Parallel, Perpendicular, and Oblique Lines Using Coordinate Geometry to Find and Compare the Slopes of Lines
Parallel Lines Two lines are Parallel if they lie in the same plane and do not intersect
Perpendicular Lines Two lines are Perpendicular if they intersect at a right (90°)
Oblique Lines Two lines are Oblique if they lie in the same plane but are neither Perpendicular nor Parallel
Skew Lines Two lines are Skew if they do not lie in the same plane
Slope Recall that slope = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 , so draw in a slope triangle to find the rise and run l 3 4 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 8 6 = 4 3 6 8
Parallel Lines Slope of line l = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 4 3 Slope of line m Since Parallel lines never intersect but lie in the same plane, they must have the same slope Slope of line l = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 4 3 l m 3 3 4 4 Slope of line m = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 4 3
Perpendicular Lines Slope of line l = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 4 3 Slope of line n Since Perpendicular lines intersect at right angles, there slopes are opposite reciprocals Slope of line l = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 4 3 l 3 n 4 -3 Slope of line n = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = −3 4 4
Oblique Lines Slope of line l = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 4 3 Slope of line q Since Oblique lines are neither parallel nor perpendicular, there slopes are not equal, nor opposite reciprocals Slope of line l = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 4 3 l 3 q 4 -3 Slope of line q = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = −3 7 7
Review Parallel Lines Never intersect Same Slope Perpendicular Lines Intersect at a Right Angle Opposite Reciprocal Slope Oblique Lines intersect at a non-right angle Non-equal and non-opposite recriprocal slopes