CHAPTER 3 Lines in a Plane

Exploring Lines and Planes Parallel lines Perpendicular lines Oblique lines Skew lines Parallel planes Perpendicular planes Intersecting planes

Parallel lines ( l 1 // l 2 ) Parallel lines: coplanar lines that do not intersect l1l1 l2l2

Properties of parallel lines Algebraic property: two non vertical lines are parallel if and only if they have the same slope. Transitivity of parallel lines: If two lines are parallel to the same line, then they are parallel to each other.

Perpendicular lines ( l 1  l 2 ) Perpendicular lines: coplanar lines that intersect to form a right angle (measure is 90 o )

Properties of Perpendicular lines Algebraic property: two nonvertical lines are perpendicular if and only if the product of their slopes is -1. (slopes are Opposite reciprocals) Property of perpendicular lines: if two coplanar lines are perpendicular to the same line, then they are parallel to each other.

Oblique Lines Lines that intersect at a point AND are not perpendicular are oblique lines.

Skew lines Lines that do not intersect AND are not coplanar are called skew lines.

Parallel Planes Parallel planes are planes that DO NOT intersect.

Perpendicular Planes Perpendicular planes intersect at a right angle. a b c

Intersecting Planes Planes that intersect create a line at all of the intersecting points.