Solve problems using perpendicular lines Set up and solve inequalities using the distance from a point to a line

1. Obj. 14 Perpendicular Lines
The student will be able to (I can):
• Solve problems using perpendicular lines
• Set up and solve inequalities using the distance from a
point to a line

2. Perpendicular
Transversal
Theorem
If two intersecting lines form a linear pair of
congruent angles, then the lines are
perpendicular.
∠1 ≅ ∠2 ⇒ m ⊥ n
If a transversal is perpendicular to one of
two parallel lines, then it is perpendicular to
the other line.
n p & n ⊥q ⇒ p ⊥ q
1 2m
n
n
p
q

3. Distance From
a Point to a
Line
If two coplanar lines are perpendicular to
the same line, then the two lines are
parallel to each other.
r ⊥ t & s ⊥t ⇒ r s
The distance from a point to a line is the
length of the perpendicular segment from
the point to the line.
The distance from A
to the line t is AB
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4. Example Solve to find x and y in the diagram.
10x = 90
x = 9
8(9) + 4y = 90
4y = 18
y = 4.5
(8x+4y)°
(10x)°

5. Distance From a Point to a Line
1. Name the shortest segment from R to FO.
Since RG ⊥ FO, RG is the shortest segment
2. Write and solve an inequality for x.
FR > RG
x + 5 > 9
x > 4
F G O
R
x + 5x + 5x + 5x + 5 9999