (rise) to the horizontal change (run) of each line must be equivalent. In other words, parallel lines have the same slope. 1 l 2 l 1 riseof l 2 riseof l 1 run of l 2 run of l The ratios of the vertical rise to the horizontal run of two parallel lines are equal:...
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