Transcript Parallel, Perpendicular, and Oblique Lines

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
𝑟𝑖𝑠𝑒
,
𝑟𝑢𝑛
Recall that slope =
so draw in a slope
triangle to find the rise and run
l
3
6 4
8
𝑟𝑖𝑠𝑒 8 4
= =
𝑟𝑢𝑛 6 3
Parallel Lines
Since Parallel lines never intersect but lie in the
same plane, they must have the same slope
l
3
3
4
4
m
Slope of line l
𝑟𝑖𝑠𝑒
4
=
=
𝑟𝑢𝑛
3
Slope of line m
𝑟𝑖𝑠𝑒
4
=
=
𝑟𝑢𝑛
3
Perpendicular Lines
Since Perpendicular lines intersect at right
angles, there slopes are opposite reciprocals
l
3
n
4
-3
4
Slope of line l
𝑟𝑖𝑠𝑒
4
=
=
𝑟𝑢𝑛
3
Slope of line n
𝑟𝑖𝑠𝑒
−3
=
=
𝑟𝑢𝑛
4
Oblique Lines
Since Oblique lines are neither parallel nor
perpendicular, there slopes are not equal, nor
opposite reciprocals
l
3
q
4
-3
7
Slope of line l
𝑟𝑖𝑠𝑒
4
=
=
𝑟𝑢𝑛
3
Slope of line q
𝑟𝑖𝑠𝑒
−3
=
=
𝑟𝑢𝑛
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