Properties of Perpendicular Lines
Perpendicular Lines Postulate:
• l1⊥l2 if and only if
m1∙m2 = -1
• That is, m2 = -1/m1,
The slopes are
of each other.
• Two non-vertical lines are perpendicular if and
only if the product of their slopes is -1.
Vertical and horizontal lines are perpendicular.
• In a plane, if a line is perpendicular to
one of two parallel lines, then it is
perpendicular to the other.
Theorem: Perpendicular to Parallel Lines:
• If two coplanar lines are each
perpendicular to the same line, then
they are parallel to each other.
Theorem: Two Perpendiculars:
Proof of Perpendicular to Parallel Lines Theorem
1 l ll m, l ⊥ n Given
2 ∠1 is a right angle Definition of lines⊥
m∠1 = 90o
Definition of a right angle
m 2∠ = m∠1
Corresponding angles postulate
m∠2 = 90o
Substitution property of equality
6 ∠2 is a right angle Definition of a right angle
7 m ⊥ n Definition of lines⊥
Given: l ll m and l ⊥ n
Prove: m ⊥ n
1. Line r contains the points (-2,2) and (5,8).
Line s contains the points (-8,7) and (-2,0).
Is r ⊥ s?
2. Given the equation of line v is
and line w is
Is v ⊥ w?
Given the line
3.Find the equation of the line passing through (
6,1) and perpendicular to the given line.
4. Find the equation of the line passing through
( 6,1) and parallel to the given line.